<div id="pf1" class="pf w0 h0" data-page-no="1"><div class="pc pc1 w0 h0"><img class="bi x0 y0 w1 h1" alt="" src="https://files.passeidireto.com/07bebfca-1ca3-4db1-8f6c-0a20e70e33d8/bg1.png"><div class="t m0 x1 h2 y1 ff1 fs0 fc0 sc0 ls11 wsd">Equilíbrio de Fases em <span class="_0 blank"></span>Sistemas Simples <span class="_0 blank"></span>\u2013 A Regra das Fases <span class="_1 blank"> </span>Página 1 </div><div class="t m1 x1 h3 y2 ff2 fs1 fc0 sc0 ls11 wsd"> </div><div class="t m1 x2 h3 y3 ff3 fs1 fc0 sc0 ls11 wsd">ESCOLA DE ENGENHARIA DE LORENA \u2013 EEL/USP </div><div class="t m1 x3 h3 y4 ff3 fs1 fc0 sc0 ls11 wsd">TERMODINÂMICA QUÍMICA \u2013 PROF. ANTONIO CARLOS DA SILVA </div><div class="t m1 x1 h3 y5 ff3 fs1 fc0 sc0 ls11 wsd"> </div><div class="t m2 x4 h4 y6 ff4 fs2 fc0 sc0 ls11 wsd">EQUILÍBRI<span class="_2 blank"> </span>O DE FASES EM<span class="_2 blank"> </span> SISTEM<span class="_2 blank"> </span>AS SIMPLE<span class="_2 blank"> </span>S </div><div class="t m2 x5 h4 y7 ff4 fs2 fc0 sc0 ls11 wsd">A REGRA DAS<span class="_2 blank"> </span> FASES<span class="_2 blank"> </span> </div><div class="t m1 x1 h3 y8 ff3 fs1 fc0 sc0 ls11 wsd"> </div><div class="t m1 x1 h5 y9 ff4 fs1 fc0 sc0 ls11 ws0">1.<span class="ff5 ls0 wsd"> </span><span class="wsd">CONDIÇÃO DE EQUILÍBRIO </span></div><div class="t m0 x6 h6 ya ff3 fs0 fc0 sc0 ls11 wsd"> </div><div class="t m1 x7 h7 yb ff6 fs1 fc0 sc0 ls11 wsd">\u201cO <span class="_3 blank"> </span>potencial <span class="_3 blank"> </span>químico <span class="_3 blank"> </span>de <span class="_3 blank"> </span>cada <span class="_3 blank"> </span>constitu<span class="_2 blank"> </span>inte <span class="_3 blank"> </span>deve <span class="_3 blank"> </span>possuir <span class="_3 blank"> </span>o <span class="_3 blank"> </span>m<span class="_2 blank"> </span>esmo </div><div class="t m1 x7 h7 yc ff6 fs1 fc0 sc0 ls11 wsd">valor em todos os pontos do sistema (para s<span class="_2 blank"> </span>iste<span class="_0 blank"></span>ma em equil<span class="_2 blank"> </span>íbrio)\u201d </div><div class="t m0 x6 h6 yd ff3 fs0 fc0 sc0 ls11 wsd"> </div><div class="t m1 x6 h3 ye ff3 fs1 fc0 sc0 ls11 wsd">Se <span class="_4 blank"> </span>uma <span class="_4 blank"> </span>substância <span class="_4 blank"> </span>estiver <span class="_4 blank"> </span>presente <span class="_4 blank"> </span>em <span class="_4 blank"> </span>vária<span class="_0 blank"></span>s <span class="_4 blank"> </span>fa<span class="_2 blank"> </span>ses, <span class="_4 blank"> </span>seu <span class="_4 blank"> </span>potencial <span class="_4 blank"> </span>químico <span class="_4 blank"> </span>dever <span class="_4 blank"> </span>ter <span class="_4 blank"> </span>o <span class="_4 blank"> </span>mesmo </div><div class="t m1 x1 h3 yf ff3 fs1 fc0 sc0 ls11 wsd">valor em todas as fases. </div><div class="t m1 x6 h8 y10 ff1 fs1 fc0 sc0 ls11 wsd">Exemplo: água(g) = água(l) <span class="ff7 ws1">\ue001\ue002</span></div><div class="t m3 x8 h9 y11 ff7 fs3 fc0 sc0 ls11 ws2">\ue003\ue004\ue005\ue006</div><div class="t m1 x9 h8 y10 ff7 fs1 fc0 sc0 ls11">\ue007</div><div class="t m3 xa h9 y12 ff7 fs3 fc0 sc0 ls11">\ue008</div><div class="t m1 xb h8 y10 ff7 fs1 fc0 sc0 ls11 ws3">\ue009 \ue001\ue002</div><div class="t m3 xc h9 y11 ff7 fs3 fc0 sc0 ls11 ws2">\ue003\ue004\ue005\ue006</div><div class="t m1 xd h8 y10 ff7 fs1 fc0 sc0 ls11">\ue007</div><div class="t m3 xe h9 y12 ff7 fs3 fc0 sc0 ls11">\ue00a</div><div class="t m1 xf ha y10 ff1 fs1 fc0 sc0 ls11 wsd"> </div><div class="t m1 x6 h8 y13 ff3 fs1 fc0 sc0 ls11 wsd">Se o <span class="_5 blank"> </span>sistema for <span class="_5 blank"> </span>constituído <span class="_5 blank"> </span>por apenas um <span class="_5 blank"> </span>com<span class="_2 blank"> </span>ponente: <span class="ff7 ws4">\ue002<span class="_6 blank"> </span>\ue009 \ue00b<span class="_7 blank"> </span>\ue00c</span></div><div class="t m1 x10 h8 y14 ff7 fs1 fc0 sc0 ls1">\ue00d<span class="ff3 ls11 wsd v1"> . Di<span class="_2 blank"> </span>vidindo a equa<span class="_2 blank"> </span>ção </span></div><div class="t m1 x1 hb y15 ff3 fs1 fc0 sc0 ls11 wsd">fundamental <span class="ff7 ls2 v2">\ue00e</span><span class="ff7 ws5">\ue00f\ue00b<span class="_6 blank"> </span>\ue009<span class="_6 blank"> </span>\ue010\ue011\ue00f\ue012 \ue013 \ue014\ue00f\ue015<span class="_2 blank"> </span><span class="ls3 v2">\ue016</span></span> por n: </div><div class="t m1 x1 hc y16 ff3 fs1 fc0 sc0 ls11 wsd"> <span class="_8 blank"> </span> <span class="ff7 ws4">\ue00f\ue002 \ue009 \ue010<span class="_2 blank"></span>\ue011<span class="ls4 v3">\ue017</span><span class="ws6">\ue00f\ue012<span class="_9 blank"> </span>\ue013 \ue014</span></span></div><div class="t m1 x11 h8 y17 ff7 fs1 fc0 sc0 ls5">\ue018<span class="ls11 ws1 v4">\ue00f\ue015<span class="ff3 wsd"> <span class="_a blank"> </span>(1) </span></span></div><div class="t m1 x6 h3 y18 ff3 fs1 fc0 sc0 ls11 wsd">Onde: </div><div class="t m1 x1 hc y19 ff3 fs1 fc0 sc0 ls11 wsd"> <span class="_b blank"> </span>Entropia molar: <span class="ff7 ws1">\ue010\ue011<span class="ls6 v3">\ue017</span><span class="ws3">\ue009 \ue019</span></span></div><div class="t m3 xd h9 y1a ff7 fs3 fc0 sc0 ls11 ws2">\ue01a\ue01b</div><div class="t m3 xd h9 y1b ff7 fs3 fc0 sc0 ls11 ws2">\ue01a\ue01c</div><div class="t m1 x12 h8 y19 ff7 fs1 fc0 sc0 ls11">\ue01d</div><div class="t m3 x13 h9 y1c ff7 fs3 fc0 sc0 ls11">\ue01e</div><div class="t m1 x14 h3 y19 ff3 fs1 fc0 sc0 ls11 wsd"> <span class="_c blank"> </span>(2a) </div><div class="t m1 x1 h8 y1d ff3 fs1 fc0 sc0 ls11 wsd"> <span class="_d blank"> </span>Volume molar: <span class="ff7">\ue014</span></div><div class="t m1 x15 h8 y1e ff7 fs1 fc0 sc0 ls7">\ue018<span class="ls11 ws3 v4">\ue009 \ue019</span></div><div class="t m3 xd h9 y1f ff7 fs3 fc0 sc0 ls11 ws2">\ue01a\ue01b</div><div class="t m3 xd h9 y20 ff7 fs3 fc0 sc0 ls11 ws2">\ue01a\ue01e</div><div class="t m1 x12 h8 y1d ff7 fs1 fc0 sc0 ls11">\ue01d</div><div class="t m3 x13 h9 y21 ff7 fs3 fc0 sc0 ls11">\ue01c</div><div class="t m1 x14 h3 y1d ff3 fs1 fc0 sc0 ls11 wsd"> <span class="_e blank"> </span>(2b) </div><div class="t m1 x6 h3 y22 ff3 fs1 fc0 sc0 ls11 wsd">As <span class="_2 blank"> </span>derivadas <span class="_2 blank"> </span>que <span class="_2 blank"> </span>aparec<span class="_2 blank"> </span>em <span class="_2 blank"> </span>nas <span class="_2 blank"> </span>equações <span class="_2 blank"> </span>(2a) <span class="_f blank"> </span>e <span class="_2 blank"> </span>(2b) <span class="_2 blank"> </span>dão <span class="_2 blank"> </span>os <span class="_2 blank"> </span>co<span class="_2 blank"> </span>eficientes <span class="_2 blank"> </span>angulares <span class="_2 blank"> </span>das <span class="_f blank"> </span>curvas <span class="_2 blank"> </span>de </div><div class="t m1 x1 h8 y23 ff7 fs1 fc0 sc0 ls8">\ue002<span class="ff3 ls11 wsd"> em função de <span class="ff1 ls9">T</span> e </span>\ue002<span class="ff3 ls11 wsd"> em função de <span class="ff1 lsa">p</span>, respectivamente. </span></div><div class="t m1 x1 h5 y24 ff4 fs1 fc0 sc0 ls11 ws0">2.<span class="ff5 ls0 wsd"> </span><span class="wsd">ESTABILIDADE <span class="_10 blank"> </span>DAS <span class="_10 blank"> </span>FASES <span class="_7 blank"> </span>FORMADAS <span class="_10 blank"> </span>POR <span class="_10 blank"> </span>UMA <span class="_7 blank"> </span>S<span class="_2 blank"> </span>UBSTÂNCIA <span class="_10 blank"> </span>PURA <span class="_7 blank"> </span>\u2013<span class="_2 blank"> </span> </span></div><div class="t m1 x16 h5 y25 ff4 fs1 fc0 sc0 ls11 wsd">INFLUÊNCIA DA TEMPERATURA </div><div class="t m1 x6 h3 y26 ff3 fs1 fc0 sc0 ls11 wsd">Para as três fases de uma substância temos: </div><div class="t m1 x6 h3 y27 ff3 fs1 fc0 sc0 ls11 wsd">De <span class="_f blank"> </span>acordo <span class="_3 blank"> </span>com <span class="_3 blank"> </span>o <span class="_3 blank"> </span>Terceiro <span class="_3 blank"> </span>Princípio <span class="_f blank"> </span>da<span class="_2 blank"> </span> <span class="_f blank"> </span>Termodinâmi<span class="_2 blank"> </span>ca, <span class="_f blank"> </span>a <span class="_3 blank"> </span>entropia <span class="_f blank"> </span>d<span class="_2 blank"> </span>e <span class="_f blank"> </span>u<span class="_2 blank"> </span>ma <span class="_f blank"> </span>substância <span class="_3 blank"> </span>é <span class="_3 blank"> </span>sempre </div><div class="t m1 x1 hb y28 ff3 fs1 fc0 sc0 ls11 wsd">positiva. <span class="_3 blank"> </span> <span class="_11 blank"> </span>Assim, <span class="_3 blank"> </span>na <span class="_11 blank"> </span>equação <span class="_11 blank"> </span>(2a), <span class="_3 blank"> </span><span class="ff7 lsb v2">\ue01f</span><span class="ff7 ws7">\ue020<span class="_2 blank"></span>\ue002 \ue020\ue012</span></div><div class="t m1 x17 h8 y29 ff7 fs1 fc0 sc0 ls11 ws8">\ue00d \ue021</div><div class="t m3 x8 h9 y2a ff7 fs3 fc0 sc0 ls11">\ue01e</div><div class="t m1 x18 h8 y28 ff3 fs1 fc0 sc0 ls11 wsd"> <span class="_3 blank"> </span> <span class="_11 blank"> </span>é <span class="_3 blank"> </span>sempre <span class="_11 blank"> </span>negativa. <span class="_3 blank"> </span> <span class="_11 blank"> </span>O <span class="_11 blank"> </span>gráfico <span class="_3 blank"> </span>de <span class="_11 blank"> </span><span class="ff7 ls8">\ue002</span> <span class="_3 blank"> </span>em<span class="_2 blank"> </span> <span class="_3 blank"> </span>função <span class="_3 blank"> </span>de <span class="_11 blank"> </span><span class="ff1 ls9">T</span>, <span class="_11 blank"> </span>a </div><div class="t m1 x1 h3 y2b ff3 fs1 fc0 sc0 ls11 wsd">pressão constante, é uma curva de coeficiente angular negativo. </div><div class="t m1 x1 h8 y2c ff3 fs1 fc0 sc0 lsc wsd"> <span class="ff7 ls11">\ue019</span></div><div class="t m3 x19 h9 y2d ff7 fs3 fc0 sc0 ls11 ws2">\ue01a\ue01b<span class="fs4 ws9 v5">\ue022\ue023\ue024\ue025\ue026\ue027</span></div><div class="t m3 x1a h9 y2e ff7 fs3 fc0 sc0 ls11 ws2">\ue01a\ue01c</div><div class="t m1 x1b h8 y2c ff7 fs1 fc0 sc0 ls11">\ue01d</div><div class="t m3 x1c h9 y2f ff7 fs3 fc0 sc0 ls11">\ue01e</div><div class="t m1 x1d hc y2c ff7 fs1 fc0 sc0 ls11 wsa">\ue009 \ue010\ue011<span class="v3">\ue017</span></div><div class="t m3 x1e h9 y30 ff7 fs3 fc0 sc0 ls11 ws2">\ue028\ue023\ue00a\ue029\ue02a\ue02b</div><div class="t m1 x1f h8 y2c ff3 fs1 fc0 sc0 lsd wsd"> <span class="ff7 ls11">\ue019</span></div><div class="t m3 x20 h9 y31 ff7 fs3 fc0 sc0 ls11 ws2">\ue01a\ue01b<span class="fs4 ws9 v5">\ue024\ue02c\ue02d\ue02e\ue025\ue026\ue027</span></div><div class="t m3 x21 h9 y2e ff7 fs3 fc0 sc0 ls11 ws2">\ue01a\ue01c</div><div class="t m1 x22 h8 y2c ff7 fs1 fc0 sc0 ls11">\ue01d</div><div class="t m3 x23 h9 y2f ff7 fs3 fc0 sc0 ls11">\ue01e</div><div class="t m1 x24 hc y2c ff7 fs1 fc0 sc0 ls11 ws3">\ue009 \ue010\ue011<span class="v3">\ue017</span></div><div class="t m3 x25 h9 y30 ff7 fs3 fc0 sc0 ls11 ws2">\ue00a\ue02c\ue02f\ue005\ue029\ue02a\ue02b</div><div class="t m1 x26 h8 y2c ff3 fs1 fc0 sc0 lsd wsd"> <span class="ff7 ls11">\ue019</span></div><div class="t m3 x27 h9 y31 ff7 fs3 fc0 sc0 ls11 ws2">\ue01a\ue01b<span class="fs4 ws9 v5">\ue030\ue003\ue022</span></div><div class="t m3 x28 h9 y2e ff7 fs3 fc0 sc0 ls11 ws2">\ue01a\ue01c</div><div class="t m1 x29 h8 y2c ff7 fs1 fc0 sc0 ls11">\ue01d</div><div class="t m3 x2a h9 y2f ff7 fs3 fc0 sc0 ls11">\ue01e</div><div class="t m1 x2b hc y2c ff7 fs1 fc0 sc0 ls11 ws3">\ue009 \ue010\ue011<span class="v3">\ue017</span></div><div class="t m3 x2c h9 y30 ff7 fs3 fc0 sc0 ls11 ws2">\ue004\ue003\ue028</div><div class="t m1 x2d h3 y2c ff3 fs1 fc0 sc0 ls11 wsd"> <span class="_12 blank"> </span>(3) </div><div class="t m1 x1 hc y32 ff3 fs1 fc0 sc0 lse wsd"> <span class="ff7 lsf">\ue011<span class="ls11 v3">\ue017</span></span></div><div class="t m3 x2e h9 y33 ff7 fs3 fc0 sc0 ls11 ws2">\ue004\ue003\ue028</div><div class="t m1 x2f hc y32 ff7 fs1 fc0 sc0 ls11 wsb">\ue031 \ue011<span class="v3">\ue017</span></div><div class="t m3 x30 h9 y33 ff7 fs3 fc0 sc0 ls11 ws2">\ue00a\ue02c\ue02f\ue005\ue029\ue02a\ue02b</div><div class="t m1 x31 hc y32 ff7 fs1 fc0 sc0 ls11 wsc">\ue032 \ue011<span class="v3">\ue017</span></div><div class="t m3 x32 h9 y33 ff7 fs3 fc0 sc0 ls11 ws2">\ue028\ue023\ue00a\ue029\ue02a\ue02b</div><div class="t m1 x12 h3 y32 ff3 fs1 fc0 sc0 ls11 wsd"> <span class="_13 blank"> </span>(4) </div><div class="t m0 x6 h6 y34 ff3 fs0 fc0 sc0 ls11 wsd"> </div><div class="t m1 x33 h5 y35 ff4 fs1 fc0 sc0 ls10 wsd"> <span class="ff6 ls11">\u201cA fase que apresenta o potencial químico mais<span class="_2 blank"> </span> baixo é a </span></div><div class="t m1 x8 h7 y36 ff6 fs1 fc0 sc0 ls11 wsd">mais estável\u201d </div><div class="t m0 x6 h6 y37 ff3 fs0 fc0 sc0 ls11 wsd"> </div><div class="t m1 x6 h3 y38 ff3 fs1 fc0 sc0 ls11 wsd">Representando em um <span class="_5 blank"> </span>gráfico, mostrado a se<span class="_2 blank"> </span>guir, a reta S<span class="_2 blank"> </span> para o estado <span class="_5 blank"> </span>sólido <span class="_5 blank"> </span>apresenta </div><div class="t m1 x1 h3 y39 ff3 fs1 fc0 sc0 ls11 wsd">inclinação ligeiramente <span class="_2 blank"> </span>negativa, <span class="_2 blank"> </span>a r<span class="_2 blank"> </span>eta <span class="_2 blank"> </span>L para <span class="_2 blank"> </span>o <span class="_2 blank"> </span>estado <span class="_2 blank"> </span>líquido <span class="_2 blank"> </span>possui <span class="_2 blank"> </span>coeficiente angular l<span class="_2 blank"> </span>igeiramente </div></div><div class="pi" data-data='{"ctm":[1.000000,0.000000,0.000000,1.000000,0.000000,0.000000]}'></div></div> <div id="pf2" class="pf w0 h0" data-page-no="2"><div class="pc pc2 w0 h0"><img class="bi x0 y3a w1 hd" alt="" src="https://files.passeidireto.com/07bebfca-1ca3-4db1-8f6c-0a20e70e33d8/bg2.png"><div class="t m0 x1 h2 y3b ff1 fs0 fc0 sc0 ls11 wsd">Escola de Engenharia<span class="_0 blank"></span> de Lorena \u2013 EEL/USP <span class="_14 blank"> </span>Termodinâmica Q<span class="_0 blank"></span>uímica \u2013 Prof. Antonio Car<span class="_0 blank"></span>los da Silva </div><div class="t m0 x1 h6 y3c ff2 fs0 fc0 sc0 ls11 wsd"> </div><div class="t m0 x1 h2 y3d ff1 fs0 fc0 sc0 ls11 wsd">Equilíbrio de Fases em <span class="_0 blank"></span>Sistemas Simples <span class="_0 blank"></span>\u2013 A Regra das Fases <span class="_0 blank"></span> <span class="_15 blank"> </span>Página 2 </div><div class="t m1 x1 h3 y3e ff3 fs1 fc0 sc0 ls11 wsd">mais <span class="_16 blank"> </span>negativo <span class="_16 blank"> </span>e <span class="_16 blank"> </span>a <span class="_16 blank"> </span>curva <span class="_16 blank"> </span>G, <span class="_16 blank"> </span>para <span class="_16 blank"> </span>o <span class="_17 blank"> </span>estado <span class="_16 blank"> </span>gasoso, <span class="_16 blank"> </span>apresenta <span class="_16 blank"> </span>coeficiente <span class="_16 blank"> </span>angular <span class="_16 blank"> </span>com <span class="_17 blank"> </span>grande <span class="_16 blank"> </span>valor </div><div class="t m1 x1 h3 y3f ff3 fs1 fc0 sc0 ls11 wsd">negativo. </div><div class="t m1 x6 h3 y40 ff3 fs1 fc0 sc0 ls11 wsd"> </div><div class="t m1 x6 h3 y41 ff3 fs1 fc0 sc0 ls11 wsd"> </div><div class="t m1 x6 h3 y42 ff3 fs1 fc0 sc0 ls11 wsd"> </div><div class="t m1 x6 h3 y43 ff3 fs1 fc0 sc0 ls11 wsd"> </div><div class="t m1 x6 h3 y44 ff3 fs1 fc0 sc0 ls11 wsd"> </div><div class="t m1 x6 h3 y45 ff3 fs1 fc0 sc0 ls11 wsd"> </div><div class="t m1 x6 h3 y46 ff3 fs1 fc0 sc0 ls11 wsd"> </div><div class="t m1 x6 h3 y47 ff3 fs1 fc0 sc0 ls11 wsd"> </div><div class="t m1 x6 h3 y48 ff3 fs1 fc0 sc0 ls11 wsd"> </div><div class="t m1 x6 h3 y49 ff3 fs1 fc0 sc0 ls11 wsd"> </div><div class="t m1 x6 h3 y4a ff3 fs1 fc0 sc0 ls11 wsd"> </div><div class="t m1 x34 h8 y4b ff3 fs1 fc0 sc0 ls11 wsd">Figura 1 - <span class="ff7 ls8">\ue002</span> em função de <span class="ff1">T </span>a pressão constante </div><div class="t m1 x6 h3 y4c ff3 fs1 fc0 sc0 ls11 wsd"> </div><div class="t m1 x6 h8 y4d ff3 fs1 fc0 sc0 ls11 wsd">Na <span class="_2 blank"> </span>Figura <span class="_f blank"> </span>1, <span class="_f blank"> </span>na <span class="_f blank"> </span>interseção <span class="_f blank"> </span>entre <span class="_f blank"> </span>as <span class="_f blank"> </span>curvas <span class="_f blank"> </span>S <span class="_f blank"> </span>e <span class="_f blank"> </span>L, <span class="_f blank"> </span><span class="ff7">\ue002</span></div><div class="t m3 xc h9 y4e ff7 fs3 fc0 sc0 ls11 ws2">\ue028\ue023\ue00a\ue029\ue02a\ue02b</div><div class="t m1 x35 h8 y4d ff7 fs1 fc0 sc0 ls11 ws3">\ue009 \ue002</div><div class="t m3 x36 h9 y4e ff7 fs3 fc0 sc0 ls11 ws2">\ue00a\ue02c\ue02f\ue005\ue029\ue02a\ue02b</div><div class="t m1 x37 h3 y4d ff3 fs1 fc0 sc0 ls11 wsd"> <span class="_2 blank"> </span>e <span class="_f blank"> </span>há <span class="_f blank"> </span>equilíbrio <span class="_f blank"> </span>entre <span class="_2 blank"> </span>as<span class="_2 blank"> </span> <span class="_2 blank"> </span>f<span class="_2 blank"> </span>ases </div><div class="t m1 x1 h3 y4f ff3 fs1 fc0 sc0 ls11 wsd">sólido e líquido. A temperatura neste ponto é a temperatura de fusão. </div><div class="t m1 x6 h3 y50 ff3 fs1 fc0 sc0 ls11 wsd">Da <span class="_4 blank"> </span>mesma <span class="_4 blank"> </span>forma, <span class="_16 blank"> </span>g<span class="_0 blank"></span>ás <span class="_4 blank"> </span>e <span class="_18 blank"> </span>líquido <span class="_4 blank"> </span>ex<span class="_2 blank"> </span>istem <span class="_4 blank"> </span>em <span class="_4 blank"> </span>equilíbrio <span class="_18 blank"> </span>nas <span class="_4 blank"> </span>condições <span class="_4 blank"> </span>indicadas <span class="_4 blank"> </span>pelo <span class="_18 blank"> </span>ponto <span class="_4 blank"> </span>de<span class="_2 blank"> </span> </div><div class="t m1 x1 h3 y51 ff3 fs1 fc0 sc0 ls11 wsd">interseção entre as curvas G e L, na temperatura de ebulição. </div><div class="t m1 x6 h3 y52 ff3 fs1 fc0 sc0 ls11 wsd">Para <span class="_2 blank"> </span>temperaturas <span class="_f blank"> </span>inferio<span class="_2 blank"> </span>res <span class="_2 blank"> </span>a <span class="_f blank"> </span><span class="ff1">T</span></div><div class="t m0 x1f h2 y53 ff1 fs0 fc0 sc0 ls11">f</div><div class="t m1 x38 h8 y52 ff3 fs1 fc0 sc0 ls11 wsd"> <span class="_2 blank"> </span>, <span class="_f blank"> </span>a <span class="_f blank"> </span>fase <span class="_f blank"> </span>que <span class="_f blank"> </span>apresenta <span class="_f blank"> </span>menor <span class="_f blank"> </span>valor <span class="_f blank"> </span>de <span class="_f blank"> </span><span class="ff7 ls8">\ue002</span> <span class="_f blank"> </span>é <span class="_f blank"> </span>a <span class="_2 blank"> </span>f<span class="_2 blank"> </span>ase <span class="_2 blank"> </span>sólida,<span class="_2 blank"> </span> <span class="_2 blank"> </span>que <span class="_f blank"> </span>é <span class="_f blank"> </span>a </div><div class="t m1 x1 h3 y54 ff3 fs1 fc0 sc0 ls11 wsd">mais <span class="_f blank"> </span>estável. <span class="_3 blank"> </span> <span class="_f blank"> </span>Entre <span class="_3 blank"> </span><span class="ff1">T</span></div><div class="t m0 x39 h2 y55 ff1 fs0 fc0 sc0 ls11">f</div><div class="t m1 x2 h3 y54 ff3 fs1 fc0 sc0 ls11 wsd"> <span class="_f blank"> </span> <span class="_3 blank"> </span>e <span class="_f blank"> </span><span class="ff1">T</span></div><div class="t m0 x34 h2 y55 ff1 fs0 fc0 sc0 ls11 wse">eb</div><div class="t m1 x3a h3 y54 ff3 fs1 fc0 sc0 ls11 wsd"> <span class="_f blank"> </span>a <span class="_3 blank"> </span>fase <span class="_f blank"> </span>que <span class="_f blank"> </span>apresenta<span class="_2 blank"> </span> <span class="_f blank"> </span>menor <span class="_3 blank"> </span>potencial <span class="_f blank"> </span>químico <span class="_3 blank"> </span>e <span class="_f blank"> </span>que <span class="_3 blank"> </span>é <span class="_f blank"> </span>a <span class="_3 blank"> </span>mais <span class="_f blank"> </span>estável <span class="_3 blank"> </span>é <span class="_3 blank"> </span>a </div><div class="t m1 x1 h3 y56 ff3 fs1 fc0 sc0 ls11 wsd">fase líquida. Para temperaturas superiores a <span class="ff1">T</span></div><div class="t m0 x21 h2 y57 ff1 fs0 fc0 sc0 ls11 wse">eb</div><div class="t m1 x3b h3 y56 ff3 fs1 fc0 sc0 ls11 wsd"> a fase gasosa é a mais estável. </div><div class="t m1 x6 h3 y58 ff3 fs1 fc0 sc0 ls11 wsd"> </div><div class="t m1 x6 h3 y59 ff3 fs1 fc0 sc0 ls11 wsd"> </div><div class="t m1 x6 h3 y5a ff3 fs1 fc0 sc0 ls11 wsd"> </div><div class="t m1 x6 h3 y5b ff3 fs1 fc0 sc0 ls11 wsd"> </div><div class="t m1 x6 h3 y5c ff3 fs1 fc0 sc0 ls11 wsd"> </div><div class="t m1 x6 h3 y5d ff3 fs1 fc0 sc0 ls11 wsd"> </div><div class="t m1 x6 h3 y5e ff3 fs1 fc0 sc0 ls11 wsd"> </div><div class="t m1 x6 h3 y5f ff3 fs1 fc0 sc0 ls11 wsd"> </div><div class="t m1 x6 h3 y60 ff3 fs1 fc0 sc0 ls11 wsd"> </div><div class="t m1 x6 h3 y61 ff3 fs1 fc0 sc0 ls11 wsd"> </div><div class="t m1 x6 h3 y62 ff3 fs1 fc0 sc0 ls11 wsd"> </div><div class="t m1 x34 h8 y63 ff3 fs1 fc0 sc0 ls11 wsd">Figura 2 - <span class="ff7 ls8">\ue002</span> em função de <span class="ff1">T </span>a pressão constante </div><div class="t m1 x6 h3 y64 ff3 fs1 fc0 sc0 ls11 wsd"> </div><div class="t m1 x6 h3 y65 ff3 fs1 fc0 sc0 ls11 wsd">Na <span class="_11 blank"> </span>Figura <span class="_11 blank"> </span>2, <span class="_11 blank"> </span>se <span class="_11 blank"> </span>o <span class="_4 blank"> </span>líquido <span class="_11 blank"> </span>estivesse <span class="_11 blank"> </span>presente <span class="_11 blank"> </span>em <span class="_11 blank"> </span>um <span class="_4 blank"> </span>sistema <span class="_11 blank"> </span>numa <span class="_11 blank"> </span>temperatura <span class="_11 blank"> </span>inferior <span class="_11 blank"> </span>a <span class="_11 blank"> </span><span class="ff1">T</span></div><div class="t m0 x3c h2 y66 ff1 fs0 fc0 sc0 ls11">f</div><div class="t m1 x3d h3 y65 ff3 fs1 fc0 sc0 ls11 wsd"> <span class="_11 blank"> </span>, <span class="_11 blank"> </span>o </div><div class="t m1 x1 h3 y67 ff3 fs1 fc0 sc0 ls11 wsd">potencial <span class="_f blank"> </span>químico <span class="_3 blank"> </span>do <span class="_f blank"> </span>l<span class="_2 blank"> </span>íquido <span class="_3 blank"> </span>teria <span class="_f blank"> </span>valor </div><div class="t m4 x3e he y67 ff8 fs5 fc0 sc0 ls11">µ</div><div class="t m0 x3f h2 y68 ff1 fs0 fc0 sc0 ls11">a</div><div class="t m1 x40 h3 y67 ff3 fs1 fc0 sc0 ls11 wsd"> <span class="_f blank"> </span>maior<span class="_2 blank"> </span> <span class="_f blank"> </span>que <span class="_3 blank"> </span>o <span class="_f blank"> </span>pot<span class="_2 blank"> </span>encial <span class="_f blank"> </span>químico <span class="_3 blank"> </span>do <span class="_3 blank"> </span>sólido </div><div class="t m4 x41 he y67 ff8 fs5 fc0 sc0 ls11">µ</div><div class="t m0 x42 h2 y68 ff1 fs0 fc0 sc0 ls11">b</div><div class="t m1 x43 h3 y67 ff1 fs1 fc0 sc0 ls12 wsd"> <span class="ff3 ls11">e <span class="_f blank"> </span>o <span class="_3 blank"> </span>líquido <span class="_3 blank"> </span>se </span></div><div class="t m1 x1 h3 y69 ff3 fs1 fc0 sc0 ls11 wsd">congelaria espontaneamente a essa temperatura pois iss<span class="_2 blank"> </span>o acarre<span class="_0 blank"></span>taria a dimi<span class="_2 blank"> </span>nuição da energia de Gibbs. </div><div class="t m1 x1 h3 y6a ff3 fs1 fc0 sc0 ls11 wsd"> <span class="_19 blank"> </span> </div><div class="t m4 x44 he y6b ff8 fs5 fc0 sc0 ls11 wsd">µ </div><div class="t m1 x45 ha y6c ff1 fs1 fc0 sc0 ls11">T</div><div class="t m0 x46 h2 y6d ff1 fs0 fc0 sc0 ls11 wsd">eb </div><div class="t m1 x2f ha y6e ff1 fs1 fc0 sc0 ls11">T</div><div class="t m0 x47 h2 y6f ff1 fs0 fc0 sc0 ls11 wsd">f </div><div class="t m1 x48 ha y6c ff1 fs1 fc0 sc0 ls11">T</div><div class="t m0 x49 h2 y6d ff1 fs0 fc0 sc0 ls11 wsd"> </div><div class="t m1 x4a h5 y70 ff4 fs1 fc0 sc0 ls11">S</div><div class="c x48 y71 w2 hf"><div class="t m1 x4b h5 y72 ff4 fs1 fc0 sc0 ls11 wsd"> </div></div><div class="t m1 x4a h5 y73 ff4 fs1 fc0 sc0 ls11">L</div><div class="c x14 y74 w3 hf"><div class="t m1 x4b h5 y75 ff4 fs1 fc0 sc0 ls11 wsd"> </div></div><div class="t m1 x4a h5 y76 ff4 fs1 fc0 sc0 ls11">G</div><div class="c x4c y77 w4 hf"><div class="t m1 x4b h5 y78 ff4 fs1 fc0 sc0 ls11 wsd"> </div></div><div class="t m4 x44 he y79 ff8 fs5 fc0 sc0 ls11 wsd">µ </div><div class="t m1 x22 ha y7a ff1 fs1 fc0 sc0 ls11">T</div><div class="t m0 xb h2 y7b ff1 fs0 fc0 sc0 ls11 wsd">f </div><div class="t m1 x48 ha y7c ff1 fs1 fc0 sc0 ls11">T</div><div class="t m0 x49 h2 y7d ff1 fs0 fc0 sc0 ls11 wsd"> </div><div class="t m1 x4a h5 y7e ff4 fs1 fc0 sc0 ls11">S</div><div class="c x14 y7f w2 hf"><div class="t m1 x4b h5 y80 ff4 fs1 fc0 sc0 ls11 wsd"> </div></div><div class="t m1 x4a h5 y81 ff4 fs1 fc0 sc0 ls11">L</div><div class="c x4c y82 w3 hf"><div class="t m1 x4b h5 y83 ff4 fs1 fc0 sc0 ls11 wsd"> </div></div><div class="c x44 y84 w5 h10"><div class="t m5 x4b h11 y85 ff8 fs6 fc0 sc0 ls11">µ</div></div><div class="t m6 x4d h12 y86 ff1 fs4 fc0 sc0 ls11">a</div><div class="t m7 x4e h13 y86 ff8 fs7 fc0 sc0 ls11 wsd"> </div><div class="c x44 y87 w5 h10"><div class="t m5 x4b h11 y88 ff8 fs6 fc0 sc0 ls11">µ</div></div><div class="t m6 x4d h12 y89 ff1 fs4 fc0 sc0 ls11">b</div><div class="t m7 x4e h13 y89 ff8 fs7 fc0 sc0 ls11 wsd"> </div><div class="t m8 x3f h14 y8a ff1 fs8 fc0 sc0 ls11">a</div><div class="t m6 x2f h12 y8b ff1 fs4 fc0 sc0 ls11 wsd"> </div><div class="t m8 x3f h14 y8c ff1 fs8 fc0 sc0 ls11">b</div><div class="t m6 x2f h12 y8d ff1 fs4 fc0 sc0 ls11 wsd"> </div></div><div class="pi" data-data='{"ctm":[1.000000,0.000000,0.000000,1.000000,0.000000,0.000000]}'></div></div> <div id="pf3" class="pf w0 h0" data-page-no="3"><div class="pc pc3 w0 h0"><img fetchpriority="low" loading="lazy" class="bi x0 y3a w1 hd" alt="" src="https://files.passeidireto.com/07bebfca-1ca3-4db1-8f6c-0a20e70e33d8/bg3.png"><div class="t m0 x1 h2 y3b ff1 fs0 fc0 sc0 ls11 wsd">Escola de Engenharia<span class="_0 blank"></span> de Lorena \u2013 EEL/USP <span class="_14 blank"> </span>Termodinâmica Q<span class="_0 blank"></span>uímica \u2013 Prof. Antonio Car<span class="_0 blank"></span>los da Silva </div><div class="t m0 x1 h6 y3c ff2 fs0 fc0 sc0 ls11 wsd"> </div><div class="t m0 x1 h2 y3d ff1 fs0 fc0 sc0 ls11 wsd">Equilíbrio de Fases em <span class="_0 blank"></span>Sistemas Simples <span class="_0 blank"></span>\u2013 A Regra das Fases <span class="_0 blank"></span> <span class="_15 blank"> </span>Página 3 </div><div class="t m1 x1 h8 y8e ff4 fs1 fc0 sc0 ls11 ws0">3.<span class="ff5 ls0 wsd"> </span><span class="wsd">VARIAÇÃO DAS CURVAS <span class="ff7 ws3">\ue033<span class="_6 blank"> </span>\ue009 \ue034\ue01f\ue035\ue021</span> COM A PRESSÃO </span></div><div class="t m1 x6 h8 y8f ff3 fs1 fc0 sc0 ls11 wsd">Da <span class="_f blank"> </span>Equação <span class="_3 blank"> </span>(2b), <span class="_f blank"> </span><span class="ff7">\ue014</span></div><div class="t m1 x4f h8 y90 ff7 fs1 fc0 sc0 ls13">\ue018<span class="ls11 wsa v4">\ue009 \ue01f\ue020\ue002<span class="_2 blank"></span>\ue036\ue020\ue037\ue021</span></div><div class="t m3 x50 h9 y91 ff7 fs3 fc0 sc0 ls11">\ue01c</div><div class="t m1 x17 h8 y8f ff3 fs1 fc0 sc0 ls11 wsd"> <span class="_f blank"> </span>, <span class="_3 blank"> </span>que <span class="_f blank"> </span>pode <span class="_3 blank"> </span>ser <span class="_f blank"> </span>escrita <span class="_f blank"> </span>como <span class="_3 blank"> </span><span class="ff7 ws4">\ue00f\ue002<span class="_6 blank"> </span>\ue009 \ue014</span></div><div class="t m1 x29 h8 y90 ff7 fs1 fc0 sc0 ls5">\ue018<span class="ls11 ws1 v4">\ue00f\ue037<span class="ff3 wsd"> <span class="_f blank"> </span>, <span class="_f blank"> </span>s<span class="_2 blank"> </span>e <span class="_f blank"> </span>a <span class="_f blank"> </span>pressão <span class="_3 blank"> </span>diminui, </span></span></div><div class="t m1 x1 h8 y92 ff7 fs1 fc0 sc0 ls11 ws1">\ue00f\ue037<span class="ff3 wsd"> <span class="_2 blank"> </span>é negativo, <span class="_2 blank"> </span></span>\ue014</div><div class="t m1 x51 h8 y93 ff7 fs1 fc0 sc0 ls14">\ue018<span class="ff3 ls11 wsd v4"> é posit<span class="_2 blank"> </span>ivo e </span><span class="ls11 ws1 v4">\ue00f\ue002<span class="_2 blank"> </span><span class="ff3 wsd"> <span class="_2 blank"> </span>diminui. <span class="_2 blank"> </span>O potencial quím<span class="_2 blank"> </span>ico decresce proporcio<span class="_2 blank"> </span>nalmente ao volume </span></span></div><div class="t m1 x1 h3 y94 ff3 fs1 fc0 sc0 ls11 wsd">da fase. </div><div class="t m1 x6 h3 y7 ff3 fs1 fc0 sc0 ls11 wsd"> </div><div class="t m1 x6 h3 y95 ff3 fs1 fc0 sc0 ls11 wsd"> </div><div class="t m1 x6 h3 y96 ff3 fs1 fc0 sc0 ls11 wsd"> </div><div class="t m1 x6 h3 y97 ff3 fs1 fc0 sc0 ls11 wsd"> </div><div class="t m1 x6 h3 y98 ff3 fs1 fc0 sc0 ls11 wsd"> </div><div class="t m1 x6 h3 y99 ff3 fs1 fc0 sc0 ls11 wsd"> </div><div class="t m1 x6 h3 y9a ff3 fs1 fc0 sc0 ls11 wsd"> </div><div class="t m1 x6 h3 y9b ff3 fs1 fc0 sc0 ls11 wsd"> </div><div class="t m1 x6 h3 y6d ff3 fs1 fc0 sc0 ls11 wsd"> </div><div class="t m1 x6 h3 y9c ff3 fs1 fc0 sc0 ls11 wsd"> </div><div class="t m1 x6 h3 y9d ff3 fs1 fc0 sc0 ls11 wsd"> </div><div class="t m1 x52 h3 y9e ff3 fs1 fc0 sc0 ls11 wsd">Figura 3 \u2013 Efeito da pressão nos pontos de fusão e ebulição. As linhas contínuas </div><div class="t m1 x53 h3 y9f ff3 fs1 fc0 sc0 ls11 wsd">correspondem a uma pressão alta e as linhas tracejadas correspondem a uma pressão baix<span class="_2 blank"> </span>a </div><div class="t m1 x54 h3 ya0 ff3 fs1 fc0 sc0 ls11 wsd"> </div><div class="t m1 x6 h3 ya1 ff3 fs1 fc0 sc0 ls11 wsd">Quando a pressão diminui o potencial químico também diminui: </div><div class="t m1 x55 h3 ya2 ff9 fs1 fc0 sc0 ls15">\ue001<span class="ff2 ls16 wsd"> <span class="ff3 ls11">Sólidos e líquidos: pequena variação de volume </span></span></div><div class="t m1 x55 h3 ya3 ff9 fs1 fc0 sc0 ls15">\ue001<span class="ff2 ls16 wsd"> <span class="ff3 ls11">Gases: grande variação de volume (logo, maior variação de <span class="ff8 ws0">µ</span>) </span></span></div><div class="t m1 x6 h3 ya4 ff3 fs1 fc0 sc0 ls11 wsd">Conclui-se que: </div><div class="t m1 x55 h3 ya5 ff9 fs1 fc0 sc0 ls15">\ue001<span class="ff2 ls16 wsd"> <span class="ff3 ls11">Quando va<span class="_2 blank"> </span>ria a <span class="_5 blank"> </span>press<span class="_2 blank"> </span>ão, <span class="_5 blank"> </span>alteram-se <span class="_5 blank"> </span>a <span class="_5 blank"> </span>temperaturas <span class="_5 blank"> </span>de <span class="_5 blank"> </span>fusão <span class="_5 blank"> </span>e <span class="_5 blank"> </span>de <span class="_5 blank"> </span>ebul<span class="_2 blank"> </span>ição de <span class="_5 blank"> </span>uma<span class="_2 blank"> </span> </span></span></div><div class="t m1 x4 h3 ya6 ff3 fs1 fc0 sc0 ls11 wsd">substância. </div><div class="t m1 x55 h3 ya7 ff9 fs1 fc0 sc0 ls15">\ue001<span class="ff2 ls16 wsd"> <span class="ff3 ls11">A temperatura de ebulição é muito maior que a temperatura de fusão. </span></span></div><div class="t m1 x55 h3 ya8 ff9 fs1 fc0 sc0 ls15">\ue001<span class="ff2 ls16 wsd"> <span class="ff3 ls11">Se <span class="_3 blank"> </span>a <span class="_3 blank"> </span>pressão <span class="_11 blank"> </span>for <span class="_3 blank"> </span>reduzida <span class="_11 blank"> </span>a <span class="_3 blank"> </span>um <span class="_3 blank"> </span>valor <span class="_11 blank"> </span>suficientemente <span class="_3 blank"> </span>baixo <span class="_11 blank"> </span>de <span class="_3 blank"> </span>forma <span class="_3 blank"> </span>que<span class="_2 blank"> </span> <span class="_3 blank"> </span>a <span class="_3 blank"> </span>temperatura<span class="_2 blank"> </span> </span></span></div><div class="t m1 x4 h3 ya9 ff3 fs1 fc0 sc0 ls11 wsd">de <span class="_1a blank"> </span>ebulição <span class="_1a blank"> </span>se <span class="_1a blank"> </span>torne <span class="_1a blank"> </span>menor <span class="_1a blank"> </span>que <span class="_1a blank"> </span>a <span class="_1a blank"> </span>t<span class="_2 blank"> </span>emperatura <span class="_1a blank"> </span>de <span class="_1a blank"> </span>fusão, <span class="_1a blank"> </span>o <span class="_1a blank"> </span>líqui<span class="_2 blank"> </span>do <span class="_1a blank"> </span>não <span class="_1a blank"> </span>possuirá </div><div class="t m1 x4 h3 yaa ff3 fs1 fc0 sc0 ls11 wsd">estabilidade e ocorre a sublimação do sólido. </div><div class="t m1 x6 h3 yab ff3 fs1 fc0 sc0 ls11 wsd"> </div><div class="t m1 x6 h3 yac ff3 fs1 fc0 sc0 ls11 wsd"> </div><div class="t m1 x6 h3 yad ff3 fs1 fc0 sc0 ls11 wsd"> </div><div class="t m1 x6 h3 yae ff3 fs1 fc0 sc0 ls11 wsd"> </div><div class="t m1 x6 h3 yaf ff3 fs1 fc0 sc0 ls11 wsd"> </div><div class="t m1 x6 h3 yb0 ff3 fs1 fc0 sc0 ls11 wsd"> </div><div class="t m1 x6 h3 yb1 ff3 fs1 fc0 sc0 ls11 wsd"> </div><div class="t m1 x6 h3 yb2 ff3 fs1 fc0 sc0 ls11 wsd"> </div><div class="t m1 x6 h3 yb3 ff3 fs1 fc0 sc0 ls11 wsd"> </div><div class="t m1 x6 h3 yb4 ff3 fs1 fc0 sc0 ls11 wsd"> </div><div class="t m1 x56 h15 yb5 ff3 fs1 fc0 sc0 ls11 wsd">Figura 4 \u2013 <span class="ff7 ws1 v0">\ue038</span><span class="v0"> em função de T para uma substância que sublima </span></div><div class="t m4 x57 he yb6 ff8 fs5 fc0 sc0 ls11 wsd">µ </div><div class="t m1 x58 ha yb7 ff1 fs1 fc0 sc0 ls11">T</div><div class="t m0 x21 h2 yb8 ff1 fs0 fc0 sc0 ls11 wsd"> </div><div class="t m1 x20 h5 yb9 ff4 fs1 fc0 sc0 ls11">S</div><div class="c x58 yba w2 hf"><div class="t m1 x4b h5 ybb ff4 fs1 fc0 sc0 ls11 wsd"> </div></div><div class="t m1 x20 h5 ybc ff4 fs1 fc0 sc0 ls11">L</div><div class="c x8 ybd w3 hf"><div class="t m1 x4b h5 ybe ff4 fs1 fc0 sc0 ls11 wsd"> </div></div><div class="t m1 x20 h5 ybf ff4 fs1 fc0 sc0 ls11">G</div><div class="c x8 yc0 w4 hf"><div class="t m1 x4b h5 yc1 ff4 fs1 fc0 sc0 ls11 wsd"> </div></div><div class="c x59 yc2 w6 h16"><div class="t m9 x4b h17 yc3 ff1 fs9 fc0 sc0 ls11">a</div></div><div class="c x5a yc2 w7 h16"><div class="t m9 x4b h17 yc3 ff1 fs9 fc0 sc0 ls11 wsd"> </div></div><div class="c x5b yc4 w8 h16"><div class="t m9 x4b h17 yc5 ff1 fs9 fc0 sc0 ls11 wsd">a\u2019 </div></div><div class="c x5 yc6 w9 h16"><div class="t m9 x4b h17 yc7 ff1 fs9 fc0 sc0 ls11 wsd">b\u2019 </div></div><div class="c x5c yc6 w7 h16"><div class="t m9 x4b h17 yc7 ff1 fs9 fc0 sc0 ls11 wsd"> </div></div><div class="c x5d yc8 wa h16"><div class="t m9 x4b h17 yc9 ff1 fs9 fc0 sc0 ls11 wsd">b </div></div><div class="c x5e yc8 w7 h16"><div class="t m9 x4b h17 yc9 ff1 fs9 fc0 sc0 ls11 wsd"> </div></div><div class="c x5d yca wb h16"><div class="t m9 x4b h17 ycb ff1 fs9 fc0 sc0 ls11">c</div></div><div class="c x5f yca w7 h16"><div class="t m9 x4b h17 ycb ff1 fs9 fc0 sc0 ls11 wsd"> </div></div><div class="c x5 ycc wc h16"><div class="t m9 x4b h17 ycd ff1 fs9 fc0 sc0 ls11 wsd">c\u2019 </div></div><div class="c x60 ycc w7 h16"><div class="t m9 x4b h17 ycd ff1 fs9 fc0 sc0 ls11 wsd"> </div></div><div class="t m4 x61 he yb6 ff8 fs5 fc0 sc0 ls11 wsd">µ </div><div class="t m1 x43 ha yb7 ff1 fs1 fc0 sc0 ls11">T</div><div class="t m0 x62 h2 yb8 ff1 fs0 fc0 sc0 ls11 wsd"> </div><div class="t m1 x2d h5 yb9 ff4 fs1 fc0 sc0 ls11">S</div><div class="c x43 yba w2 hf"><div class="t m1 x4b h5 ybb ff4 fs1 fc0 sc0 ls11 wsd"> </div></div><div class="t m1 x2d h5 yce ff4 fs1 fc0 sc0 ls11">L</div><div class="c x63 ycf w3 hf"><div class="t m1 x4b h5 ybe ff4 fs1 fc0 sc0 ls11 wsd"> </div></div><div class="t m1 x2d h5 ybf ff4 fs1 fc0 sc0 ls11">G</div><div class="c x64 yc0 w4 hf"><div class="t m1 x4b h5 yc1 ff4 fs1 fc0 sc0 ls11 wsd"> </div></div><div class="t m1 x65 ha yb7 ff1 fs1 fc0 sc0 ls11">T</div><div class="t m0 x66 h2 yb8 ff1 fs0 fc0 sc0 ls11">f</div><div class="c x4a yd0 wd h18"><div class="t m0 x4b h2 yd1 ff1 fs0 fc0 sc0 ls11">\u2019</div></div><div class="c x13 yd0 we h18"><div class="t m0 x4b h2 yd1 ff1 fs0 fc0 sc0 ls11 wsd"> </div></div><div class="t m1 x14 ha yb7 ff1 fs1 fc0 sc0 ls11">T</div><div class="t m0 x67 h2 yb8 ff1 fs0 fc0 sc0 ls11">f</div><div class="c x68 yd0 we h18"><div class="t m0 x4b h2 yd1 ff1 fs0 fc0 sc0 ls11 wsd"> </div></div><div class="t m1 x69 ha yb7 ff1 fs1 fc0 sc0 ls11">T</div><div class="t m0 x10 h2 yb8 ff1 fs0 fc0 sc0 ls11 wse">eb</div><div class="c x2a yd0 wd h18"><div class="t m0 x4b h2 yd1 ff1 fs0 fc0 sc0 ls11">\u2019</div></div><div class="c x6a yd0 we h18"><div class="t m0 x4b h2 yd1 ff1 fs0 fc0 sc0 ls11 wsd"> </div></div><div class="t m1 x6b ha yb7 ff1 fs1 fc0 sc0 ls11">T</div><div class="t m0 x6c h2 yb8 ff1 fs0 fc0 sc0 ls11 wse">eb</div><div class="c x6d yd0 we h18"><div class="t m0 x4b h2 yd1 ff1 fs0 fc0 sc0 ls11 wsd"> </div></div><div class="t m4 x44 he yd2 ff8 fs5 fc0 sc0 ls11 wsd">µ </div><div class="t m1 x48 ha yd3 ff1 fs1 fc0 sc0 ls11">T</div><div class="t m0 x49 h2 yd4 ff1 fs0 fc0 sc0 ls11 wsd"> </div><div class="t m1 x4a h5 yd5 ff4 fs1 fc0 sc0 ls11">S</div><div class="c x14 yd6 w2 hf"><div class="t m1 x4b h5 yd7 ff4 fs1 fc0 sc0 ls11 wsd"> </div></div><div class="t m1 x4a h5 yd8 ff4 fs1 fc0 sc0 ls11">L</div><div class="c x4c yd9 w3 hf"><div class="t m1 x4b h5 yda ff4 fs1 fc0 sc0 ls11 wsd"> </div></div><div class="t m1 x31 h5 ydb ff4 fs1 fc0 sc0 ls11">G</div><div class="c x6e ydc w4 hf"><div class="t m1 x4b h5 ydd ff4 fs1 fc0 sc0 ls11 wsd"> </div></div></div><div class="pi" data-data='{"ctm":[1.000000,0.000000,0.000000,1.000000,0.000000,0.000000]}'></div></div> <div id="pf4" class="pf w0 h0" data-page-no="4"><div class="pc pc4 w0 h0"><img fetchpriority="low" loading="lazy" class="bi x0 y3a w1 hd" alt="" src="https://files.passeidireto.com/07bebfca-1ca3-4db1-8f6c-0a20e70e33d8/bg4.png"><div class="t m0 x1 h2 y3b ff1 fs0 fc0 sc0 ls11 wsd">Escola de Engenharia<span class="_0 blank"></span> de Lorena \u2013 EEL/USP <span class="_14 blank"> </span>Termodinâmica Q<span class="_0 blank"></span>uímica \u2013 Prof. Antonio Car<span class="_0 blank"></span>los da Silva </div><div class="t m0 x1 h6 y3c ff2 fs0 fc0 sc0 ls11 wsd"> </div><div class="t m0 x1 h2 y3d ff1 fs0 fc0 sc0 ls11 wsd">Equilíbrio de Fases em <span class="_0 blank"></span>Sistemas Simples <span class="_0 blank"></span>\u2013 A Regra das Fases <span class="_0 blank"></span> <span class="_15 blank"> </span>Página 4 </div><div class="t m1 x6 h3 y3e ff3 fs1 fc0 sc0 ls11 wsd">A pressão<span class="_2 blank"> </span> ab<span class="_2 blank"> </span>aixo <span class="_2 blank"> </span>da qual <span class="_2 blank"> </span>ocorre <span class="_2 blank"> </span>sublimação <span class="_2 blank"> </span>pode <span class="_2 blank"> </span>ser <span class="_2 blank"> </span>determinada p<span class="_2 blank"> </span>ela <span class="_2 blank"> </span>equação <span class="_2 blank"> </span>conhecida com<span class="_2 blank"> </span>o </div><div class="t m1 x1 h3 y3f ff3 fs1 fc0 sc0 ls11 wsd">Regra de Trouton: </div><div class="t m1 x1 h8 yde ff3 fs1 fc0 sc0 ls11 wsd"> <span class="_1b blank"> </span> <span class="ff7 wsf">\ue039\ue03a \ue037<span class="_5 blank"> </span>\ue009<span class="_6 blank"> </span>\ue010\ue03b\ue03c\ue03d\ue03e \ue03f</span></div><div class="t m3 x15 h9 ydf ff7 fs3 fc0 sc0 ls17">\ue01c<span class="fs4 ls11 ws10 v5">\ue040\ue041 </span><span class="ls11 ws2">\ue042\ue01c<span class="fs4 v5">\ue043</span></span></div><div class="t m3 x6f h9 ye0 ff7 fs3 fc0 sc0 ls17">\ue01c<span class="fs4 ls11 v5">\ue043</span></div><div class="t m1 x70 h8 yde ff7 fs1 fc0 sc0 ls11 ws1">\ue044<span class="ff3 wsd"> <span class="_1c blank"> </span>(5) </span></div><div class="t m1 x1 h5 ye1 ff4 fs1 fc0 sc0 ls11 ws0">4.<span class="ff5 ls0 wsd"> </span><span class="wsd">A EQUAÇÃO DE CLAPEYRON </span></div><div class="t m1 x6 h3 ye2 ff3 fs1 fc0 sc0 ls11 wsd">Para duas fases </div><div class="t m4 x33 he ye2 ff8 fs5 fc0 sc0 ls11">\u03b1</div><div class="t m1 x71 h3 ye2 ff3 fs1 fc0 sc0 ls11 wsd"> e </div><div class="t m4 x72 he ye2 ff8 fs5 fc0 sc0 ls11">\u03b2</div><div class="t m1 x1d h3 ye2 ff3 fs1 fc0 sc0 ls11 wsd"> de uma substância pura, a condição de equilíbrio é: </div><div class="t m1 x1 h8 ye3 ff3 fs1 fc0 sc0 ls11 wsd"> <span class="_1d blank"> </span> <span class="ff7">\ue002</span></div><div class="t m3 x20 h9 ye4 ff7 fs3 fc0 sc0 ls11">\ue045</div><div class="t m1 x58 h8 ye5 ff7 fs1 fc0 sc0 lsb">\ue01f<span class="ls11 ws11 v1">\ue012\ue03d \ue037<span class="_2 blank"> </span></span><span class="ls18">\ue021<span class="ls11 ws3 v1">\ue009 \ue002</span></span></div><div class="t m3 x31 h9 ye4 ff7 fs3 fc0 sc0 ls11">\ue046</div><div class="t m1 x61 h8 ye5 ff7 fs1 fc0 sc0 lsb">\ue01f<span class="ls11 ws11 v1">\ue012\ue03d \ue037<span class="_2 blank"> </span></span><span class="ls11 ws1">\ue021<span class="ff3 wsd v1"> <span class="_1e blank"> </span>(6) </span></span></div><div class="t m1 x6 h3 ye6 ff3 fs1 fc0 sc0 ls11 wsd">Se <span class="_18 blank"> </span>a <span class="_16 blank"> </span>pressão <span class="_18 blank"> </span>variar: <span class="_18 blank"> </span> <span class="_16 blank"> </span><span class="ff1 lsa">p</span><span class="ls19"> </span><span class="ffa ws12">\u21d2</span><span class="ls1a"> <span class="ff1 lsa">p</span></span> <span class="_18 blank"> </span>+ <span class="_16 blank"> </span><span class="ff1 ws0">dp</span> <span class="_18 blank"> </span>, <span class="_16 blank"> </span>a <span class="_18 blank"> </span>temperatura <span class="_18 blank"> </span>de <span class="_16 blank"> </span>equilíbrio <span class="_18 blank"> </span>muda: <span class="_16 blank"> </span><span class="ff1 ls9">T</span><span class="ls1b"> </span><span class="ffa ws12">\u21d2</span><span class="ls1a"> </span><span class="ff1 ws0">T</span> <span class="_18 blank"> </span>+ <span class="_18 blank"> </span><span class="ff1 ws0">dT</span> <span class="_16 blank"> </span> <span class="_18 blank"> </span>e <span class="_16 blank"> </span>cada </div><div class="t m1 x1 h3 ye7 ff3 fs1 fc0 sc0 ls11 wsd">potencial químico muda: </div><div class="t m4 x73 he ye7 ff8 fs5 fc0 sc0 ls11">µ</div><div class="t m1 x34 h3 ye7 ff3 fs1 fc0 sc0 ls1c wsd"> <span class="ffa ls11 ws12">\u21d2</span><span class="ls11"> </span></div><div class="t m4 x74 he ye7 ff8 fs5 fc0 sc0 ls11">µ</div><div class="t m1 x59 h3 ye7 ff3 fs1 fc0 sc0 ls11 wsd"> + <span class="ff1">d</span></div><div class="t m4 x75 he ye7 ff8 fs5 fc0 sc0 ls11">µ</div><div class="t m1 x5c h3 ye7 ff1 fs1 fc0 sc0 ls10 wsd"> <span class="ff3 ls11">. </span></div><div class="t m1 x6 h3 ye8 ff3 fs1 fc0 sc0 ls11 wsd">Então, no estado <span class="ff1">T + dT</span> e <span class="ff1">p + dp</span>, no equilíbrio: </div><div class="t m1 x1 h8 ye9 ff3 fs1 fc0 sc0 ls11 wsd"> <span class="_e blank"> </span> <span class="ff7">\ue002</span></div><div class="t m3 x5f h9 yea ff7 fs3 fc0 sc0 ls11">\ue045</div><div class="t m1 x60 h8 yeb ff7 fs1 fc0 sc0 lsb">\ue01f<span class="ls11 ws11 v1">\ue012\ue03d \ue037<span class="_2 blank"> </span></span><span class="ls1d">\ue021<span class="ls11 ws13 v1">\ue013<span class="_17 blank"> </span>\ue00f \ue002</span></span></div><div class="t m3 x76 h9 yea ff7 fs3 fc0 sc0 ls11">\ue045</div><div class="t m1 x22 h8 ye9 ff7 fs1 fc0 sc0 ls11 ws4">\ue009 \ue002</div><div class="t m3 x31 h9 yea ff7 fs3 fc0 sc0 ls11">\ue046</div><div class="t m1 x61 h8 yeb ff7 fs1 fc0 sc0 lsb">\ue01f<span class="ls11 ws14 v1">\ue012\ue03d \ue037<span class="_2 blank"> </span></span><span class="ls1e">\ue021<span class="ls11 ws13 v1">\ue013<span class="_17 blank"> </span>\ue00f \ue002</span></span></div><div class="t m3 x67 h9 yea ff7 fs3 fc0 sc0 ls11">\ue046</div><div class="t m1 x77 h3 ye9 ff3 fs1 fc0 sc0 ls11 wsd"> <span class="_1f blank"> </span>(7) </div><div class="t m1 x1 h8 yec ff3 fs1 fc0 sc0 ls11 wsd"> <span class="_20 blank"> </span> <span class="ff7 ws13">\ue00f \ue002</span></div><div class="t m3 x76 h9 yed ff7 fs3 fc0 sc0 ls11">\ue045</div><div class="t m1 x22 h8 yec ff7 fs1 fc0 sc0 ls11 ws13">\ue009<span class="_5 blank"> </span>\ue00f \ue002</div><div class="t m3 x61 h9 yed ff7 fs3 fc0 sc0 ls11">\ue046</div><div class="t m1 x11 h3 yec ff3 fs1 fc0 sc0 ls11 wsd"> <span class="_21 blank"> </span>(8) </div><div class="t m1 x6 h3 yee ff3 fs1 fc0 sc0 ls11 wsd">Explicitando cada <span class="ff1">d</span></div><div class="t m4 x72 he yee ff8 fs5 fc0 sc0 ls11">µ</div><div class="t m1 x1d h3 yee ff3 fs1 fc0 sc0 ls11 wsd"> em termos de <span class="ff1 ws0">dp</span> e <span class="ff1 ws0">dT</span> mediante a equação fundament<span class="_2 blank"> </span>al: </div><div class="t m1 x1 h8 yef ff3 fs1 fc0 sc0 ls11 wsd"> <span class="_22 blank"> </span> <span class="ff7 ws13">\ue00f \ue002</span></div><div class="t m3 x78 h9 yf0 ff7 fs3 fc0 sc0 ls11">\ue045</div><div class="t m1 x79 hc yef ff7 fs1 fc0 sc0 ls11 wsa">\ue009 \ue010\ue011<span class="v3">\ue017</span></div><div class="t m3 x4d h9 yf0 ff7 fs3 fc0 sc0 ls11">\ue045</div><div class="t m1 x60 h8 yef ff7 fs1 fc0 sc0 ls11 ws6">\ue00f\ue012 \ue013 \ue014</div><div class="t m1 x20 h8 yf1 ff7 fs1 fc0 sc0 ls11">\ue018</div><div class="t m3 x2f h9 yf0 ff7 fs3 fc0 sc0 ls11">\ue045</div><div class="t m1 x47 h8 yef ff7 fs1 fc0 sc0 ls11 ws1">\ue00f\ue015<span class="ff3 lsd wsd"> e </span><span class="ws13">\ue00f \ue002</span></div><div class="t m3 x45 h9 yf0 ff7 fs3 fc0 sc0 ls11">\ue046</div><div class="t m1 x7a hc yef ff7 fs1 fc0 sc0 ls11 ws4">\ue009 \ue010\ue011<span class="v3">\ue017</span></div><div class="t m3 x26 h9 yf0 ff7 fs3 fc0 sc0 ls11">\ue046</div><div class="t m1 x36 h8 yef ff7 fs1 fc0 sc0 ls11 ws6">\ue00f\ue012 \ue013 \ue014</div><div class="t m1 x37 h8 yf1 ff7 fs1 fc0 sc0 ls11">\ue018</div><div class="t m3 x7b h9 yf0 ff7 fs3 fc0 sc0 ls11">\ue046</div><div class="t m1 x7c h8 yef ff7 fs1 fc0 sc0 ls11 ws1">\ue00f\ue015<span class="ff3 wsd"> </span></div><div class="t m1 x1 hc yf2 ff3 fs1 fc0 sc0 ls11 wsd"> <span class="_23 blank"> </span><span class="ff7 ws1">\ue010\ue011<span class="v3">\ue017</span></span></div><div class="t m3 x5e h9 yf3 ff7 fs3 fc0 sc0 ls11">\ue045</div><div class="t m1 x38 h8 yf2 ff7 fs1 fc0 sc0 ls11 ws6">\ue00f\ue012<span class="_9 blank"> </span>\ue013 \ue014</div><div class="t m1 x8 h8 yf4 ff7 fs1 fc0 sc0 ls11">\ue018</div><div class="t m3 x7d h9 yf3 ff7 fs3 fc0 sc0 ls11">\ue045</div><div class="t m1 x7e hc yf2 ff7 fs1 fc0 sc0 ls11 ws4">\ue00f\ue015 \ue009 \ue010\ue011<span class="_2 blank"></span><span class="v3">\ue017</span></div><div class="t m3 x61 h9 yf3 ff7 fs3 fc0 sc0 ls11">\ue046</div><div class="t m1 x11 h8 yf2 ff7 fs1 fc0 sc0 ls11 ws6">\ue00f\ue012 \ue013 \ue014</div><div class="t m1 x7f h8 yf4 ff7 fs1 fc0 sc0 ls11">\ue018</div><div class="t m3 x66 h9 yf3 ff7 fs3 fc0 sc0 ls11">\ue046</div><div class="t m1 x26 h8 yf2 ff7 fs1 fc0 sc0 ls11 ws1">\ue00f\ue015<span class="ff3 wsd"> <span class="_24 blank"> </span>(9) </span></div><div class="t m1 x6 h3 yf5 ff3 fs1 fc0 sc0 ls11 wsd">Se a transformação for </div><div class="t m4 x3a he yf5 ff8 fs5 fc0 sc0 ls11">\u03b1</div><div class="t m1 x80 h8 yf5 ff3 fs1 fc0 sc0 ls1f wsd"> <span class="ff7 ls20">\ue047</span><span class="ls11"> </span></div><div class="t m4 x81 he yf5 ff8 fs5 fc0 sc0 ls11">\u03b2</div><div class="t m1 x4d h3 yf5 ff8 fs1 fc0 sc0 ls11 wsd"> <span class="ff3">então: </span></div><div class="t m1 x1 h8 yf6 ff3 fs1 fc0 sc0 ls11 wsd"> <span class="_25 blank"> </span> <span class="ff7 ws15">\ue048\ue049 \ue009 \ue049</span></div><div class="t m1 x82 h8 yf7 ff7 fs1 fc0 sc0 ls11">\ue018</div><div class="t m3 x3e h9 yf8 ff7 fs3 fc0 sc0 ls11">\ue04a</div><div class="t m1 x20 h8 yf6 ff7 fs1 fc0 sc0 ls11 ws6">\ue010 \ue049</div><div class="t m1 x7d h8 yf7 ff7 fs1 fc0 sc0 ls11">\ue018</div><div class="t m3 x83 h9 yf8 ff7 fs3 fc0 sc0 ls11">\ue04b</div><div class="t m1 x84 h8 yf6 ff3 fs1 fc0 sc0 lsd wsd"> e <span class="ff7 ls11 ws4">\ue048\ue014<span class="_6 blank"> </span>\ue009 \ue014</span></div><div class="t m1 x65 h8 yf9 ff7 fs1 fc0 sc0 ls11">\ue018</div><div class="t m3 x7f h9 yf8 ff7 fs3 fc0 sc0 ls11">\ue046</div><div class="t m1 x26 h8 yf6 ff7 fs1 fc0 sc0 ls11 ws6">\ue010 \ue014</div><div class="t m1 x68 h8 yf9 ff7 fs1 fc0 sc0 ls11">\ue018</div><div class="t m3 x85 h9 yf8 ff7 fs3 fc0 sc0 ls11">\ue045</div><div class="t m1 x86 h3 yf6 ff3 fs1 fc0 sc0 ls11 wsd"> </div><div class="t m1 x1 h3 yfa ff3 fs1 fc0 sc0 ls11 wsd"> <span class="_26 blank"> </span> </div><div class="t ma x2f h19 yfb ff7 fsa fc0 sc0 ls11 ws16">\ue02a\ue01c</div><div class="t ma x2f h19 yfc ff7 fsa fc0 sc0 ls11 ws16">\ue02a\ue01e</div><div class="t m2 x84 h1a yfa ff7 fs2 fc0 sc0 ls11">\ue009</div><div class="t ma x87 h19 yfb ff7 fsa fc0 sc0 ls11 ws16">\ue048\ue04c</div><div class="t ma x87 h19 yfc ff7 fsa fc0 sc0 ls11 ws16">\ue048\ue04d</div><div class="t m1 x88 h3 yfa ff3 fs1 fc0 sc0 lsd wsd"> ou <span class="_27 blank"> </span>(10) </div><div class="t m1 x1 h3 yfd ff3 fs1 fc0 sc0 ls11 wsd"> <span class="_28 blank"> </span> </div><div class="t ma x83 h19 yfe ff7 fsa fc0 sc0 ls11 ws16">\ue02a\ue01e</div><div class="t ma x83 h19 yff ff7 fsa fc0 sc0 ls11 ws16">\ue02a\ue01c</div><div class="t m2 x22 h1a yfd ff7 fs2 fc0 sc0 ls11">\ue009</div><div class="t ma x88 h19 yfe ff7 fsa fc0 sc0 ls11 ws16">\ue048\ue04e</div><div class="t ma x24 h19 yff ff7 fsa fc0 sc0 ls11 ws16">\ue048\ue04f</div><div class="t m1 x6e h3 yfd ff3 fs1 fc0 sc0 ls11 wsd"> <span class="_29 blank"> </span>(11) </div><div class="t m0 x6 h6 y100 ff3 fs0 fc0 sc0 ls11 wsd"> </div><div class="t m1 x6 h3 y101 ff3 fs1 fc0 sc0 ls11 wsd">A <span class="_2 blank"> </span>equação <span class="_f blank"> </span>de <span class="_2 blank"> </span>Clap<span class="_2 blank"> </span>eyron <span class="_2 blank"> </span>m<span class="_2 blank"> </span>ostra <span class="_2 blank"> </span>a <span class="_2 blank"> </span>dep<span class="_2 blank"> </span>endência <span class="_2 blank"> </span>d<span class="_2 blank"> </span>a <span class="_2 blank"> </span>temperatura <span class="_2 blank"> </span>de<span class="_2 blank"> </span> <span class="_2 blank"> </span>equilíbr<span class="_2 blank"> </span>io <span class="_2 blank"> </span>com <span class="_f blank"> </span>a <span class="_f blank"> </span>pressão, <span class="_2 blank"> </span>poi<span class="_2 blank"> </span>s </div><div class="t m1 x1 h3 y102 ff3 fs1 fc0 sc0 ls11 wsd">a <span class="_4 blank"> </span>posição<span class="_2 blank"> </span> <span class="_4 blank"> </span>do <span class="_18 blank"> </span>ponto <span class="_18 blank"> </span>de <span class="_18 blank"> </span>i<span class="_2 blank"> </span>nterseção <span class="_4 blank"> </span>das<span class="_2 blank"> </span> <span class="_4 blank"> </span>ret<span class="_2 blank"> </span>as <span class="_4 blank"> </span>repr<span class="_2 blank"> </span>esentativas <span class="_4 blank"> </span>d<span class="_2 blank"> </span>as <span class="_4 blank"> </span>duas<span class="_2 blank"> </span> <span class="_4 blank"> </span>fases <span class="_18 blank"> </span>depende <span class="_18 blank"> </span>da <span class="_18 blank"> </span>pressão <span class="_18 blank"> </span>ou <span class="_18 blank"> </span>a </div><div class="t m1 x1 h3 y103 ff3 fs1 fc0 sc0 ls11 wsd">variação da temperatura de equilíbrio com a temperatura. <span class="_2 blank"> </span> </div><div class="t m1 x6 h3 y104 ff3 fs1 fc0 sc0 ls11 wsd">Essa <span class="_2a blank"> </span>equação <span class="_1a blank"> </span>permite <span class="_2b blank"> </span>esquematizar <span class="_1a blank"> </span>o<span class="_2 blank"> </span> <span class="_1a blank"> </span>di<span class="_2 blank"> </span>agrama <span class="_1a blank"> </span>da <span class="_2a blank"> </span>pressão <span class="_2a blank"> </span>de <span class="_2a blank"> </span>equ<span class="_2 blank"> </span>ilíbrio <span class="_2a blank"> </span>em <span class="_2a blank"> </span>função <span class="_2a blank"> </span>da </div><div class="t m1 x1 h3 y105 ff3 fs1 fc0 sc0 ls11 wsd">temperatura para qualquer transformação de fase. </div><div class="t m1 x1 h5 y106 ff4 fs1 fc0 sc0 ls11 ws0">5.<span class="ff5 ls0 wsd"> </span><span class="wsd">EQUILÍBRIO SÓLIDO-LÍQUIDO </span></div><div class="t m1 x6 h3 y107 ff3 fs1 fc0 sc0 ls11 wsd">Aplicando a equação de Clapeyron à transformação sólido <span class="ff9 ls21">\ue002</span>l<span class="_2 blank"> </span>íquido, temos: </div><div class="t m1 x1 hc y108 ff3 fs1 fc0 sc0 ls22 wsd"> <span class="ff7 ls11 ws4">\ue048\ue011 \ue009 \ue011<span class="_2 blank"></span><span class="v3">\ue017</span></span></div><div class="t m3 x20 h9 y109 ff7 fs3 fc0 sc0 ls11 ws2">\ue00a\ue02c\ue02f\ue005\ue029\ue02a\ue02b</div><div class="t m1 x89 hc y108 ff7 fs1 fc0 sc0 ls11 ws6">\ue010 \ue011<span class="v3">\ue017</span></div><div class="t m3 x8a h9 y109 ff7 fs3 fc0 sc0 ls11 ws2">\ue028\ue023\ue00a\ue029\ue02a\ue02b</div><div class="t m1 x8b h8 y108 ff7 fs1 fc0 sc0 ls11 ws3">\ue009 \ue048\ue011</div><div class="t m3 x66 h9 y109 ff7 fs3 fc0 sc0 ls11 ws2">\ue050\ue005\ue028</div><div class="t m1 x49 h3 y108 ff3 fs1 fc0 sc0 ls11 wsd"> </div><div class="t m1 x1 h8 y10a ff3 fs1 fc0 sc0 ls23 wsd"> <span class="ff7 ls11 ws4">\ue048\ue014<span class="_6 blank"> </span>\ue009 \ue014</span></div><div class="t m1 x8c h8 y10b ff7 fs1 fc0 sc0 ls11">\ue018</div><div class="t m3 x20 h9 y10c ff7 fs3 fc0 sc0 ls11 ws2">\ue00a\ue02c\ue02f\ue005\ue029\ue02a\ue02b</div><div class="t m1 x89 h8 y10a ff7 fs1 fc0 sc0 ls11 ws6">\ue010 \ue014</div><div class="t m1 x8d h8 y10b ff7 fs1 fc0 sc0 ls11">\ue018</div><div class="t m3 x8a h9 y10c ff7 fs3 fc0 sc0 ls11 ws2">\ue028\ue023\ue00a\ue029\ue02a\ue02b</div><div class="t m1 x8b h8 y10a ff7 fs1 fc0 sc0 ls11 ws3">\ue009 \ue048\ue014</div><div class="t m3 x66 h9 y10c ff7 fs3 fc0 sc0 ls11 ws2">\ue050\ue005\ue028</div><div class="t m1 x49 h3 y10a ff3 fs1 fc0 sc0 ls11 wsd"> </div><div class="t m1 x6 h8 y10d ff3 fs1 fc0 sc0 ls11 wsd">Na temperatura de equilíbrio, a transformação é reversível, <span class="ff7 ws4">\ue048\ue00b<span class="_2c blank"> </span>\ue009 \ue03c</span>. </div><div class="t m1 x6 h8 y10e ff3 fs1 fc0 sc0 ls11 wsd">Assim: <span class="ff7 ws1">\ue048\ue011</span></div><div class="t m3 x8e h9 y10f ff7 fs3 fc0 sc0 ls11 ws2">\ue050\ue005\ue028</div><div class="t m1 x8f h8 y10e ff7 fs1 fc0 sc0 ls11 wsa">\ue009 \ue048\ue051</div><div class="t m3 x72 h9 y10f ff7 fs3 fc0 sc0 ls11 ws2">\ue050\ue005\ue028</div><div class="t m1 x90 h8 y10e ff7 fs1 fc0 sc0 ls11">\ue012</div><div class="t m1 x3a h8 y110 ff7 fs1 fc0 sc0 ls24">\ue00d<span class="ff3 ls25 wsd v1"> . </span></div><div class="t m1 x6 h8 y111 ff3 fs1 fc0 sc0 ls11 wsd">A transformação de sól<span class="_2 blank"> </span>ido para líquido <span class="_2 blank"> </span>envolve absorção de calor, <span class="_2 blank"> </span>logo <span class="ff7 ws1">\ue048\ue051</span></div><div class="t m3 x91 h9 y112 ff7 fs3 fc0 sc0 ls11 ws2">\ue050\ue005\ue028</div><div class="t m1 x2c h3 y111 ff3 fs1 fc0 sc0 ls11 wsd"> é sempre po<span class="_2 blank"> </span>sitivo, </div><div class="t m1 x1 h3 y113 ff3 fs1 fc0 sc0 ls11 wsd">então: </div><div class="t m1 x1 h8 y114 ff3 fs1 fc1 sc0 ls26 wsd"> <span class="ff7 fc0 ls11 ws1">\ue048\ue011</span></div><div class="t m3 x59 h9 y115 ff7 fs3 fc0 sc0 ls11 ws2">\ue050\ue005\ue028</div><div class="t m1 x4d h3 y114 ff3 fs1 fc0 sc0 ls11 wsd"> é positivo para todas as substâncias<span class="fc1"> </span></div><div class="t m1 x6 h3 y116 ff3 fs1 fc1 sc0 ls11 wsd"> </div><div class="t m1 x33 h3 y117 ff3 fs1 fc0 sc0 ls11 wsd">Equação de </div><div class="t m1 x2 h3 y118 ff3 fs1 fc0 sc0 ls11 wsd">Clapeyron </div></div><div class="pi" data-data='{"ctm":[1.000000,0.000000,0.000000,1.000000,0.000000,0.000000]}'></div></div> <div id="pf5" class="pf w0 h0" data-page-no="5"><div class="pc pc5 w0 h0"><img fetchpriority="low" loading="lazy" class="bi x0 y3a w1 hd" alt="" src="https://files.passeidireto.com/07bebfca-1ca3-4db1-8f6c-0a20e70e33d8/bg5.png"><div class="t m0 x1 h2 y3b ff1 fs0 fc0 sc0 ls11 wsd">Escola de Engenharia<span class="_0 blank"></span> de Lorena \u2013 EEL/USP <span class="_14 blank"> </span>Termodinâmica Q<span class="_0 blank"></span>uímica \u2013 Prof. Antonio Car<span class="_0 blank"></span>los da Silva </div><div class="t m0 x1 h6 y3c ff2 fs0 fc0 sc0 ls11 wsd"> </div><div class="t m0 x1 h2 y3d ff1 fs0 fc0 sc0 ls11 wsd">Equilíbrio de Fases em <span class="_0 blank"></span>Sistemas Simples <span class="_0 blank"></span>\u2013 A Regra das Fases <span class="_0 blank"></span> <span class="_15 blank"> </span>Página 5 </div><div class="t m1 x6 h8 y8e ff3 fs1 fc0 sc0 ls11 wsd">A <span class="_3 blank"> </span>quantidade <span class="_3 blank"> </span><span class="ff7 ws1">\ue048\ue014</span></div><div class="t m3 x2 h9 y119 ff7 fs3 fc0 sc0 ls11 ws2">\ue050\ue005\ue028\ue052\ue02b</div><div class="t m1 x78 h3 y8e ff3 fs1 fc0 sc0 ls11 wsd"> <span class="_3 blank"> </span>pode <span class="_3 blank"> </span>ser <span class="_3 blank"> </span>tanto <span class="_3 blank"> </span>posi<span class="_2 blank"> </span>tiva <span class="_3 blank"> </span>quando <span class="_f blank"> </span>n<span class="_2 blank"> </span>egativa, <span class="_3 blank"> </span>conforme <span class="_11 blank"> </span>a <span class="_f blank"> </span>d<span class="_2 blank"> </span>ensidade <span class="_f blank"> </span>do<span class="_2 blank"> </span> <span class="_3 blank"> </span>sólido </div><div class="t m1 x1 h3 y11a ff3 fs1 fc0 sc0 ls11 wsd">seja maior ou menor que a do líquido: </div><div class="t m1 x1 h8 y11b ff3 fs1 fc1 sc0 ls27 wsd"> <span class="ff7 fc0 ls11 ws1">\ue048\ue014</span></div><div class="t m3 x79 h9 y92 ff7 fs3 fc0 sc0 ls11 ws2">\ue050\ue005\ue028</div><div class="t m1 x1e h3 y11b ff3 fs1 fc0 sc0 ls11 wsd"> é positivo para a maioria das substâncias </div><div class="t m1 x1 h8 y11c ff3 fs1 fc1 sc0 ls28 wsd"> <span class="ff7 fc0 ls11 ws1">\ue048\ue014</span></div><div class="t m3 x92 h9 y11d ff7 fs3 fc0 sc0 ls11 ws2">\ue050\ue005\ue028</div><div class="t m1 x93 h3 y11c ff3 fs1 fc0 sc0 ls11 wsd"> é negativo para algumas substâncias (exemplo: água) </div><div class="t m1 x6 h3 y11e ff3 fs1 fc0 sc0 ls11 wsd">Ordinariamente, essas grandezas apresentam os seguintes valores: </div><div class="t m1 x1 h8 y11f ff3 fs1 fc1 sc0 ls29 wsd"> <span class="ff7 fc0 ls11 ws1">\ue048\ue011</span></div><div class="t m3 x94 h9 y120 ff7 fs3 fc0 sc0 ls11 ws2">\ue050\ue005\ue028</div><div class="t m1 x8 h3 y11f ff3 fs1 fc0 sc0 ls11 wsd"> = 8 a 25 J/(K.mol) </div><div class="t m1 x1 h8 y121 ff3 fs1 fc1 sc0 ls2a wsd"> <span class="ff7 fc0 ls11 ws1">\ue048\ue014</span></div><div class="t m3 x95 h9 y122 ff7 fs3 fc0 sc0 ls11 ws2">\ue050\ue005\ue028</div><div class="t m1 x2f h3 y121 ff3 fs1 fc0 sc0 ls11 wsd"> = +(1 a 10) cm</div><div class="t m0 x8b h6 y123 ff3 fs0 fc0 sc0 ls11">3</div><div class="t m1 x7a h3 y121 ff3 fs1 fc0 sc0 ls11 wsd">/mol </div><div class="t m1 x6 h8 y124 ff3 fs1 fc0 sc0 ls11 wsd">Como exemplo, suponha que <span class="ff7 ws1">\ue048\ue011</span></div><div class="t m3 x1f h9 y125 ff7 fs3 fc0 sc0 ls11 ws2">\ue050\ue005\ue028\ue052\ue02b</div><div class="t m1 x20 h8 y124 ff3 fs1 fc0 sc0 ls11 wsd"> = 16 J/(K.mol) e <span class="ff7 ws1">\ue048\ue014</span></div><div class="t m3 xf h9 y125 ff7 fs3 fc0 sc0 ls11 ws2">\ue050\ue005\ue028\ue052\ue02b</div><div class="t m1 x68 h3 y124 ff3 fs1 fc0 sc0 ls11 wsd"> = + 4 cm</div><div class="t m0 x96 h6 y126 ff3 fs0 fc0 sc0 ls11">3</div><div class="t m1 x97 h3 y124 ff3 fs1 fc0 sc0 ls11 wsd">/mol. Teremos: </div><div class="t m1 x1 h3 y127 ff3 fs1 fc1 sc0 ls11 wsd"> </div><div class="t m3 x98 h9 y128 ff7 fs3 fc0 sc0 ls11 ws2">\ue02a\ue01e</div><div class="t m3 x98 h9 y129 ff7 fs3 fc0 sc0 ls11 ws2">\ue02a\ue01c</div><div class="t m1 x1d h8 y127 ff7 fs1 fc0 sc0 ls11">\ue009</div><div class="t m3 x59 h9 y128 ff7 fs3 fc0 sc0 ls11 ws2">\ue053\ue054\ue055\ue056\ue036\ue01f\ue057\ue058\ue059\ue05a\ue05b\ue021</div><div class="t m3 x79 h1b y129 ff7 fs3 fc0 sc0 ls11 ws2">\ue05c\ue055\ue05d<span class="v2">\ue01f</span>\ue053\ue05e<span class="fs4 ws17 v3">\ue05f\ue060 </span><span class="v2">\ue021</span>\ue055\ue059<span class="fs4 ls2b v3">\ue061</span>\ue036\ue059\ue05a\ue05b</div><div class="t m1 x21 hb y127 ff7 fs1 fc0 sc0 ls11 ws4">\ue009 \ue05c\ue062<span class="lsb v2">\ue01f</span><span class="ws1">\ue03b\ue03c</span></div><div class="t m3 x99 h9 y12a ff7 fs3 fc0 sc0 ls11">\ue054</div><div class="t m1 x9a h8 y12b ff7 fs1 fc0 sc0 lsb">\ue021<span class="ls11 ws18 v1">\ue063\ue064\ue036\ue065 \ue009 \ue05c\ue055\ue062\ue03c\ue055\ue064\ue066\ue067\ue036\ue065<span class="ff3 wsd"> </span></span></div><div class="t m1 x6 h8 y12c ff3 fs1 fc0 sc0 ls11 wsd">Inversamente, <span class="_f blank"> </span><span class="ff7 ws1">\ue00f\ue012<span class="_2 blank"> </span>\ue036\ue00f\ue037</span> <span class="_f blank"> </span>= <span class="_f blank"> </span><span class="ff7 ls2c">\ue05c</span>0,02 <span class="_3 blank"> </span>K/atm. <span class="_f blank"> </span> <span class="_f blank"> </span>Este <span class="_f blank"> </span>valor <span class="_f blank"> </span>mostra <span class="_f blank"> </span>que <span class="_f blank"> </span>uma <span class="_f blank"> </span>variação <span class="_f blank"> </span>de <span class="_f blank"> </span>1 <span class="_f blank"> </span>atm <span class="_f blank"> </span>na <span class="_f blank"> </span>pressão </div><div class="t m1 x1 h3 y12d ff3 fs1 fc0 sc0 ls11 wsd">causa <span class="_18 blank"> </span>um<span class="_2 blank"> </span>a <span class="_16 blank"> </span>alteração <span class="_16 blank"> </span>de <span class="_16 blank"> </span>alguns <span class="_16 blank"> </span>centésimos <span class="_16 blank"> </span>de <span class="_16 blank"> </span>Kelvin<span class="_2 blank"> </span> <span class="_18 blank"> </span>no<span class="_2 blank"> </span> <span class="_18 blank"> </span>pon<span class="_2 blank"> </span>to <span class="_16 blank"> </span>de <span class="_16 blank"> </span>fusão. <span class="_16 blank"> </span> <span class="_16 blank"> </span>O <span class="_16 blank"> </span>coeficiente <span class="_16 blank"> </span>angular <span class="_16 blank"> </span>é </div><div class="t m1 x1 h8 y12e ff3 fs1 fc0 sc0 ls11 wsd">elevado e a curva é quase vertical. Se <span class="ff7 ws1">\ue00f\ue037<span class="_2 blank"></span>\ue036\ue00f\ue012<span class="_2 blank"></span></span> for positivo, a representação gráfica é a seguinte: </div><div class="t m0 x6 h6 y12f ff3 fs0 fc0 sc0 ls11 wsd"> </div><div class="t m1 x6 h3 y130 ff3 fs1 fc0 sc0 ls11 wsd"> </div><div class="t m1 x6 h3 y131 ff3 fs1 fc0 sc0 ls11 wsd"> </div><div class="t m1 x6 h3 y132 ff3 fs1 fc0 sc0 ls11 wsd"> </div><div class="t m1 x6 h3 y133 ff3 fs1 fc0 sc0 ls11 wsd"> </div><div class="t m1 x6 h3 y134 ff3 fs1 fc0 sc0 ls11 wsd"> </div><div class="t m1 x54 h3 y135 ff3 fs1 fc0 sc0 ls11 wsd"> </div><div class="t m1 x9b h3 y136 ff3 fs1 fc0 sc0 ls11 wsd">Figura 5 \u2013 Linha de equilíbrio Sólido-Líquido </div><div class="t m1 x1 h5 y137 ff4 fs1 fc0 sc0 ls11 ws0">6.<span class="ff5 ls0 wsd"> </span><span class="wsd">EQUILÍBRIO LÍQUIDO-GÁS </span></div><div class="t m1 x6 h3 y138 ff3 fs1 fc0 sc0 ls11 wsd">Aplicando a equação de Clapeyron à transformação líquido <span class="ff9 ls21">\ue002</span>gás, temos:<span class="_2 blank"> </span> </div><div class="t m1 x1 hc y139 ff3 fs1 fc0 sc0 ls2d wsd"> <span class="ff7 ls11 wsa">\ue048\ue011 \ue009 \ue011<span class="_2 blank"></span><span class="v3">\ue017</span></span></div><div class="t m3 x17 h9 y13a ff7 fs3 fc0 sc0 ls11 ws2">\ue004\ue003\ue028</div><div class="t m1 x20 hc y139 ff7 fs1 fc0 sc0 ls11 ws19">\ue010 \ue011<span class="v3">\ue017</span></div><div class="t m3 x7e h9 y13a ff7 fs3 fc0 sc0 ls11 ws2">\ue00a\ue02c\ue02f\ue005\ue029\ue02a\ue02b</div><div class="t m1 x24 h8 y139 ff7 fs1 fc0 sc0 ls11 ws4">\ue009 \ue048\ue011</div><div class="t m3 x9c h9 y13a ff7 fs3 fc0 sc0 ls11 ws2">\ue008\ue006\ue01e</div><div class="t m1 x65 h8 y139 ff7 fs1 fc0 sc0 ls11">\ue009</div><div class="t m3 x26 h9 y13b ff7 fs3 fc0 sc0 ls11 ws2">\ue048\ue068</div><div class="t m3 x49 h1c y13c ff7 fs4 fc0 sc0 ls11 ws9">\ue069\ue06a\ue06b</div><div class="t m3 x49 h9 y13d ff7 fs3 fc0 sc0 ls11">\ue01c</div><div class="t m1 x27 h3 y139 ff3 fs1 fc0 sc0 ls11 wsd"> </div><div class="t m1 x1 h8 y13e ff3 fs1 fc0 sc0 ls2e wsd"> <span class="ff7 ls11 ws4">\ue048\ue014<span class="_6 blank"> </span>\ue009 \ue014</span></div><div class="t m1 x40 h8 y13f ff7 fs1 fc0 sc0 ls11">\ue018</div><div class="t m3 x2f h9 y140 ff7 fs3 fc0 sc0 ls11 ws2">\ue004\ue003\ue028</div><div class="t m1 x3b h8 y13e ff7 fs1 fc0 sc0 ls11 ws6">\ue010 \ue014</div><div class="t m1 xa h8 y13f ff7 fs1 fc0 sc0 ls11">\ue018</div><div class="t m3 x87 h9 y140 ff7 fs3 fc0 sc0 ls11 ws2">\ue00a\ue02c\ue02f\ue005\ue029\ue02a\ue02b</div><div class="t m1 x9d h8 y13e ff7 fs1 fc0 sc0 ls11 ws3">\ue009 \ue048\ue014</div><div class="t m3 x65 h9 y140 ff7 fs3 fc0 sc0 ls11 ws2">\ue008\ue006\ue01e</div><div class="t m1 x14 h3 y13e ff3 fs1 fc0 sc0 ls11 wsd"> </div><div class="t m1 x1 h8 y141 ff3 fs1 fc1 sc0 ls2f wsd"> <span class="ff7 fc0 ls11 ws1">\ue048\ue011</span></div><div class="t m3 x59 h9 y142 ff7 fs3 fc0 sc0 ls11 ws2">\ue008\ue006\ue01e</div><div class="t m1 x5f h3 y141 ff3 fs1 fc0 sc0 ls11 wsd"> é positivo para todas as substâncias<span class="fc1"> </span></div><div class="t m1 x1 h8 y143 ff3 fs1 fc1 sc0 ls30 wsd"> <span class="ff7 fc0 ls11 ws1">\ue048\ue014</span></div><div class="t m3 x59 h9 y144 ff7 fs3 fc0 sc0 ls11 ws2">\ue008\ue006\ue01e</div><div class="t m1 x4d h3 y143 ff3 fs1 fc0 sc0 ls11 wsd"> é positivo para todas as substâncias </div><div class="t m1 x1 h8 y145 ff3 fs1 fc0 sc0 ls31 wsd"> <span class="ff7 ls11 ws1">\ue00f\ue037\ue036\ue00f\ue012<span class="_2 blank"> </span></span><span class="ls11"> é positivo para todas as subst<span class="_2 blank"> </span>âncias<span class="fc1"> </span></span></div><div class="t m1 x6 h3 y146 ff3 fs1 fc0 sc0 ls11 wsd">Ordinariamente, essas grandezas apresentam os seguintes valores: </div><div class="t m1 x1 h8 y147 ff3 fs1 fc1 sc0 ls32 wsd"> <span class="ff7 fc0 ls11 ws1">\ue048\ue011</span></div><div class="t m3 x40 h9 y148 ff7 fs3 fc0 sc0 ls11 ws2">\ue008\ue006\ue01e</div><div class="t m1 x3b h8 y147 ff7 fs1 fc0 sc0 ls11 ws1">\ue06c<span class="ff3 wsd"> 90 J/(K.mol) </span></div><div class="t m1 x1 h8 y149 ff3 fs1 fc1 sc0 ls33 wsd"> <span class="ff7 fc0 ls11 ws1">\ue048\ue014</span></div><div class="t m3 x2e h9 y14a ff7 fs3 fc0 sc0 ls11 ws2">\ue050\ue005\ue028\ue052\ue02b</div><div class="t m1 x7d h3 y149 ff3 fs1 fc0 sc0 ls11 wsd"> = +20.000 cm</div><div class="t m0 x46 h6 y14b ff3 fs0 fc0 sc0 ls11">3</div><div class="t m1 x9e h3 y149 ff3 fs1 fc0 sc0 ls11 wsd">/mol </div><div class="t m1 x1 h3 y34 ff3 fs1 fc1 sc0 ls11 wsd"> </div><div class="t m3 x9b h9 y14c ff7 fs3 fc0 sc0 ls11 ws2">\ue02a\ue01e</div><div class="t m3 x9b h9 y14d ff7 fs3 fc0 sc0 ls11 ws2">\ue02a\ue01c</div><div class="t m1 x5b h8 y34 ff7 fs1 fc0 sc0 ls11">\ue009</div><div class="t m3 x81 h9 y14c ff7 fs3 fc0 sc0 ls11 ws2">\ue06d\ue05e\ue055\ue056\ue036\ue01f\ue057\ue058\ue059\ue05a\ue05b\ue021</div><div class="t m3 x81 h1d y14d ff7 fs3 fc0 sc0 ls11 ws2">\ue05e\ue03d\ue05e\ue06e\ue055\ue059<span class="fs4 ls2b v3">\ue061</span>\ue036\ue059\ue05a\ue05b</div><div class="t m1 x47 h8 y34 ff7 fs1 fc0 sc0 ls11 ws3">\ue009 \ue062\ue03c\ue03c\ue03c\ue055\ue063\ue064\ue036\ue065 \ue009 \ue03c\ue03d\ue03c\ue062\ue055\ue064\ue066\ue067\ue036\ue065<span class="ff3 wsd"> </span></div><div class="t m1 x6 h3 y14e ff3 fs1 fc0 sc0 ls11 wsd">A <span class="_2 blank"> </span>linha <span class="_f blank"> </span>representativa <span class="_2 blank"> </span>do<span class="_2 blank"> </span> <span class="_2 blank"> </span>equilíbrio <span class="_f blank"> </span>líquid<span class="_2 blank"> </span>o-gás <span class="_2 blank"> </span>possui, <span class="_f blank"> </span>sempre, <span class="_2 blank"> </span>um <span class="_f blank"> </span>coeficiente <span class="_2 blank"> </span>an<span class="_2 blank"> </span>gular <span class="_2 blank"> </span>positivo. </div><div class="t m1 x1 h3 y14f ff3 fs1 fc0 sc0 ls11 wsd">Entretanto, </div><div class="t m4 x9f he y14f ff8 fs5 fc0 sc0 ls11">\u2206</div><div class="t m1 x3 h3 y14f ff1 fs1 fc0 sc0 ls11 ws0">V<span class="ff3 wsd"> depende fortemente da </span><span class="ls9">T</span><span class="ff3 wsd"> e </span><span class="lsa">p</span><span class="ff3 wsd">, visto que o volum<span class="_2 blank"> </span>e do gás depende de </span><span class="ls9">T</span><span class="ff3 wsd"> e </span><span class="lsa">p</span><span class="ff3 wsd">. A inclinação </span></div><div class="t m1 x1 h3 y150 ff3 fs1 fc0 sc0 ls11 wsd">da curva líquido-gás é menor que a inclinação da curva sólido-líquido. </div><div class="t m1 x6 h3 y151 ff3 fs1 fc0 sc0 ls11 wsd"> </div><div class="t m1 x6 h3 y152 ff3 fs1 fc0 sc0 ls11 wsd"> </div><div class="t m1 x6 h3 y153 ff3 fs1 fc0 sc0 ls11 wsd"> </div><div class="t m1 x25 ha y154 ff1 fs1 fc0 sc0 ls11 wsd">T </div><div class="t m1 xa0 ha y155 ff1 fs1 fc0 sc0 ls11 wsd">p </div><div class="t m9 x89 h17 y156 ff1 fs9 fc0 sc0 ls11 wsd">s <span class="_2b blank"> </span><span class="v1">l</span></div><div class="c x8d y157 wf h1e"><div class="t m1 x4b ha y158 ff1 fs1 fc0 sc0 ls11 wsd"> </div></div></div><div class="pi" data-data='{"ctm":[1.000000,0.000000,0.000000,1.000000,0.000000,0.000000]}'></div></div> <div id="pf6" class="pf w0 h0" data-page-no="6"><div class="pc pc6 w0 h0"><img fetchpriority="low" loading="lazy" class="bi x0 y3a w1 hd" alt="" src="https://files.passeidireto.com/07bebfca-1ca3-4db1-8f6c-0a20e70e33d8/bg6.png"><div class="t m0 x1 h2 y3b ff1 fs0 fc0 sc0 ls11 wsd">Escola de Engenharia<span class="_0 blank"></span> de Lorena \u2013 EEL/USP <span class="_14 blank"> </span>Termodinâmica Q<span class="_0 blank"></span>uímica \u2013 Prof. Antonio Car<span class="_0 blank"></span>los da Silva </div><div class="t m0 x1 h6 y3c ff2 fs0 fc0 sc0 ls11 wsd"> </div><div class="t m0 x1 h2 y3d ff1 fs0 fc0 sc0 ls11 wsd">Equilíbrio de Fases em <span class="_0 blank"></span>Sistemas Simples <span class="_0 blank"></span>\u2013 A Regra das Fases <span class="_0 blank"></span> <span class="_15 blank"> </span>Página 6 </div><div class="t m1 x6 h3 y3e ff3 fs1 fc0 sc0 ls11 wsd"> </div><div class="t m0 x6 h6 y159 ff3 fs0 fc0 sc0 ls11 wsd"> </div><div class="t m1 x6 h3 y15a ff3 fs1 fc0 sc0 ls11 wsd"> </div><div class="t m1 x6 h3 y15b ff3 fs1 fc0 sc0 ls11 wsd"> </div><div class="t m1 x6 h3 y15c ff3 fs1 fc0 sc0 ls11 wsd"> </div><div class="t m1 x6 h3 y15d ff3 fs1 fc0 sc0 ls11 wsd"> </div><div class="t m1 x54 h3 y15e ff3 fs1 fc0 sc0 ls11 wsd"> </div><div class="t m1 x56 h3 y15f ff3 fs1 fc0 sc0 ls11 wsd">Figura 6 \u2013 Linhas de equilíbrio Sólido<span class="_2 blank"> </span>-L<span class="_0 blank"></span>íquido e Líquido-Gás </div><div class="t m0 x6 h6 y160 ff3 fs0 fc0 sc0 ls11 wsd"> </div><div class="t m1 x6 h3 y161 ff3 fs1 fc0 sc0 ls11 wsd">Na <span class="_4 blank"> </span>Figura <span class="_11 blank"> </span>6, <span class="_4 blank"> </span>a <span class="_4 blank"> </span>linha <span class="_4 blank"> </span>l-<span class="_2 blank"> </span>g <span class="_4 blank"> </span>é <span class="_4 blank"> </span>o <span class="_4 blank"> </span>lugar <span class="_4 blank"> </span>ge<span class="_0 blank"></span>ométrico <span class="_4 blank"> </span>dos <span class="_4 blank"> </span>valores <span class="_4 blank"> </span>de <span class="_4 blank"> </span>pressão <span class="_4 blank"> </span>e <span class="_4 blank"> </span>temperatura <span class="_4 blank"> </span>em <span class="_4 blank"> </span>que <span class="_4 blank"> </span>o </div><div class="t m1 x1 h3 y162 ff3 fs1 fc0 sc0 ls11 wsd">líquido <span class="_3 blank"> </span>e <span class="_3 blank"> </span>o <span class="_3 blank"> </span>gás <span class="_f blank"> </span>coex<span class="_2 blank"> </span>istem <span class="_f blank"> </span>em <span class="_3 blank"> </span>equilíbrio. <span class="_3 blank"> </span> <span class="_3 blank"> </span>Os <span class="_3 blank"> </span>pontos <span class="_3 blank"> </span>imediatamente <span class="_3 blank"> </span>à <span class="_3 blank"> </span>esquerda <span class="_f blank"> </span>de <span class="_3 blank"> </span>l-<span class="_2 blank"> </span>g <span class="_f blank"> </span>estão <span class="_3 blank"> </span>abaix<span class="_2 blank"> </span>o <span class="_3 blank"> </span>do </div><div class="t m1 x1 h3 y163 ff3 fs1 fc0 sc0 ls11 wsd">ponto <span class="_f blank"> </span>de <span class="_3 blank"> </span>ebulição <span class="_f blank"> </span>e <span class="_3 blank"> </span>representam, <span class="_f blank"> </span>assim<span class="_2 blank"> </span>, <span class="_f blank"> </span>as <span class="_3 blank"> </span>condições <span class="_f blank"> </span>em <span class="_f blank"> </span>que <span class="_3 blank"> </span>o <span class="_3 blank"> </span>líquido <span class="_3 blank"> </span>é <span class="_f blank"> </span>estável. <span class="_f blank"> </span> <span class="_3 blank"> </span>Os <span class="_3 blank"> </span>pontos <span class="_f blank"> </span>à <span class="_3 blank"> </span>direita </div><div class="t m1 x1 h3 y164 ff3 fs1 fc0 sc0 ls11 wsd">de l-g representam as condições nas quais o gás é estável. </div><div class="t m1 x6 h3 y165 ff3 fs1 fc0 sc0 ls11 wsd">A <span class="_2 blank"> </span>interseção <span class="_f blank"> </span>das <span class="_f blank"> </span>curvas <span class="_f blank"> </span>s-l <span class="_f blank"> </span>e <span class="_2 blank"> </span>l-<span class="_2 blank"> </span>g <span class="_2 blank"> </span>correspondem <span class="_f blank"> </span>à <span class="_f blank"> </span>temperatura <span class="_f blank"> </span>e <span class="_2 blank"> </span>p<span class="_2 blank"> </span>ressão <span class="_f blank"> </span>em <span class="_f blank"> </span>que <span class="_2 blank"> </span>o <span class="_f blank"> </span>sólido, <span class="_f blank"> </span>líquido </div><div class="t m1 x1 h5 y166 ff3 fs1 fc0 sc0 ls11 wsd">e gás coexistem, todos, em equilíbrio <span class="ff9 ls34">\ue003</span><span class="ls10"> </span><span class="ff4">ponto triplo</span>. </div><div class="t m1 x1 h5 y167 ff4 fs1 fc0 sc0 ls11 ws0">7.<span class="ff5 ls0 wsd"> </span><span class="wsd">EQUILÍBRIO SÓLIDO-GÁS </span></div><div class="t m1 x6 h3 y168 ff3 fs1 fc0 sc0 ls11 wsd">Aplicando a equação de Clapeyron à transformação sólido <span class="ff9 ls21">\ue002</span>gás, temos:<span class="_2 blank"> </span> </div><div class="t m1 x1 hc y50 ff3 fs1 fc0 sc0 ls35 wsd"> <span class="ff7 ls11 wsa">\ue048\ue011 \ue009 \ue011<span class="_2 blank"></span><span class="v3">\ue017</span></span></div><div class="t m3 x82 h9 y169 ff7 fs3 fc0 sc0 ls11 ws2">\ue004\ue003\ue028</div><div class="t m1 x2f hc y50 ff7 fs1 fc0 sc0 ls11 ws19">\ue010 \ue011<span class="v3">\ue017</span></div><div class="t m3 xa1 h9 y169 ff7 fs3 fc0 sc0 ls11 ws2">\ue028\ue023\ue00a\ue029\ue02a\ue02b</div><div class="t m1 x8a h8 y50 ff7 fs1 fc0 sc0 ls11 ws4">\ue009 \ue048\ue011</div><div class="t m3 x45 h9 y169 ff7 fs3 fc0 sc0 ls11 ws2">\ue028\ue005\ue06f</div><div class="t m1 xa2 h8 y50 ff7 fs1 fc0 sc0 ls11">\ue009</div><div class="t m3 x4a h9 y16a ff7 fs3 fc0 sc0 ls11 ws2">\ue048\ue068<span class="fs4 ws9 v5">\ue022\ue02e\ue041</span></div><div class="t m3 x4c h9 y16b ff7 fs3 fc0 sc0 ls11">\ue01c</div><div class="t m1 xa3 h3 y50 ff3 fs1 fc0 sc0 ls11 wsd"> </div><div class="t m1 x1 h8 y16c ff3 fs1 fc0 sc0 ls36 wsd"> <span class="ff7 ls11 ws4">\ue048\ue014<span class="_6 blank"> </span>\ue009 \ue014</span></div><div class="t m1 x2f h8 y16d ff7 fs1 fc0 sc0 ls11">\ue018</div><div class="t m3 xa4 h9 y16e ff7 fs3 fc0 sc0 ls11 ws2">\ue004\ue003\ue028</div><div class="t m1 x30 h8 y16c ff7 fs1 fc0 sc0 ls11 ws6">\ue010 \ue014</div><div class="t m1 x22 h8 y16d ff7 fs1 fc0 sc0 ls11">\ue018</div><div class="t m3 x54 h9 y16e ff7 fs3 fc0 sc0 ls11 ws2">\ue028\ue023\ue00a\ue029\ue02a\ue02b</div><div class="t m1 x11 h8 y16c ff7 fs1 fc0 sc0 ls11 ws4">\ue009 \ue048\ue014</div><div class="t m3 x65 h9 y16e ff7 fs3 fc0 sc0 ls11 ws2">\ue028\ue005\ue06f</div><div class="t m1 x48 h3 y16c ff3 fs1 fc0 sc0 ls11 wsd"> </div><div class="t m1 x1 h8 y16f ff3 fs1 fc1 sc0 ls2f wsd"> <span class="ff7 fc0 ls11 ws1">\ue048\ue011</span></div><div class="t m3 x59 h9 y170 ff7 fs3 fc0 sc0 ls11 ws2">\ue008\ue006\ue01e</div><div class="t m1 x5f h3 y16f ff3 fs1 fc0 sc0 ls11 wsd"> é positivo para todas as substâncias<span class="fc1"> </span></div><div class="t m1 x1 h8 y171 ff3 fs1 fc1 sc0 ls30 wsd"> <span class="ff7 fc0 ls11 ws1">\ue048\ue014</span></div><div class="t m3 x59 h9 y172 ff7 fs3 fc0 sc0 ls11 ws2">\ue008\ue006\ue01e</div><div class="t m1 x4d h3 y171 ff3 fs1 fc0 sc0 ls11 wsd"> é positivo para todas as substâncias </div><div class="t m1 x1 h8 y173 ff3 fs1 fc0 sc0 ls31 wsd"> <span class="ff7 ls11 ws1">\ue00f\ue037\ue036\ue00f\ue012<span class="_2 blank"> </span></span><span class="ls11"> é positivo para todas as subst<span class="_2 blank"> </span>âncias<span class="fc1"> </span></span></div><div class="t m1 x6 h3 y174 ff3 fs1 fc0 sc0 ls11 wsd">A inclinação da curva s-g é mais pronunciada no ponto t<span class="_2 blank"> </span>riplo que a curva l-g. No ponto triplo, </div><div class="t m1 x1 h8 y175 ff3 fs1 fc0 sc0 ls37 wsd"> <span class="ff7 ls11 ws1">\ue048\ue051</span></div><div class="t m3 x8c h9 y176 ff7 fs3 fc0 sc0 ls11 ws2">\ue028\ue005\ue06f</div><div class="t m1 x21 h8 y175 ff7 fs1 fc0 sc0 ls11 ws4">\ue009 \ue048\ue051</div><div class="t m3 x54 h9 y176 ff7 fs3 fc0 sc0 ls11 ws2">\ue008\ue006\ue01e</div><div class="t m1 x99 h8 y175 ff7 fs1 fc0 sc0 ls11 ws6">\ue013 \ue048\ue051</div><div class="t m3 x9e h9 y176 ff7 fs3 fc0 sc0 ls11 ws2">\ue050\ue005\ue028</div><div class="t m1 x12 h3 y175 ff3 fs1 fc0 sc0 ls11 wsd"> </div><div class="t m1 x6 h8 y177 ff3 fs1 fc0 sc0 ls11 ws0">Como<span class="fc1 ls38 wsd"> </span><span class="ff7 ws1">\ue048\ue051</span></div><div class="t m3 xa5 h9 y178 ff7 fs3 fc0 sc0 ls11 ws2">\ue028\ue005\ue06f</div><div class="t m1 xa6 h8 y177 ff3 fs1 fc0 sc0 ls11 wsd"> <span class="_2 blank"> </span>é <span class="_f blank"> </span>maior <span class="_2 blank"> </span>qu<span class="_2 blank"> </span>e <span class="_f blank"> </span><span class="ff7 ws1">\ue048\ue051</span></div><div class="t m3 x4d h9 y178 ff7 fs3 fc0 sc0 ls11 ws2">\ue008\ue006\ue01e</div><div class="t m1 xa0 h3 y177 ff3 fs1 fc0 sc0 ls11 wsd">, <span class="_2 blank"> </span>a <span class="_f blank"> </span>inclinação <span class="_f blank"> </span>da <span class="_f blank"> </span>curva <span class="_f blank"> </span>s-g <span class="_f blank"> </span>é <span class="_f blank"> </span>mais <span class="_f blank"> </span>pronunciada <span class="_2 blank"> </span>que<span class="_2 blank"> </span> <span class="_2 blank"> </span>a <span class="_f blank"> </span>inclinação<span class="_2 blank"> </span> </div><div class="t m1 x1 h3 y179 ff3 fs1 fc0 sc0 ls11 wsd">da curva l-g. </div><div class="t m1 x1 h8 y17a ff3 fs1 fc0 sc0 ls39 wsd"> <span class="ff7 ls11">\ue019</span></div><div class="t m3 x5b h9 y17b ff7 fs3 fc0 sc0 ls11 ws2">\ue02a\ue01e</div><div class="t m3 x5b h9 y17c ff7 fs3 fc0 sc0 ls11 ws2">\ue02a\ue01c</div><div class="t m1 x81 h8 y17a ff7 fs1 fc0 sc0 ls11">\ue01d</div><div class="t m3 xa7 h9 y17d ff7 fs3 fc0 sc0 ls11 ws1a">\ue00a\ue042 \ue004</div><div class="t m1 xa0 h8 y17a ff7 fs1 fc0 sc0 ls11">\ue009</div><div class="t m3 x94 h9 y26 ff7 fs3 fc0 sc0 ls11 ws2">\ue048\ue068</div><div class="t m3 x2f h1c y17e ff7 fs4 fc0 sc0 ls11 ws9">\ue069\ue06a\ue06b</div><div class="t m3 x3f h9 y17c ff7 fs3 fc0 sc0 ls11 ws1b">\ue01c \ue048\ue04c</div><div class="t m1 x7e h8 y17a ff3 fs1 fc0 sc0 lsd wsd"> e <span class="ff7 ls11">\ue019</span></div><div class="t m3 xc h9 y17b ff7 fs3 fc0 sc0 ls11 ws2">\ue02a\ue01e</div><div class="t m3 xc h9 y17c ff7 fs3 fc0 sc0 ls11 ws2">\ue02a\ue01c</div><div class="t m1 x25 h8 y17a ff7 fs1 fc0 sc0 ls11">\ue01d</div><div class="t m3 x9e h9 y17d ff7 fs3 fc0 sc0 ls11 ws2">\ue028\ue042\ue004</div><div class="t m1 x4a h8 y17a ff7 fs1 fc0 sc0 ls11">\ue009</div><div class="t m3 x49 h9 y17b ff7 fs3 fc0 sc0 ls11 ws2">\ue048\ue068<span class="fs4 ws9 v5">\ue022\ue02e\ue041</span></div><div class="t m3 x68 h9 y17c ff7 fs3 fc0 sc0 ls11 ws2">\ue01c\ue048\ue04c</div><div class="t m1 xa8 h3 y17a ff3 fs1 fc0 sc0 ls11 wsd"> </div><div class="t m1 x6 h3 y17f ff3 fs1 fc0 sc0 ls11 wsd"> </div><div class="t m0 x6 h6 y180 ff3 fs0 fc0 sc0 ls11 wsd"> </div><div class="t m1 x6 h3 y181 ff3 fs1 fc0 sc0 ls11 wsd"> </div><div class="t m1 x6 h3 y182 ff3 fs1 fc0 sc0 ls11 wsd"> </div><div class="t m1 x6 h3 y183 ff3 fs1 fc0 sc0 ls11 wsd"> </div><div class="t m1 x6 h3 y184 ff3 fs1 fc0 sc0 ls11 wsd"> </div><div class="t m1 x6 h3 y185 ff3 fs1 fc0 sc0 ls11 wsd"> </div><div class="t m1 x6 h3 y186 ff3 fs1 fc0 sc0 ls11 wsd"> </div><div class="t m1 x6 h3 y187 ff3 fs1 fc0 sc0 ls11 wsd"> </div><div class="t m1 x54 h3 y188 ff3 fs1 fc0 sc0 ls11 wsd"> </div><div class="t m1 x2 h3 y189 ff3 fs1 fc0 sc0 ls11 wsd">Figura 7 \u2013 Diagrama de fase para uma substância simp<span class="_2 blank"> </span>les </div><div class="t m1 x45 ha y18a ff1 fs1 fc0 sc0 ls11 wsd">T </div><div class="t m1 x5c ha y18b ff1 fs1 fc0 sc0 ls11 wsd">p </div><div class="t m9 xa9 h17 y18c ff1 fs9 fc0 sc0 ls11 wsd">s <span class="_2b blank"> </span><span class="v1">l <span class="_2d blank"> </span>l <span class="_5 blank"> </span>g </span></div><div class="t m1 x70 ha y18d ff1 fs1 fc0 sc0 ls11 wsd">T </div><div class="t m1 xaa ha y18e ff1 fs1 fc0 sc0 ls11 wsd">p </div><div class="t ma xa0 h1f y18f ff1 fsb fc0 sc0 ls11 wsd">Sólido </div><div class="t ma x87 h1f y190 ff1 fsb fc0 sc0 ls11 wsd">Líquido </div><div class="t ma x8b h1f y191 ff1 fsb fc0 sc0 ls11 wsd">Gás </div><div class="t m9 x3b h17 y192 ff1 fs9 fc0 sc0 ls11">T</div><div class="t ma x76 h20 y193 ff1 fsc fc0 sc0 ls11 wsd">f </div><div class="t m9 x61 h17 y192 ff1 fs9 fc0 sc0 ls11">T</div><div class="t ma xc h20 y193 ff1 fsc fc0 sc0 ls11 wsd">eb </div></div><div class="pi" data-data='{"ctm":[1.000000,0.000000,0.000000,1.000000,0.000000,0.000000]}'></div></div> <div id="pf7" class="pf w0 h0" data-page-no="7"><div class="pc pc7 w0 h0"><img fetchpriority="low" loading="lazy" class="bi x0 y3a w1 hd" alt="" src="https://files.passeidireto.com/07bebfca-1ca3-4db1-8f6c-0a20e70e33d8/bg7.png"><div class="t m0 x1 h2 y3b ff1 fs0 fc0 sc0 ls11 wsd">Escola de Engenharia<span class="_0 blank"></span> de Lorena \u2013 EEL/USP <span class="_14 blank"> </span>Termodinâmica Q<span class="_0 blank"></span>uímica \u2013 Prof. Antonio Car<span class="_0 blank"></span>los da Silva </div><div class="t m0 x1 h6 y3c ff2 fs0 fc0 sc0 ls11 wsd"> </div><div class="t m0 x1 h2 y3d ff1 fs0 fc0 sc0 ls11 wsd">Equilíbrio de Fases em <span class="_0 blank"></span>Sistemas Simples <span class="_0 blank"></span>\u2013 A Regra das Fases <span class="_0 blank"></span> <span class="_15 blank"> </span>Página 7 </div><div class="t m1 x1 h5 y8e ff4 fs1 fc0 sc0 ls11 ws0">8.<span class="ff5 ls0 wsd"> </span><span class="wsd">DIAGRAMA DE FASE </span></div><div class="t m1 x6 h5 y194 ff4 fs1 fc0 sc0 ls11 wsd">O Diagrama de Fase do CO</div><div class="t m0 xa7 h21 y195 ff4 fs0 fc0 sc0 ls11">2</div><div class="t m1 x4e h5 y194 ff4 fs1 fc0 sc0 ls11 wsd"> </div><div class="t m1 x6 h3 yde ff3 fs1 fc0 sc0 ls11 wsd"> </div><div class="t m1 x1 h5 y196 ff4 fs1 fc0 sc0 ls11 wsd"> </div><div class="t m1 x1 h5 y197 ff4 fs1 fc0 sc0 ls11 wsd"> </div><div class="t m1 x1 h5 y198 ff4 fs1 fc0 sc0 ls11 wsd"> </div><div class="t m1 x1 h5 y199 ff4 fs1 fc0 sc0 ls11 wsd"> </div><div class="t m1 x1 h5 y19a ff4 fs1 fc0 sc0 ls11 wsd"> </div><div class="t m1 x1 h5 y19b ff4 fs1 fc0 sc0 ls11 wsd"> </div><div class="t m1 x1 h5 y19c ff4 fs1 fc0 sc0 ls3a wsd"> <span class="ff3 ls11 v6">Figura 8 \u2013 Diagrama de fase para o CO</span></div><div class="t m0 x86 h6 y19d ff3 fs0 fc0 sc0 ls11 wsd">2 </div><div class="t m1 x6 h3 y19e ff3 fs1 fc0 sc0 ls11 wsd"> </div><div class="t m1 x6 h8 y19f ff3 fs1 fc0 sc0 ls11 wsd">A <span class="_3 blank"> </span>linha <span class="_11 blank"> </span>sólido-líquido <span class="_3 blank"> </span>inclina-se <span class="_11 blank"> </span>ligeiramente <span class="_3 blank"> </span>par<span class="_2 blank"> </span>a <span class="_3 blank"> </span>a <span class="_11 blank"> </span>direita, <span class="_3 blank"> </span>pois <span class="_11 blank"> </span><span class="ff7">\ue014</span></div><div class="t m1 xab h8 y1a0 ff7 fs1 fc0 sc0 ls11">\ue018</div><div class="t m3 xac h9 y1a1 ff7 fs3 fc0 sc0 ls11 ws2">\ue00a\ue02c\ue02f</div><div class="t m1 x6a h8 y19f ff7 fs1 fc0 sc0 ls11 wsc">\ue032 \ue014</div><div class="t m1 xad h8 y1a0 ff7 fs1 fc0 sc0 ls11">\ue018</div><div class="t m3 x91 h9 y1a1 ff7 fs3 fc0 sc0 ls11 ws2">\ue028\ue023\ue00a</div><div class="t m1 x6d h3 y19f ff3 fs1 fc0 sc0 ls11 wsd"> <span class="_3 blank"> </span>. <span class="_11 blank"> </span>Nota-se <span class="_3 blank"> </span>que <span class="_11 blank"> </span>CO</div><div class="t m0 xae h6 y1a2 ff3 fs0 fc0 sc0 ls11">2</div><div class="t m1 xaf h3 y19f ff3 fs1 fc0 sc0 ls11 wsd"> </div><div class="t m1 x1 h3 y1a3 ff3 fs1 fc0 sc0 ls11 wsd">líquido <span class="_f blank"> </span>não <span class="_f blank"> </span>é <span class="_f blank"> </span>estável <span class="_f blank"> </span>a <span class="_f blank"> </span>p<span class="_2 blank"> </span>ressões <span class="_f blank"> </span>inferiores <span class="_f blank"> </span>a <span class="_f blank"> </span>5 <span class="_3 blank"> </span>atm. <span class="_f blank"> </span> <span class="_f blank"> </span>Po<span class="_2 blank"> </span>r <span class="_2 blank"> </span>esta <span class="_f blank"> </span>r<span class="_2 blank"> </span>azão, <span class="_f blank"> </span>o <span class="_f blank"> </span>\u201cgelo<span class="_2 blank"> </span> <span class="_2 blank"> </span>s<span class="_2 blank"> </span>eco\u201d <span class="_2 blank"> </span>perman<span class="_2 blank"> </span>ece <span class="_2 blank"> </span>s<span class="_2 blank"> </span>eco <span class="_f blank"> </span>sob </div><div class="t m1 x1 h3 y1a4 ff3 fs1 fc0 sc0 ls11 wsd">as <span class="_18 blank"> </span>pressões <span class="_18 blank"> </span>atmosféricas <span class="_16 blank"> </span>ordinárias. <span class="_18 blank"> </span> <span class="_18 blank"> </span>Quando <span class="_16 blank"> </span>se <span class="_18 blank"> </span>confina <span class="_18 blank"> </span>o <span class="_18 blank"> </span>di<span class="_2 blank"> </span>óxido <span class="_18 blank"> </span>de <span class="_18 blank"> </span>c<span class="_2 blank"> </span>arbono <span class="_18 blank"> </span>sob <span class="_18 blank"> </span>pressão <span class="_18 blank"> </span>em <span class="_16 blank"> </span>um </div><div class="t m1 x1 h3 y1a5 ff3 fs1 fc0 sc0 ls11 wsd">cilindro <span class="_3 blank"> </span>a <span class="_3 blank"> </span>25ºC, <span class="_3 blank"> </span>o <span class="_3 blank"> </span>diagram<span class="_2 blank"> </span>a <span class="_f blank"> </span>most<span class="_2 blank"> </span>ra <span class="_f blank"> </span>que,<span class="_2 blank"> </span> <span class="_f blank"> </span>a <span class="_3 blank"> </span>67 <span class="_11 blank"> </span>atm, <span class="_3 blank"> </span>forma-se <span class="_3 blank"> </span>CO</div><div class="t m0 x4a h6 y1a6 ff3 fs0 fc0 sc0 ls11">2</div><div class="t m1 x26 h3 y1a5 ff3 fs1 fc0 sc0 ls11 wsd"> <span class="_3 blank"> </span>líquido. <span class="_3 blank"> </span> <span class="_3 blank"> </span>Os <span class="_3 blank"> </span>cilindros <span class="_3 blank"> </span>comerciais <span class="_11 blank"> </span>de </div><div class="t m1 x1 h3 y1a7 ff3 fs1 fc0 sc0 ls11 ws0">CO</div><div class="t m0 xb0 h6 y1a8 ff3 fs0 fc0 sc0 ls11">2</div><div class="t m1 x16 h3 y1a7 ff3 fs1 fc0 sc0 ls11 wsd"> <span class="_3 blank"> </span>contêm <span class="_3 blank"> </span>comumente <span class="_f blank"> </span>líquido <span class="_3 blank"> </span>e <span class="_3 blank"> </span>gás <span class="_f blank"> </span>em <span class="_3 blank"> </span>equilí<span class="_2 blank"> </span>brio; <span class="_3 blank"> </span>a <span class="_f blank"> </span>pressão <span class="_3 blank"> </span>no <span class="_3 blank"> </span>cilindro <span class="_3 blank"> </span>está <span class="_3 blank"> </span>em <span class="_3 blank"> </span>torno <span class="_3 blank"> </span>de <span class="_3 blank"> </span>67 <span class="_3 blank"> </span>atm <span class="_3 blank"> </span>a </div><div class="t m1 x1 h3 y1a9 ff3 fs1 fc0 sc0 ls11 wsd">25ºC. </div><div class="t m1 x1 h5 y1aa ff4 fs1 fc0 sc0 ls11 wsd"> </div><div class="t m1 x6 h5 y1ab ff4 fs1 fc0 sc0 ls11 wsd">O Diagrama de Fase da Água </div><div class="t m1 x6 h3 y1ac ff3 fs1 fc0 sc0 ls11 wsd"> </div><div class="t m1 x6 h3 y1ad ff3 fs1 fc0 sc0 ls11 wsd"> </div><div class="t m1 x6 h3 y1ae ff3 fs1 fc0 sc0 ls11 wsd"> </div><div class="t m1 x6 h3 y1af ff3 fs1 fc0 sc0 ls11 wsd"> </div><div class="t m1 x6 h3 y1b0 ff3 fs1 fc0 sc0 ls11 wsd"> </div><div class="t m1 x6 h3 y1b1 ff3 fs1 fc0 sc0 ls11 wsd"> </div><div class="t m1 x6 h3 y1b2 ff3 fs1 fc0 sc0 ls11 wsd"> </div><div class="t m1 x6 h3 y1b3 ff3 fs1 fc0 sc0 ls11 wsd"> </div><div class="t m1 x6 h3 y1b4 ff3 fs1 fc0 sc0 ls11 wsd"> </div><div class="t m1 x6 h3 y1b5 ff3 fs1 fc0 sc0 ls11 wsd"> </div><div class="t m1 xb1 h3 y1b6 ff3 fs1 fc0 sc0 ls11 ws0">(a)<span class="ff2 ls3b wsd"> <span class="ff3 lsd"> (b) </span></span></div><div class="t m1 x6 h3 y1b7 ff3 fs1 fc0 sc0 ls11 wsd">Figura 9 \u2013 (a) Diagrama de fase da Água; (b) Diagrama de fase para a água a pressões altas</div><div class="t m0 xb2 h6 y1b8 ff3 fs0 fc0 sc0 ls11 wsd"> </div><div class="t m1 x6 h3 y1b9 ff3 fs1 fc0 sc0 ls11 wsd"> </div><div class="t m1 x6 h3 y1ba ff3 fs1 fc0 sc0 ls11 wsd">A <span class="_2 blank"> </span>Figura <span class="_f blank"> </span>9 <span class="_f blank"> </span>(a) <span class="_2 blank"> </span>most<span class="_2 blank"> </span>ra <span class="_2 blank"> </span>o <span class="_f blank"> </span>di<span class="_2 blank"> </span>agrama <span class="_2 blank"> </span>de <span class="_f blank"> </span>fase <span class="_2 blank"> </span>da<span class="_2 blank"> </span> <span class="_2 blank"> </span>água <span class="_f blank"> </span>a <span class="_2 blank"> </span>pr<span class="_2 blank"> </span>essões <span class="_2 blank"> </span>mode<span class="_2 blank"> </span>radas. <span class="_2 blank"> </span> <span class="_f blank"> </span>A <span class="_2 blank"> </span>l<span class="_2 blank"> </span>inha <span class="_2 blank"> </span>sólido-líquido </div><div class="t m1 x1 h8 y1bb ff3 fs1 fc0 sc0 ls11 wsd">inclina-se, <span class="_3 blank"> </span>ligeiramente, <span class="_11 blank"> </span>à <span class="_3 blank"> </span>esquerda, <span class="_3 blank"> </span>visto <span class="_11 blank"> </span>que <span class="_3 blank"> </span><span class="ff7">\ue014</span></div><div class="t m1 x3b h8 y1bc ff7 fs1 fc0 sc0 ls11">\ue018</div><div class="t m3 xa9 h9 y1bd ff7 fs3 fc0 sc0 ls11 ws2">\ue00a\ue02c\ue02f</div><div class="t m1 x54 h8 y1bb ff7 fs1 fc0 sc0 ls11 wsc">\ue070 \ue014</div><div class="t m1 x88 h8 y1bc ff7 fs1 fc0 sc0 ls11">\ue018</div><div class="t m3 x99 h9 y1bd ff7 fs3 fc0 sc0 ls11 ws2">\ue028\ue023\ue00a</div><div class="t m1 x6f h3 y1bb ff3 fs1 fc0 sc0 ls11 wsd"> <span class="_3 blank"> </span>. <span class="_3 blank"> </span>O <span class="_11 blank"> </span>ponto <span class="_3 blank"> </span>triplo <span class="_11 blank"> </span>encontra-se <span class="_3 blank"> </span>a <span class="_3 blank"> </span>0,01ºC <span class="_11 blank"> </span>e <span class="_3 blank"> </span>611 </div><div class="t m1 x1 h3 y1be ff3 fs1 fc0 sc0 ls11 wsd">Pa. O ponto de congelamento normal da água é 0,0002ºC. </div><div class="t m1 x6 h3 y1bf ff3 fs1 fc0 sc0 ls11 wsd"> </div><div class="t m9 xb3 h17 y1c0 ff1 fs9 fc0 sc0 ls11 wsd">73 </div><div class="t m9 xa7 h17 y1c1 ff1 fs9 fc0 sc0 ls11 wsd">1 </div><div class="t m9 x17 h17 y1c2 ff1 fs9 fc0 sc0 ls11 wsd">-78,2 <span class="_4 blank"> </span>-5<span class="_2 blank"> </span>6,6 </div><div class="t m9 xb3 h17 y197 ff1 fs9 fc0 sc0 ls11 wsd">67 </div><div class="t m9 x59 h17 y1c3 ff1 fs9 fc0 sc0 ls11 wsd">5,11 </div><div class="t m9 xa2 h17 y1c4 ff1 fs9 fc0 sc0 ls11 wsd">25 <span class="_4 blank"> </span>31<span class="_2 blank"> </span>,1 </div><div class="t m9 xb4 h17 y1c5 ff1 fs9 fc0 sc0 ls11 wsd">t / ºC </div><div class="t m9 xb5 h17 y1c6 ff1 fs9 fc0 sc0 ls11 wsd">p / atm </div><div class="t m9 xb6 h17 y1c7 ff1 fs9 fc0 sc0 ls11 wsd">220 a<span class="_2 blank"> </span>tm </div><div class="t m9 xb7 h22 y1c8 ff1 fs9 fc0 sc0 ls11 wsd">0 <span class="v2">0,0098 </span></div><div class="t m9 xb8 h17 y1c9 ff1 fs9 fc0 sc0 ls11 wsd">1 atm </div><div class="t m9 xb0 h17 y1ca ff1 fs9 fc0 sc0 ls11 wsd">611 Pa </div><div class="t m9 xb9 h17 y1c8 ff1 fs9 fc0 sc0 ls11 wsd">100 <span class="_7 blank"> </span>374 </div><div class="t m9 x98 h17 y1cb ff1 fs9 fc0 sc0 ls11 wsd">t / ºC </div><div class="t m9 xba h17 y1cc ff1 fs9 fc0 sc0 ls11 wsd">p <span class="_2e blank"> </span><span class="v7">10.000 </span></div><div class="t m9 x2b h17 y1cd ff1 fs9 fc0 sc0 ls11 wsd">0 </div><div class="t m9 x11 h17 y1ce ff1 fs9 fc0 sc0 ls11 wsd">5.000 </div><div class="t m9 xbb h17 y1cf ff1 fs9 fc0 sc0 ls11 wsd">-50 <span class="_2f blank"> </span><span class="v1">50 </span></div><div class="t m9 x6a h17 y1d0 ff1 fs9 fc0 sc0 ls11 wsd">t / ºC </div><div class="t m9 x22 h17 y1d1 ff1 fs9 fc0 sc0 ls11 wsd">p / atm </div><div class="t m9 xbc h23 y1d2 ff3 fs9 fc0 sc0 ls11 wsd">VI </div><div class="t m9 xbd h23 y1d3 ff3 fs9 fc0 sc0 ls11 wsd">V </div><div class="t m9 x48 h23 y1d4 ff3 fs9 fc0 sc0 ls11 wsd">II <span class="_30 blank"> </span><span class="v8">III </span></div><div class="t m9 xa3 h23 y1d5 ff3 fs9 fc0 sc0 ls11 wsd">I </div><div class="t m9 xbe h23 y1d6 ff3 fs9 fc0 sc0 ls11 wsd">Líquido </div></div><div class="pi" data-data='{"ctm":[1.000000,0.000000,0.000000,1.000000,0.000000,0.000000]}'></div></div> <div id="pf8" class="pf w0 h0" data-page-no="8"><div class="pc pc8 w0 h0"><img fetchpriority="low" loading="lazy" class="bi x0 y3a w1 hd" alt="" src="https://files.passeidireto.com/07bebfca-1ca3-4db1-8f6c-0a20e70e33d8/bg8.png"><div class="t m0 x1 h2 y3b ff1 fs0 fc0 sc0 ls11 wsd">Escola de Engenharia<span class="_0 blank"></span> de Lorena \u2013 EEL/USP <span class="_14 blank"> </span>Termodinâmica Q<span class="_0 blank"></span>uímica \u2013 Prof. Antonio Car<span class="_0 blank"></span>los da Silva </div><div class="t m0 x1 h6 y3c ff2 fs0 fc0 sc0 ls11 wsd"> </div><div class="t m0 x1 h2 y3d ff1 fs0 fc0 sc0 ls11 wsd">Equilíbrio de Fases em <span class="_0 blank"></span>Sistemas Simples <span class="_0 blank"></span>\u2013 A Regra das Fases <span class="_0 blank"></span> <span class="_15 blank"> </span>Página 8 </div><div class="t m1 x6 h5 y8e ff4 fs1 fc0 sc0 ls11 wsd">O Diagrama de Fase do Enxof<span class="_2 blank"> </span>re </div><div class="t m1 x6 h3 y1d7 ff3 fs1 fc0 sc0 ls11 wsd"> </div><div class="t m1 x6 h3 y1d8 ff3 fs1 fc0 sc0 ls11 wsd"> </div><div class="t m1 x6 h3 y1d9 ff3 fs1 fc0 sc0 ls11 wsd"> </div><div class="t m1 x6 h3 y1da ff3 fs1 fc0 sc0 ls11 wsd"> </div><div class="t m1 x6 h3 y1db ff3 fs1 fc0 sc0 ls11 wsd"> </div><div class="t m1 x6 h3 y1dc ff3 fs1 fc0 sc0 ls11 wsd"> </div><div class="t m1 x6 h3 y9 ff3 fs1 fc0 sc0 ls11 wsd"> </div><div class="t m1 x6 h3 y1dd ff3 fs1 fc0 sc0 ls11 wsd"> </div><div class="t m1 x6 h3 y1de ff3 fs1 fc0 sc0 ls11 wsd"> </div><div class="t m1 x6 h3 y1df ff3 fs1 fc0 sc0 ls11 wsd"> </div><div class="t m1 xbf h3 y1e0 ff3 fs1 fc0 sc0 lsd wsd"> (a) (b) </div><div class="t m1 x9b h3 yec ff3 fs1 fc0 sc0 ls11 wsd">Figura 10 \u2013 Diagramas de fase para o enxofre </div><div class="t m0 x54 h6 y1e1 ff3 fs0 fc0 sc0 ls11 wsd"> </div><div class="t m1 x6 h3 y1e2 ff3 fs1 fc0 sc0 ls11 wsd">A <span class="_18 blank"> </span>Figura <span class="_18 blank"> </span>10 <span class="_18 blank"> </span>mostra <span class="_18 blank"> </span>dois <span class="_18 blank"> </span>diagramas <span class="_18 blank"> </span>de <span class="_18 blank"> </span>fase <span class="_18 blank"> </span>para <span class="_18 blank"> </span>o <span class="_16 blank"> </span>enxofre. <span class="_18 blank"> </span> <span class="_18 blank"> </span>A <span class="_18 blank"> </span>forma <span class="_4 blank"> </span>estável <span class="_18 blank"> </span>do <span class="_16 blank"> </span>enxofre <span class="_18 blank"> </span>em </div><div class="t m1 x1 h3 y1e3 ff3 fs1 fc0 sc0 ls11 wsd">temperaturas <span class="_2 blank"> </span>ordinárias <span class="_2 blank"> </span>e <span class="_f blank"> </span>sob <span class="_2 blank"> </span>1 <span class="_2 blank"> </span>atm <span class="_2 blank"> </span>de <span class="_2 blank"> </span>pressão <span class="_2 blank"> </span>é <span class="_2 blank"> </span>o<span class="_2 blank"> </span> <span class="_2 blank"> </span>enxofre <span class="_2 blank"> </span>rômbico <span class="_2 blank"> </span>que, <span class="_2 blank"> </span>qu<span class="_2 blank"> </span>ando <span class="_2 blank"> </span>aquecido <span class="_2 blank"> </span>lentamente, </div><div class="t m1 x1 h3 yf3 ff3 fs1 fc0 sc0 ls11 wsd">se transforma em enxofre monoclínico sólido a 95,4ºC. </div><div class="t m1 x6 h3 y16a ff3 fs1 fc0 sc0 ls11 wsd">Na Figura 10 (a) existem três pontos triplos. As condições de equilíbrio são: </div><div class="t m1 x5e h8 y1e4 ff3 fs1 fc0 sc0 ls11 wsd">a 95,4 ºC: <span class="ff7">\ue002</span></div><div class="t m3 x23 h9 y1e5 ff7 fs3 fc0 sc0 ls11 ws2">\ue071\ue02b</div><div class="t m1 x31 h8 y1e4 ff7 fs1 fc0 sc0 ls11 ws3">\ue009 \ue002</div><div class="t m3 x45 h9 y1e5 ff7 fs3 fc0 sc0 ls11 ws2">\ue072\ue02b\ue073\ue02b</div><div class="t m1 x66 h8 y1e4 ff7 fs1 fc0 sc0 ls11 ws4">\ue009 \ue002</div><div class="t m3 xc0 h9 y1e5 ff7 fs3 fc0 sc0 ls11 ws2">\ue004\ue003\ue028</div><div class="t m1 xc1 h3 y1e4 ff3 fs1 fc0 sc0 ls11 wsd"> </div><div class="t m1 x5e h8 y1e6 ff3 fs1 fc0 sc0 ls11 wsd">a 119C: <span class="ff7">\ue002</span></div><div class="t m3 x23 h9 y1e7 ff7 fs3 fc0 sc0 ls11 ws2">\ue072\ue02b\ue073\ue02b</div><div class="t m1 x11 h8 y1e6 ff7 fs1 fc0 sc0 ls11 ws4">\ue009 \ue002</div><div class="t m3 xbb h9 y1e7 ff7 fs3 fc0 sc0 ls11 ws2">\ue00a\ue02c\ue02f</div><div class="t m1 x66 h8 y1e6 ff7 fs1 fc0 sc0 ls11 ws3">\ue009 \ue002</div><div class="t m3 xc0 h9 y1e7 ff7 fs3 fc0 sc0 ls11 ws2">\ue004\ue003\ue028</div><div class="t m1 xc1 h3 y1e6 ff3 fs1 fc0 sc0 ls11 wsd"> </div><div class="t m1 x5c h8 y1e8 ff3 fs1 fc0 sc0 ls11 wsd">a 151ºC: <span class="ff7">\ue002</span></div><div class="t m3 x8d h9 y1e9 ff7 fs3 fc0 sc0 ls11 ws2">\ue071\ue02b</div><div class="t m1 x99 h8 y1e8 ff7 fs1 fc0 sc0 ls11 ws3">\ue009 \ue002</div><div class="t m3 x8b h9 y1e9 ff7 fs3 fc0 sc0 ls11 ws2">\ue072\ue02b\ue073\ue02b</div><div class="t m1 x4a h8 y1e8 ff7 fs1 fc0 sc0 ls11 ws4">\ue009 \ue002</div><div class="t m3 x85 h9 y1e9 ff7 fs3 fc0 sc0 ls11 ws2">\ue00a\ue02c\ue02f</div><div class="t m1 xc1 h3 y1e8 ff3 fs1 fc0 sc0 ls11 wsd"> </div><div class="t m1 x1 h5 y1ea ff4 fs1 fc0 sc0 ls11 ws0">9.<span class="ff5 ls0 wsd"> </span><span class="wsd">A INTEGRAÇÃO DA EQUAÇÃO DE CLAPEYRON </span></div><div class="t m1 x6 h5 y1eb ff4 fs1 fc0 sc0 ls11 wsd">Equilíbrio Sólido-Líquido </div><div class="t m1 x6 h3 y1ec ff3 fs1 fc0 sc0 ls11 wsd">Nesse caso a equação de Clapeyron fica: </div><div class="t m1 x7d h8 y1ed ff7 fs1 fc0 sc0 ls11 ws1">\ue00f\ue037</div><div class="t m1 x7d h24 y1ee ff7 fs1 fc0 sc0 ls11 ws1c">\ue00f\ue012 <span class="ls3c v9">\ue009</span><span class="ws1 va">\ue048\ue011</span></div><div class="t m3 x88 h9 ya9 ff7 fs3 fc0 sc0 ls11 ws2">\ue050\ue005\ue028</div><div class="t m1 x23 h8 y1ee ff7 fs1 fc0 sc0 ls11 ws1">\ue048\ue014</div><div class="t m3 x88 h9 y1ef ff7 fs3 fc0 sc0 ls11 ws2">\ue050\ue005\ue028</div><div class="t m1 x11 h3 y1f0 ff3 fs1 fc0 sc0 ls11 wsd"> </div><div class="t m1 x6 h3 y1f1 ff3 fs1 fc0 sc0 ls11 wsd">Então: </div><div class="t m1 x17 h8 y1f2 ff7 fs1 fc0 sc0 ls11 ws1d">\ue074 \ue00f\ue037</div><div class="t m3 x94 h9 y1f3 ff7 fs3 fc0 sc0 ls11 ws2">\ue01e<span class="fs4 v5">\ue075</span></div><div class="t m3 x95 h9 y1f4 ff7 fs3 fc0 sc0 ls11 ws2">\ue01e<span class="fs4 v5">\ue076</span></div><div class="t m1 xc2 h25 y1f2 ff7 fs1 fc0 sc0 ls11 ws4">\ue009 \ue074<span class="_31 blank"> </span><span class="ws1 vb">\ue048\ue051</span></div><div class="t m3 x6e h9 y1f5 ff7 fs3 fc0 sc0 ls11 ws2">\ue050\ue005\ue028</div><div class="t m1 x88 h8 y1f6 ff7 fs1 fc0 sc0 ls11 ws1">\ue048\ue014</div><div class="t m3 x9a h9 y1f7 ff7 fs3 fc0 sc0 ls11 ws2">\ue050\ue005\ue028</div><div class="t m1 x7a h8 y1f8 ff7 fs1 fc0 sc0 ls11 ws1">\ue00f\ue012</div><div class="t m1 xbb h8 y1f6 ff7 fs1 fc0 sc0 ls11">\ue012</div><div class="t m3 x54 h9 y1f3 ff7 fs3 fc0 sc0 ls11">\ue01c</div><div class="t m3 x8d h1c y1f9 ff7 fs4 fc0 sc0 ls11">\ue043</div><div class="t m3 xc3 h1c y1fa ff7 fs4 fc0 sc0 ls11">\ue03d</div><div class="t m3 x22 h9 y1f4 ff7 fs3 fc0 sc0 ls17">\ue01c<span class="fs4 ls11 v5">\ue043</span></div><div class="t m1 xf h3 y1f2 ff3 fs1 fc0 sc0 ls11 wsd"> </div><div class="t m1 x1 h8 y1fb ff3 fs1 fc0 sc0 ls3d wsd"> <span class="ff7 ls11">\ue037</span></div><div class="t m3 x8c h9 y1cd ff7 fs3 fc0 sc0 ls11">\ue06e</div><div class="t m1 x2f h8 y1fb ff7 fs1 fc0 sc0 ls11 ws6">\ue010 \ue037</div><div class="t m3 x3b h9 y1cd ff7 fs3 fc0 sc0 ls11">\ue053</div><div class="t m1 x9 h8 y1fb ff7 fs1 fc0 sc0 ls11">\ue009</div><div class="t m3 x23 h9 y1fc ff7 fs3 fc0 sc0 ls11 ws2">\ue048\ue068<span class="fs4 ws9 v5">\ue043\ue02e\ue022</span></div><div class="t m3 x23 h9 y1fd ff7 fs3 fc0 sc0 ls11 ws2">\ue048\ue04c<span class="fs4 ws9 v5">\ue043\ue02e\ue022</span></div><div class="t m1 x11 h8 y1fb ff7 fs1 fc0 sc0 ls11 ws1">\ue077\ue00c</div><div class="t m3 x7a h9 y1fe ff7 fs3 fc0 sc0 ls11">\ue01c</div><div class="t m3 xbb h1c y1ff ff7 fs4 fc0 sc0 ls11">\ue043</div><div class="t m3 xc4 h1c y200 ff7 fs4 fc0 sc0 ls11">\ue03d</div><div class="t m3 xc5 h9 y1fd ff7 fs3 fc0 sc0 ls17">\ue01c<span class="fs4 ls11 v5">\ue043</span></div><div class="t m1 x70 h8 y1fb ff7 fs1 fc0 sc0 ls11 ws1e">\ue055\ue055\ue055\ue055\ue055\ue055 \ue01f\ue03b\ue078\ue021\ue055</div><div class="t m1 x6 h8 y7d ff3 fs1 fc0 sc0 ls11 wsd">Onde <span class="_11 blank"> </span><span class="ff7">\ue012</span></div><div class="t m3 x3 h9 y201 ff7 fs3 fc0 sc0 ls11">\ue050</div><div class="t m3 xc6 h9 y202 ff7 fs3 fc0 sc0 ls11">\ue03d</div><div class="t m1 xc7 h8 y7d ff3 fs1 fc0 sc0 ls11 wsd"> <span class="_11 blank"> </span>é <span class="_11 blank"> </span>o <span class="_11 blank"> </span>ponto <span class="_11 blank"> </span>de <span class="_11 blank"> </span>fusão <span class="_11 blank"> </span>sob <span class="_11 blank"> </span>a <span class="_11 blank"> </span>pressão <span class="_11 blank"> </span><span class="ff7">\ue037</span></div><div class="t m3 x87 h9 y32 ff7 fs3 fc0 sc0 ls11">\ue06e</div><div class="t m1 x8d h8 y7d ff3 fs1 fc0 sc0 ls11 wsd"> <span class="_11 blank"> </span>e <span class="_11 blank"> </span><span class="ff7">\ue012</span></div><div class="t m3 x61 h9 y32 ff7 fs3 fc0 sc0 ls11">\ue050</div><div class="t m1 x11 h8 y7d ff3 fs1 fc0 sc0 ls11 wsd"> <span class="_11 blank"> </span>é <span class="_11 blank"> </span>o <span class="_11 blank"> </span>ponto <span class="_11 blank"> </span>de <span class="_11 blank"> </span>fusão <span class="_11 blank"> </span>sob <span class="_11 blank"> </span>a <span class="_11 blank"> </span>pressão <span class="_11 blank"> </span><span class="ff7">\ue037</span></div><div class="t m3 xc8 h9 y32 ff7 fs3 fc0 sc0 ls11">\ue053</div><div class="t m1 xc9 h3 y7d ff3 fs1 fc0 sc0 ls11 wsd">. <span class="_11 blank"> </span>Como </div><div class="t m1 x1 h8 y203 ff7 fs1 fc0 sc0 ls11">\ue012</div><div class="t m3 xca h9 y204 ff7 fs3 fc0 sc0 ls11">\ue050</div><div class="t m3 xcb h9 y205 ff7 fs3 fc0 sc0 ls11">\ue03d</div><div class="t m1 xb6 h8 y203 ff7 fs1 fc0 sc0 ls11 ws5">\ue010 \ue012</div><div class="t m3 x53 h9 y206 ff7 fs3 fc0 sc0 ls11">\ue050</div><div class="t m1 xcc h8 y203 ff7 fs1 fc0 sc0 ls11 ws1">\ue055<span class="ff3 wsd">é gera<span class="_0 blank"></span>lmente muit<span class="_2 blank"> </span>o pequeno, o logaritmo pode ser desenvolvido da seguinte forma: </span></div><div class="t m1 xcd h26 y207 ff7 fs1 fc0 sc0 ls11 ws1f">\ue077\ue00c \ue079<span class="vc">\ue012</span></div><div class="t m3 xce h9 y208 ff7 fs3 fc0 sc0 ls11">\ue050</div><div class="t m3 x1d h9 y209 ff7 fs3 fc0 sc0 ls11">\ue03d</div><div class="t m1 x1c h8 y20a ff7 fs1 fc0 sc0 ls11">\ue012</div><div class="t m3 xce h9 y20b ff7 fs3 fc0 sc0 ls11">\ue050</div><div class="t m1 x34 h26 y207 ff7 fs1 fc0 sc0 ls11 ws1f">\ue07a<span class="_5 blank"> </span>\ue009<span class="_5 blank"> </span>\ue077\ue00c \ue079<span class="vc">\ue012</span></div><div class="t m3 x5e h9 y20c ff7 fs3 fc0 sc0 ls11">\ue050</div><div class="t m1 xa0 h8 y20d ff7 fs1 fc0 sc0 ls11 ws6">\ue013 \ue012</div><div class="t m3 x3f h9 y208 ff7 fs3 fc0 sc0 ls11">\ue050</div><div class="t m3 x40 h9 y209 ff7 fs3 fc0 sc0 ls11">\ue03d</div><div class="t m1 x58 h8 y20d ff7 fs1 fc0 sc0 ls11 ws6">\ue010 \ue012</div><div class="t m3 x84 h9 y20c ff7 fs3 fc0 sc0 ls11">\ue050</div><div class="t m1 x94 h8 y20a ff7 fs1 fc0 sc0 ls11">\ue012</div><div class="t m3 x3f h9 y20b ff7 fs3 fc0 sc0 ls11">\ue050</div><div class="t m1 x9 h26 y207 ff7 fs1 fc0 sc0 ls11 ws20">\ue07a<span class="_5 blank"> </span>\ue009<span class="_5 blank"> </span>\ue077\ue00c \ue079\ue03b<span class="_9 blank"> </span>\ue013<span class="_17 blank"> </span><span class="vc">\ue012</span></div><div class="t m3 x65 h9 y208 ff7 fs3 fc0 sc0 ls11">\ue050</div><div class="t m3 x7f h9 y209 ff7 fs3 fc0 sc0 ls11">\ue03d</div><div class="t m1 x4a h8 y20d ff7 fs1 fc0 sc0 ls11 ws6">\ue010 \ue012</div><div class="t m3 xc0 h9 y20c ff7 fs3 fc0 sc0 ls11">\ue050</div><div class="t m1 x4a h8 y20a ff7 fs1 fc0 sc0 ls11">\ue012</div><div class="t m3 x26 h9 y20b ff7 fs3 fc0 sc0 ls11">\ue050</div><div class="t m1 xcf h26 y207 ff7 fs1 fc0 sc0 ls11 ws21">\ue07a \ue06c <span class="vc">\ue012</span></div><div class="t m3 x29 h9 y208 ff7 fs3 fc0 sc0 ls11">\ue050</div><div class="t m3 xbc h9 y209 ff7 fs3 fc0 sc0 ls11">\ue03d</div><div class="t m1 x6a h8 y20d ff7 fs1 fc0 sc0 ls11 ws6">\ue010 \ue012</div><div class="t m3 x6b h9 y20c ff7 fs3 fc0 sc0 ls11">\ue050</div><div class="t m1 xd0 h8 y20a ff7 fs1 fc0 sc0 ls11">\ue012</div><div class="t m3 xd1 h9 y20b ff7 fs3 fc0 sc0 ls11">\ue050</div><div class="t m4 xbe h27 y207 ff7 fs5 fc0 sc0 ls11">\ue055</div><div class="t m1 x6 h3 y20e ff3 fs1 fc0 sc0 ls11 wsd">Torna-se: </div><div class="t m1 x1 h15 y20f ff3 fs1 fc0 sc0 ls3e wsd"> <span class="ff7 ls11 ws22 v0">\ue048\ue037 \ue009</span></div><div class="t m3 x22 h9 y210 ff7 fs3 fc0 sc0 ls11 ws2">\ue048\ue068<span class="fs4 ws9 v5">\ue043\ue02e\ue022</span></div><div class="t m3 x22 h28 y211 ff7 fs3 fc0 sc0 ls11 ws2">\ue048\ue04c<span class="fs4 ws23 v5">\ue043\ue02e\ue022 </span><span class="vd">\ue048\ue01c</span></div><div class="t m3 x61 h9 y211 ff7 fs3 fc0 sc0 ls11">\ue01c</div><div class="t m3 x6e h1c y115 ff7 fs4 fc0 sc0 ls11">\ue07b</div><div class="t m1 x45 h3 y212 ff3 fs1 fc0 sc0 ls11 wsd"> <span class="_32 blank"> </span>(13) </div><div class="t m1 x6 h8 y116 ff3 fs1 fc0 sc0 ls11 wsd">Onde <span class="ff7 ws1">\ue048\ue012<span class="_2 blank"></span></span> é o aumento do ponto de fusão correspondente ao aumento de pressão <span class="ff7 ws1">\ue048\ue037<span class="_2 blank"> </span></span><span class="lsd"> . </span></div><div class="t m9 xcf h17 y213 ff1 fs9 fc0 sc0 ls11 wsd">114 <span class="_30 blank"> </span><span class="ve">t / ºC </span></div><div class="t m9 xd2 h17 y214 ff1 fs9 fc0 sc0 ls11 wsd">p / atm </div><div class="t m9 x66 h17 y11d ff1 fs9 fc0 sc0 ls11 wsd">Rômbico <span class="_33 blank"> </span>Líquido </div><div class="t m9 x6c h17 y215 ff1 fs9 fc0 sc0 ls11 wsd">Vapor </div><div class="t m9 xd3 h17 y216 ff1 fs9 fc0 sc0 ls11 wsd">95,4 <span class="_30 blank"> </span>119 </div><div class="t m9 xb5 h17 y217 ff1 fs9 fc0 sc0 ls11 wsd">151ºC, </div><div class="c xb5 y218 w10 h29"><div class="t m9 x4b h17 y219 ff1 fs9 fc0 sc0 ls3f wsd">1288 atm<span class="_0 blank"></span></div></div><div class="c x5e y218 w7 h29"><div class="t m9 x4b h17 y219 ff1 fs9 fc0 sc0 ls11 wsd"> </div></div><div class="t m9 xce h17 y21a ff1 fs9 fc0 sc0 ls11 wsd">t / ºC </div><div class="t m9 x16 h17 y217 ff1 fs9 fc0 sc0 ls11 wsd">p / atm </div><div class="t m9 xc7 h17 y21b ff1 fs9 fc0 sc0 ls11 wsd">Rômbico <span class="_33 blank"> </span>Líquido </div><div class="t m9 xaa h17 y21c ff1 fs9 fc0 sc0 ls11 wsd">Vapor </div><div class="t m9 x3a h17 y21d ff1 fs9 fc0 sc0 ls11 wsd">Monoclínic<span class="_2 blank"> </span>o </div></div><div class="pi" data-data='{"ctm":[1.000000,0.000000,0.000000,1.000000,0.000000,0.000000]}'></div></div> <div id="pf9" class="pf w0 h0" data-page-no="9"><div class="pc pc9 w0 h0"><img fetchpriority="low" loading="lazy" class="bi x0 y3a w1 hd" alt="" src="https://files.passeidireto.com/07bebfca-1ca3-4db1-8f6c-0a20e70e33d8/bg9.png"><div class="t m0 x1 h2 y3b ff1 fs0 fc0 sc0 ls11 wsd">Escola de Engenharia<span class="_0 blank"></span> de Lorena \u2013 EEL/USP <span class="_14 blank"> </span>Termodinâmica Q<span class="_0 blank"></span>uímica \u2013 Prof. Antonio Car<span class="_0 blank"></span>los da Silva </div><div class="t m0 x1 h6 y3c ff2 fs0 fc0 sc0 ls11 wsd"> </div><div class="t m0 x1 h2 y3d ff1 fs0 fc0 sc0 ls11 wsd">Equilíbrio de Fases em <span class="_0 blank"></span>Sistemas Simples <span class="_0 blank"></span>\u2013 A Regra das Fases <span class="_0 blank"></span> <span class="_15 blank"> </span>Página 9 </div><div class="t m1 x6 h5 y8e ff4 fs1 fc0 sc0 ls11 wsd">Equilíbrio entre a Fase Condensad<span class="_2 blank"> </span>a e o Gás </div><div class="t m1 x6 h3 y1d7 ff3 fs1 fc0 sc0 ls11 wsd">Para o equilíbrio entre uma fase condensada, sólida ou líquida, com o vapor, temos </div><div class="t m1 x1 h3 y21e ff3 fs1 fc0 sc0 ls11 wsd"> </div><div class="t m3 x8c h9 y21f ff7 fs3 fc0 sc0 ls11 ws2">\ue02a\ue01e</div><div class="t m3 x8c h9 y220 ff7 fs3 fc0 sc0 ls11 ws2">\ue02a\ue01c</div><div class="t m1 x47 h8 y21e ff7 fs1 fc0 sc0 ls11">\ue009</div><div class="t m3 x84 h9 y21f ff7 fs3 fc0 sc0 ls11 ws2">\ue048\ue04e</div><div class="t m3 x3b h9 y220 ff7 fs3 fc0 sc0 ls11 ws2">\ue048\ue04c</div><div class="t m1 x22 h8 y21e ff7 fs1 fc0 sc0 ls11">\ue009</div><div class="t m3 x15 h9 y21f ff7 fs3 fc0 sc0 ls11 ws2">\ue048\ue068</div><div class="t m3 x8a h2a y220 ff7 fs3 fc0 sc0 ls40">\ue01c<span class="ls41 v0">\ue001</span><span class="ls11">\ue04c</span></div><div class="t m3 x99 h9 y221 ff7 fs3 fc0 sc0 ls11">\ue07c</div><div class="t m3 x15 h2b y222 ff7 fs4 fc0 sc0 ls42">\ue030<span class="fs3 ls11 ws2 vf">\ue042\ue04c</span></div><div class="t m3 x45 h9 y221 ff7 fs3 fc0 sc0 ls11">\ue07c</div><div class="t m3 x8b h2c y222 ff7 fs4 fc0 sc0 ls43">\ue07d<span class="fs3 ls11 vf">\ue007</span></div><div class="t m1 x9e h3 y21e ff1 fs1 fc0 sc0 ls10 wsd"> <span class="ff3 ls11"> <span class="_34 blank"> </span> </span></div><div class="t m1 x1 h8 y223 ff3 fs1 fc0 sc0 ls11 wsd">onde <span class="ff7 ws1">\ue048\ue051<span class="_2 blank"> </span></span> é o calor de vaporização molar do líquido o<span class="_2 blank"> </span>u o calor de sublimação do sólido e <span class="ff7">\ue014</span></div><div class="t m1 x62 h8 y224 ff7 fs1 fc0 sc0 ls11">\ue018</div><div class="t m3 xd4 h9 y225 ff7 fs3 fc0 sc0 ls11">\ue07e</div><div class="t m1 xd5 h3 y223 ff3 fs1 fc0 sc0 ls11 wsd"> é o volume </div><div class="t m1 x1 h8 y226 ff3 fs1 fc0 sc0 ls11 wsd">molar <span class="_2 blank"> </span>do <span class="_f blank"> </span>sólido <span class="_f blank"> </span>ou <span class="_f blank"> </span>do <span class="_2 blank"> </span>líquido. <span class="_f blank"> </span> <span class="_f blank"> </span>Na <span class="_2 blank"> </span>maioria <span class="_f blank"> </span>dos <span class="_2 blank"> </span>c<span class="_2 blank"> </span>asos, <span class="_2 blank"> </span><span class="ff7">\ue014</span></div><div class="t m1 x99 h8 y227 ff7 fs1 fc0 sc0 ls11">\ue018</div><div class="t m3 x15 h9 y228 ff7 fs3 fc0 sc0 ls11">\ue004</div><div class="t m1 x11 h8 y226 ff7 fs1 fc0 sc0 ls11 ws6">\ue010 \ue014</div><div class="t m1 x7a h8 y227 ff7 fs1 fc0 sc0 ls11">\ue018</div><div class="t m3 xbb h9 y228 ff7 fs3 fc0 sc0 ls11">\ue07e</div><div class="t m1 xe h8 y226 ff7 fs1 fc0 sc0 ls11 ws24">\ue06c \ue014</div><div class="t m1 x26 h8 y227 ff7 fs1 fc0 sc0 ls11">\ue018</div><div class="t m3 x48 h9 y228 ff7 fs3 fc0 sc0 ls11">\ue004</div><div class="t m1 x49 h3 y226 ff3 fs1 fc0 sc0 ls11 wsd"> <span class="_2 blank"> </span>e <span class="_f blank"> </span>isto, <span class="_f blank"> </span>admitindo-se <span class="_2 blank"> </span>que <span class="_f blank"> </span>o <span class="_f blank"> </span>gás <span class="_2 blank"> </span>sej<span class="_2 blank"> </span>a </div><div class="t m1 x1 h3 y229 ff3 fs1 fc0 sc0 ls11 wsd">ideal, equivale a <span class="ff1 ws0">RT/p</span>. Dessa forma, a equação fica: </div><div class="t m1 x1 h3 yb9 ff3 fs1 fc0 sc0 ls11 wsd"> </div><div class="t m3 x18 h9 y22a ff7 fs3 fc0 sc0 ls11 ws25">\ue02a<span class="_4 blank"> </span>\ue05b\ue07f \ue01e</div><div class="t m3 xc2 h9 y22b ff7 fs3 fc0 sc0 ls11 ws2">\ue02a\ue01c</div><div class="t m1 x87 h8 yb9 ff7 fs1 fc0 sc0 ls11">\ue009</div><div class="t m3 x88 h9 y22a ff7 fs3 fc0 sc0 ls11 ws2">\ue048\ue068</div><div class="t m3 x24 h1d y22b ff7 fs3 fc0 sc0 ls11 ws26">\ue080 \ue01c <span class="fs4 v3">\ue075</span></div><div class="t m1 x6e h3 yb9 ff1 fs1 fc0 sc0 ls10 wsd"> <span class="ff3 ls11"> <span class="_35 blank"> </span>(14) </span></div><div class="t m1 x1 h3 y22c ff3 fs1 fc0 sc0 ls11 wsd">que <span class="_2 blank"> </span>é <span class="_2 blank"> </span>conhecida <span class="_f blank"> </span>como <span class="_2 blank"> </span>Equação <span class="_f blank"> </span>de <span class="_2 blank"> </span>Clausius-Cl<span class="_2 blank"> </span>apeyron. <span class="_2 blank"> </span> <span class="_2 blank"> </span>Esta <span class="_2 blank"> </span>equação <span class="_f blank"> </span>relaciona <span class="_2 blank"> </span>a <span class="_f blank"> </span>pressão <span class="_2 blank"> </span>de <span class="_2 blank"> </span>v<span class="_2 blank"> </span>apor <span class="_2 blank"> </span>do<span class="_2 blank"> </span> </div><div class="t m1 x1 h3 y22d ff3 fs1 fc0 sc0 ls11 wsd">líquido <span class="_2 blank"> </span>(ou s<span class="_2 blank"> </span>ólido) com <span class="_2 blank"> </span>o calor <span class="_2 blank"> </span>de vaporização <span class="_2 blank"> </span>(ou <span class="_2 blank"> </span>sublimação) e <span class="_2 blank"> </span>a <span class="_2 blank"> </span>temperatura. <span class="_f blank"> </span>Integrando entre <span class="_2 blank"> </span>dois </div><div class="t m1 x1 h8 y1c1 ff3 fs1 fc0 sc0 ls11 wsd">limites, admitindo que <span class="ff7 ws1">\ue048\ue051<span class="_2 blank"> </span></span> seja independente da temperatura, obtém-se que: </div><div class="t m1 x1 h8 y22e ff3 fs1 fc0 sc0 ls44 wsd"> <span class="ff7 ls45 v1">\ue081</span><span class="ff7 ls11 ws27">\ue00f<span class="_16 blank"> </span>\ue039\ue03a \ue037</span></div><div class="t m3 x94 h9 y22f ff7 fs3 fc0 sc0 ls11">\ue01e</div><div class="t m3 xd6 h9 yeb ff7 fs3 fc0 sc0 ls11 ws2">\ue01e<span class="fs4 v5">\ue027</span></div><div class="t m1 xa h8 y22e ff7 fs1 fc0 sc0 ls3c">\ue009<span class="ls11 v1">\ue081</span></div><div class="t m3 x61 h9 y230 ff7 fs3 fc0 sc0 ls11 ws2">\ue048\ue068</div><div class="t m3 x15 h1d y231 ff7 fs3 fc0 sc0 ls11 ws26">\ue080 \ue01c <span class="fs4 v3">\ue075</span></div><div class="t m1 x46 h8 y22e ff7 fs1 fc0 sc0 ls11 ws1">\ue00f\ue012</div><div class="t m3 x88 h9 y22f ff7 fs3 fc0 sc0 ls11">\ue01c</div><div class="t m3 x24 h9 yeb ff7 fs3 fc0 sc0 ls11">\ue01c</div><div class="t m3 xd2 h1c ye ff7 fs4 fc0 sc0 ls11">\ue082</div><div class="t m1 xe h3 y22e ff1 fs1 fc0 sc0 ls10 wsd"> <span class="ff3 ls11"> </span></div><div class="t m1 x1 h8 y232 ff3 fs1 fc0 sc0 ls46 wsd"> <span class="ff7 ls11 ws1">\ue039\ue03a</span></div><div class="t m3 x60 h9 y233 ff7 fs3 fc0 sc0 ls11">\ue01e</div><div class="t m3 x75 h9 y234 ff7 fs3 fc0 sc0 ls11 ws2">\ue01e<span class="fs4 v5">\ue082</span></div><div class="t m1 xa0 h8 y232 ff7 fs1 fc0 sc0 ls11 ws3">\ue009 \ue010</div><div class="t m3 x2f h9 y233 ff7 fs3 fc0 sc0 ls11 ws2">\ue048\ue068</div><div class="t m3 xa4 h9 y234 ff7 fs3 fc0 sc0 ls11">\ue080</div><div class="t m1 x7e h8 y232 ff7 fs1 fc0 sc0 ls11">\ue019</div><div class="t m3 x30 h9 y233 ff7 fs3 fc0 sc0 ls11">\ue053</div><div class="t m3 x30 h9 y234 ff7 fs3 fc0 sc0 ls11">\ue01c</div><div class="t m1 x89 h8 y232 ff7 fs1 fc0 sc0 ls11">\ue010</div><div class="t m3 x8d h9 y233 ff7 fs3 fc0 sc0 ls11">\ue053</div><div class="t m3 xb h9 y234 ff7 fs3 fc0 sc0 ls11">\ue01c</div><div class="t m3 xc3 h1c y235 ff7 fs4 fc0 sc0 ls11">\ue082</div><div class="t m1 x24 h8 y232 ff7 fs1 fc0 sc0 ls11 ws6">\ue01d<span class="_5 blank"> </span>\ue009 \ue010</div><div class="t m3 x9e h9 y233 ff7 fs3 fc0 sc0 ls11 ws2">\ue048\ue068</div><div class="t m3 x9e h9 y234 ff7 fs3 fc0 sc0 ls11 ws2">\ue080\ue01c</div><div class="t m1 xf h8 y232 ff7 fs1 fc0 sc0 ls11">\ue013</div><div class="t m3 x48 h9 y233 ff7 fs3 fc0 sc0 ls11 ws2">\ue048\ue068</div><div class="t m3 x48 h9 y234 ff7 fs3 fc0 sc0 ls11 ws26">\ue080 \ue01c</div><div class="t m3 x67 h1c y235 ff7 fs4 fc0 sc0 ls11">\ue082</div><div class="t m1 x85 h3 y232 ff3 fs1 fc0 sc0 ls11 wsd"> <span class="_36 blank"> </span>(15) </div><div class="t m1 x1 h8 y236 ff3 fs1 fc0 sc0 ls47 wsd">onde <span class="ff7 ls11">\ue037</span></div><div class="t m3 xd7 h9 y237 ff7 fs3 fc0 sc0 ls11">\ue05e</div><div class="t m1 xd8 h8 y236 ff3 fs1 fc0 sc0 ls11 wsd"> é a pressão de vapor a <span class="ff7">\ue012</span></div><div class="t m3 x59 h9 y237 ff7 fs3 fc0 sc0 ls11">\ue05e</div><div class="t m1 x5a h8 y236 ff3 fs1 fc0 sc0 ls11 wsd"> e <span class="ff7 ls48">\ue037</span> é a pressão de vapor a <span class="ff7 ls49">\ue012</span>. <span class="_35 blank"> </span> </div><div class="t m1 xd9 h2d y238 ff7 fs1 fc0 sc0 ls11 ws27">\ue039\ue03a \ue037<span class="_5 blank"> </span>\ue009<span class="_2b blank"> </span><span class="ws1 v10">\ue048\ue051</span></div><div class="t m1 xda h8 y239 ff7 fs1 fc0 sc0 ls11 ws1">\ue083<span class="_2 blank"></span>\ue012</div><div class="t m3 xc3 h9 y23a ff7 fs3 fc0 sc0 ls11">\ue05e</div><div class="t m1 x88 h2d y238 ff7 fs1 fc0 sc0 ls4a">\ue010<span class="ls11 ws1 v10">\ue048\ue051</span></div><div class="t m1 x6e h2e y239 ff7 fs1 fc0 sc0 ls11 ws28">\ue083\ue012 <span class="ff3 wsd v9"> </span></div><div class="t m1 x1 h8 y23b ff3 fs1 fc0 sc0 ls4b wsd"> <span class="ff7 ls11 ws1">\ue039\ue084\ue085</span></div><div class="t m3 x95 h9 y23c ff7 fs3 fc0 sc0 ls11 ws2">\ue053\ue05e</div><div class="t m1 xdb h8 y23b ff7 fs1 fc0 sc0 ls11 ws29">\ue037\ue055 \ue009</div><div class="t m3 xb4 h9 y23d ff7 fs3 fc0 sc0 ls11 ws2">\ue048\ue068</div><div class="t m3 xa9 h9 y23e ff7 fs3 fc0 sc0 ls11 ws2">\ue06e\ue03d\ue086\ue05e\ue086\ue080\ue01c</div><div class="t m3 x31 h1c y23f ff7 fs4 fc0 sc0 ls11">\ue082</div><div class="t m1 x61 h8 y23b ff7 fs1 fc0 sc0 ls11">\ue010</div><div class="t m3 x9e h9 y23d ff7 fs3 fc0 sc0 ls11 ws2">\ue048\ue068</div><div class="t m3 x45 h9 y23e ff7 fs3 fc0 sc0 ls11 ws2">\ue06e\ue03d\ue086\ue05e\ue086\ue080\ue01c</div><div class="t m1 x13 h3 y23b ff3 fs1 fc0 sc0 ls11 wsd"> <span class="_37 blank"> </span>(16) </div><div class="t m1 x6 h3 y240 ff3 fs1 fc0 sc0 ls11 wsd"> </div><div class="t m1 x6 h3 y241 ff3 fs1 fc0 sc0 ls11 wsd"> </div><div class="t m1 x6 h3 y242 ff3 fs1 fc0 sc0 ls11 wsd"> </div><div class="t m1 x6 h3 y243 ff3 fs1 fc0 sc0 ls11 wsd"> </div><div class="t m1 x6 h3 y244 ff3 fs1 fc1 sc0 ls11 wsd"> </div><div class="t m1 x6 h3 y245 ff3 fs1 fc1 sc0 ls11 wsd"> </div><div class="t m1 x6 h3 y246 ff3 fs1 fc1 sc0 ls11 wsd"> </div><div class="t m1 x6 h3 y247 ff3 fs1 fc1 sc0 ls11 wsd"> </div><div class="t m1 x6 h3 y248 ff3 fs1 fc1 sc0 ls11 wsd"> </div><div class="t m1 x6 h3 y249 ff3 fs1 fc1 sc0 ls11 wsd"> </div><div class="t m1 x1c h3 y24a ff3 fs1 fc0 sc0 lsd wsd">(a) (b) </div><div class="t m1 x6 h8 y24b ff3 fs1 fc0 sc0 ls11 wsd">Figura 11 \u2013 (a) <span class="ff7 ws1">\ue039\ue084\ue085</span></div><div class="t m3 xb1 h9 y24c ff7 fs3 fc0 sc0 ls11 ws2">\ue053\ue05e</div><div class="t m1 x1d h8 y24b ff7 fs1 fc0 sc0 ls11 ws2a">\ue037 \ue036\ue055\ue087\ue087\ue051\ue088\ue055<span class="ff3 wsd">contra 1/<span class="_2 blank"> </span>T para água; (b) </span><span class="ws1">\ue039\ue084\ue085</span></div><div class="t m3 x49 h9 y24c ff7 fs3 fc0 sc0 ls11 ws2">\ue053\ue05e</div><div class="t m1 xa3 h8 y24b ff7 fs1 fc0 sc0 ls11 ws2b">\ue037 \ue036\ue055\ue087\ue087\ue051\ue088<span class="_2 blank"></span>\ue055<span class="ff3 wsd">contra 1/T para </span></div><div class="t m1 x7d h3 y24d ff3 fs1 fc0 sc0 ls11 ws0">CO</div><div class="t m0 x9 h6 y24e ff3 fs0 fc0 sc0 ls11">2</div><div class="t m1 xda h3 y24d ff3 fs1 fc0 sc0 ls11 wsd"> sólido.<span class="fc1"> </span></div><div class="t m1 x6 h3 y24f ff3 fs1 fc1 sc0 ls11 wsd"> </div><div class="t m1 x6 h3 y250 ff3 fs1 fc1 sc0 ls11 wsd"> </div><div class="t m8 xdc h14 y251 ff1 fs8 fc0 sc0 ls11 wsd">2 <span class="_38 blank"> </span>3 <span class="_33 blank"> </span><span class="v11">4 <span class="_39 blank"> </span>5 </span></div><div class="t m8 xd8 h14 y252 ff1 fs8 fc0 sc0 ls11 wsd">0 </div><div class="t m8 xdd h14 y253 ff1 fs8 fc0 sc0 ls11 wsd">1 </div><div class="t m8 xdd h14 y254 ff1 fs8 fc0 sc0 ls11 wsd">2 </div><div class="t m8 xde h14 y255 ff1 fs8 fc0 sc0 ls11 wsd">3 </div><div class="t m8 xa2 h14 y256 ff1 fs8 fc0 sc0 ls11 wsd">5 <span class="_38 blank"> </span>6 <span class="_33 blank"> </span><span class="v11">7 <span class="_39 blank"> </span>8 </span></div><div class="t m8 xbb h14 y257 ff1 fs8 fc0 sc0 ls11 wsd">0 </div><div class="t m8 xc4 h14 ya7 ff1 fs8 fc0 sc0 ls11 wsd">1 </div><div class="t m8 xc4 h14 y258 ff1 fs8 fc0 sc0 ls11 wsd">2 </div><div class="t m8 xd h14 y259 ff1 fs8 fc0 sc0 ls11 wsd">3 </div></div><div class="pi" data-data='{"ctm":[1.000000,0.000000,0.000000,1.000000,0.000000,0.000000]}'></div></div>
Compartilhar