Lista 6 1ª Lei da Termodinâmica

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Universidade Federal da Fronteira Sul
Engenharia Ambiental - Bacharelado
Disciplina: GEX037 - F´ısica II
Professor: Marcelo Correa Ribeiro
Semestre: 2018/1
Lista de Exerc´ıcios VII - Temperatura
1. A temperatura e´ uma grandeza macrosco´pica ou microsco´pica?
2. Se a pressa˜o de um ga´s isolado aumenta, necessariamente a temperatura do ga´s deve
aumentar? Explique.
3. A figura mostra um gra´fico do volume x temperatura de um ga´s isolado, num processo onde
o ga´s vai do estado A para o estado B. Explique o que acontece com o volume, temperatura
e pressa˜o durante esse processo.
586 | C H A P T E R 1 7 Temperature and Kinetic Theory of Gases
Answers to Concept Checks
17-1 Toni’s room has more air in it.
17-2 It decreases.
17-3 The rms speed of helium is about 12 percent of the
escape speed from Earth’s surface. Thus there are
enough helium molecules with speeds above escape
speed for the helium to slowly escape Earth.
Answers to Practice Problems
17-1 (a) (b)
17-2 (a) (b)
17-3
17-4 5.2 ! 102 m>sn " 0.0804 mol
N " 2.69 ! 1019 moleculesn " 4.47 ! 10#5 mol,
#40°F20°C,
Problems
In a few problems, you are given more data than you
actually need; in a few other problems, you are required to
supply data from your general knowledge, outside sources,
or informed estimate.
Interpret as significant all digits in numerical values that
have trailing zeros and no decimal points.
• Single-concept, single-step, relatively easy
•• Intermediate-level, may require synthesis of concepts
••• Challenging
Solution is in the Student Solutions Manual
Consecutive problems that are shaded are paired
problems.
SSM
P
A
B
T
V
A
B
T
F I G U R E 1 7 - 1 8
Problem 5
5 • Figure 17-18 shows a plot of volume versus ab-
solute temperature for a process that takes a fixed amount of
an ideal gas from point A to point B. What happens to the pres-
sure of the gas during this process? SSM
T
V
6 • Figure 17-19 shows a plot of pressure versus ab-
solute temperature for a process that takes a sample of an ideal
gas from point A to point B. What happens to the volume of the
gas during this process?
T
P
F I G U R E 1 7 - 1 9
Problem 6
TOPIC RELEVANT EQUATIONS AND REMARKS
6. Maxwell–Boltzmann Speed Distribution 17-36
Maxwell–Boltzmann Energy Distribution 17-38F(E) "
22p a 1kT b 3>2 E1>2e#E>(kT)
f(v) "
42p a m2kT b 3>2 v2e#mv2>(2kT)*
CONCEPTUAL PROBLEMS
1 • True or false:
(a) The zeroth law of thermodynamics states that two objects in
thermal equilibrium with each other must be in thermal equi-
librium with a third object.
(b) The Fahrenheit and Celsius temperature scales differ only in the
choice of the ice-point temperature.
(c) The Celsius degree and the kelvin are the same size.
2 • How can you determine if two objects are in thermal
equilibrium with each other when putting them into physical con-
tact with each other would have undesirable effects? (For example,
if you put a piece of sodium in contact with water there would be a
violent chemical reaction.)
3 • “Yesterday I woke up and it was in my bedroom,”
said Mert to his old friend Mort. “That’s nothing,” replied Mort.
“My room was ” Who had the colder room, Mert or
Mort?
4 • Two identical vessels contain different ideal gases at the
same pressure and temperature. It follows that (a) the number of gas
molecules is the same in both vessels, (b) the total mass of gas is the
same in both vessels, (c) the average speed of the gas molecules is
the same in both vessels, (d) None of the above.
SSM
#5.0°C.
20°F4. Um boletim meteorolo´gico informa que se espera uma queda de temperatura de 15,0 oC
para as pro´ximas quatro horas. De quantos graus da escala Fahrenheit caira´ a temperatura?
Resp.: 8,33oF
5. O seu me´dico diz que a sua temperatura e´ 310 na escala absoluta, voceˆ ficaria preocupada?
Explique.
6. Uma janela de vidro mede 200 cm por 300 cm a 10oC. De quanto aumenta sua a´rea
quando a temperatura se eleva a 40oC? Suponha que o videro tenha dilatac¸a˜o linear com
α = 9 × 10−6 oC−1. Resp.: 32,4 cm2.
7. Voceˆ precisa encaixar um anel de cobre firmemente em torno de uma haste de ac¸o com
6,0000 cm de diaˆmetro a 20oC. O diaˆmetro interno do anel, nesta temperatura, e´ 5,9800
cm. Qual deve ser a temperatura do anel de cobre, para que ele encaixe na haste sem folga,
supondo que ele permanec¸a a 20oC?
Resp.: 220oC.
8. Quando a temperatura de uma moeda de cobre e´ aumentada 100oC o diaˆmetro aumenta
18%. Com precisa˜o de dois algarismos significativos, determine o aumento percentual (a)
da a´rea (b) da espessura (c) do volume (d) da massa espec´ıfica da moedas (d) calcule o
coeficiente de dilatac¸a˜o linear da moeda.
1
9. Que massa de vapor a 100oC deve ser misturada com 150 g de gelo no ponto de fusa˜o, em
um recipiente isolado termicamente, para produzir a´gua a 50oC.
Resp.: 33g.
10. Uma amostra de 400 g e´ colocada em um sistema de resfriamento que remove calor a uma
taxa constante. O gra´fico indica a temperatura da amostra em func¸a˜o do tempo, a escala
de tempo e´ definida por ts = 80, 0 min. A amostra congela durante o processo . O calor
espec´ıfico da amostra no estado l´ıquido inicial e´ 3000 J/kg.K. (a) Determine: (a) o calor
de fusa˜o da amostra e (b) o calor espec´ıfico da fase so´lida.
542 CHAPTER 18 TEMPERATURE, HEAT, AND THE FIRST LAW OF THERMODYNAMICS
Module 18-4 Absorption of Heat 
•22 One way to keep the contents of a garage from becoming
too cold on a night when a severe subfreezing temperature is forecast
is to put a tub of water in the garage. If the mass of the water is 125 kg
and its initial temperature is 20 C, (a) how much energy must the wa-
ter transfer to its surroundings in order to freeze completely and
(b) what is the lowest possible temperature of the water and its sur-
roundings until that happens?
•23 A small electric immersion heater is used to heat 100 g
of water for a cup of instant coffee. The heater is labeled
“200 watts” (it converts electrical energy to thermal energy at this
rate). Calculate the time required to bring all this water from 
23.0 C to 100 C, ignoring any heat losses.
•24 A certain substance has a mass per mole of 50.0 g/mol. When
314 J is added as heat to a 30.0 g sample, the sample’s temperature
rises from 25.0 C to 45.0 C. What are the (a) specific heat and
(b) molar specific heat of this substance? (c) How many moles are
in the sample?
•25 A certain diet doctor encourages people to diet by drinking
ice water. His theory is that the body must burn off enough fat to
raise the temperature of the water from 0.00!C to the body tem-
perature of 37.0!C. How many liters of ice water would have to be
consumed to burn off 454 g (about 1 lb) of fat, assuming that burn-
ing this much fat requires 3500 Cal be transferred to the ice water?
Why is it not advisable to follow this diet? (One liter " 103 cm3.
The density of water is 1.00 g/cm3.)
•26 What mass of butter, which has a usable energy content of 
6.0 Cal/g (" 6000 cal/g), would be equivalent to the change in grav-
itational potential energy of a 73.0 kg man who ascends from sea
level to the top of Mt. Everest, at elevation 8.84 km? Assume that
the average g for the ascent is 9.80 m/s2.
•27 Calculate the minimum amount of energy, in joules,
required to completely melt 130 g of silver initially at 15.0 C.
•28 How much water remains unfrozen after 50.2 kJ is trans-
ferred as heat from 260 g of liquid water initially at its freezing
point?
••29 In a solar water heater, energy from the Sun is gathered by
water that circulates through tubes in a rooftop collector. The so-
lar radiation enters the collector through a transparent cover and
warms the water in the tubes; this water is pumped into a holding
tank. Assume that the efficiency of the overall system is 20%
(that is, 80% of the incident solarenergy is lost from the system).
What collector area is necessary to raise the temperature of 200
L of water in the tank from 20!C to 40°C in 1.0 h when the inten-
sity of incident sunlight is 700 W/m2?
••30 A 0.400 kg sample is placed in a cooling apparatus that re-
moves energy as heat at a con-
stant rate. Figure 18-33 gives
the temperature T of the sam-
ple versus time t; the horizon-
tal scale is set by ts" 80.0 min.
The sample freezes during the
energy removal. The specific
heat of the sample in its initial
liquid phase is 3000 J/kg #K.
What are (a) the sample’s heat
of fusion and (b) its specific
heat in the frozen phase?
!
SSM
!!
!!
SSM
!
••31 What mass of steam at 100 C must be mixed with 150 g
of ice at its melting point, in a thermally insulated container, to
produce liquid water at 50 C?
••32 The specific heat of a substance varies with temperature ac-
cording to the function c " 0.20 $ 0.14T $ 0.023T 2, with T in C
and c in cal/g #K. Find the energy required to raise the temperature
of 2.0 g of this substance from 5.0 C to 15 C.
••33 Nonmetric version: (a) How long does a 2.0% 105 Btu/h water
heater take to raise the temperature of 40 gal of water from 70 F to
100°F? Metric version: (b) How long does a 59 kW water heater take
to raise the temperature of 150 L of water from 21!C to 38!C?
••34 Samples A and B are at different initial temperatures
when they are placed in a thermally insulated container and al-
lowed to come to thermal equilibrium. Figure 18-34a gives their
temperatures T versus time t. Sample A has a mass of 5.0 kg; sam-
ple B has a mass of 1.5 kg. Figure 18-34b is a general plot for
the material of sample B. It shows the temperature change &T that
the material undergoes when energy is transferred to it as heat Q.
The change &T is plotted versus the energy Q per unit mass of the
material, and the scale of the vertical axis is set by &Ts " 4.0 C .
What is the specific heat of sample A?
!
!
!!
!
!
!ILW
Figure 18-33 Problem 30.
T
 (
K
)
300
270
250
0
t (min)
ts
T
 (
°
C
)
100
60
20
0 10 
t (min) 
20
A
B
∆T
 (
C
°
)
∆Ts
0 8
Q /m (kJ/kg)
16
(a) (b)
Figure 18-34 Problem 34.
••35 An insulated Thermos contains 130 cm3 of hot coffee at
80.0 C. You put in a 12.0 g ice cube at its melting point to cool the
coffee. By how many degrees has your coffee cooled once the ice
has melted and equilibrium is reached? Treat the coffee as
though it were pure water and neglect energy exchanges with the
environment.
••36 A 150 g copper bowl contains 220 g of water, both at 20.0 C.A
very hot 300 g copper cylinder is dropped into the water, causing the
water to boil, with 5.00 g being converted to steam. The final tem-
perature of the system is 100 C. Neglect energy transfers with the
environment. (a) How much energy (in calories) is transferred to
the water as heat? (b) How much to the bowl? (c) What is the orig-
inal temperature of the cylinder?
••37 A person makes a quantity of iced tea by mixing 500 g of hot
tea (essentially water) with an equal mass of ice at its melting
point.Assume the mixture has negligible energy exchanges with its
environment. If the tea’s initial temperature is Ti " 90 C, when
thermal equilibrium is reached what are (a) the mixture’s tempera-
ture Tf and (b) the remaining mass mf of ice? If Ti " 70 C, when
thermal equilibrium is reached what are (c) Tf and (d) mf?
••38 A 0.530 kg sample of liquid water and a sample of ice are
placed in a thermally insulated container. The container also con-
tains a device that transfers energy as heat from the liquid water
to the ice at a constant rate P, until thermal equilibrium is
!
!
!
!
!
11. O a´lcool et´ılico tem um ponto de ebulic¸a˜o de 78,0 oC, um ponto de congelamento de
−11, 4oC, um calor de vaporizac¸a˜o de 879 kJ/kg um calor de fusa˜o de 109 kJ/kg e calor
espec´ıfico de 2,43 kJ/kg.K. Quanta energia deve ser removida de 0,510 kg de a´lcool et´ılico
que esta´ inicialmente na forma de ga´s a 78,0oC para que ele se torne um so´lido a -114oC.
Resp.: 742kJ
12. Um ga´s em uma caˆmara fechada passa pelo ciclo mostrado no diagrama PV. A escala e´
definida por Vs = 4, 0m
3. Calcule a energia total adicionada ao sistema na forma de calor
durante o ciclo.
Resp: 30J saindo do ga´s.
543PROBLEMS
point of !114 C, a heat of vaporization of 879 kJ/kg, a heat of fu-
sion of 109 kJ/kg, and a specific heat of 2.43 kJ/kg"K. How much
energy must be removed from 0.510 kg of ethyl alcohol that is ini-
tially a gas at 78.0 C so that it becomes a solid at !114 C?
••40 Calculate the specific heat of a metal from the following
data. A container made of the metal has a mass of 3.6 kg and con-
tains 14 kg of water. A 1.8 kg piece of the metal initially at a tem-
perature of 180 C is dropped into the water. The container and
water initially have a temperature of 16.0 C, and the final tempera-
ture of the entire (insulated) system is 18.0 C.
•••41 (a) Two 50 g ice cubes are dropped into 200 g
of water in a thermally insulated container. If the water is initially
at 25 C, and the ice comes directly from a freezer at !15 C, what is
the final temperature at thermal equilibrium? (b) What is the final
temperature if only one ice cube is used?
##
WWWSSM
#
#
#
##
#
reached. The temperatures T of the liquid water and the ice are
given in Fig. 18-35 as functions of time t; the horizontal scale is set
by ts$ 80.0 min. (a) What is rate P? (b) What is the initial mass of
the ice in the container? (c) When thermal equilibrium is
reached, what is the mass of the ice produced in this process?
state C, and then back to A, as shown in the p-V diagram of Fig. 18-
38a. The vertical scale is set by ps$ 40 Pa, and the horizontal scale
is set by Vs$ 4.0 m3. (a)–(g) Complete the table in Fig. 18-38b by
inserting a plus sign, a minus sign, or a zero in each indicated cell.
(h) What is the net work done by the system as it moves once
through the cycle ABCA?
Pr
es
su
re
 (
Pa
) 
ps
Vs
C
BA
Volume (m3)
0
BA
CB
AC
Q W ∆ Eint 
+
(e) (f) 
(a) (b) 
(g) 
(c) (d) 
+
(a) (b)
Figure 18-36 Problem 42.
Al
d
D
Cu
Pr
es
su
re
 (
Pa
)
p0
V0 4.0V0
C B
A
Volume (m3)
0
Figure 18-37 Problem 43.
Figure 18-38 Problem 44.••39 Ethyl alcohol has a boiling point of 78.0 C, a freezing#
•45 A gas within a
closed chamber undergoes the
cycle shown in the p-V diagram
of Fig. 18-39. The horizontal
scale is set by Vs $ 4.0 m3.
Calculate the net energy added
to the system as heat during
one complete cycle.
•46 Suppose 200 J of work is
done on a system and 70.0 cal is
extracted from the system as
heat. In the sense of the first law
of thermodynamics, what are
the values (including algebraic signs) of (a) W, (b) Q, and (c) %Eint?
••47 When a system is taken from state i to state fWWWSSM
ILWSSM
along path iaf in Fig. 18-40,Q$ 50 cal and W$ 20 cal. Along path 
ibf, Q$ 36 cal. (a) What is W along path ibf? (b) If W $!13 cal
for the return path fi, what is Q for this path? (c) If Eint,i $ 10 cal,
what is Eint, f? If Eint,b $ 22 cal, what is Q for (d) path ib and (e)
path bf ?
40
20
0
–20
0
t (min)
ts
T
 (
°
C
)
Figure 18-35 Problem 38.
•••42 A 20.0 g copper ring at
0.000 C has an inner diameter of 
D $ 2.54000 cm. An aluminum
sphere at 100.0 C has a diameter
of d $ 2.545 08 cm. The sphere is
put on top of the ring (Fig. 18-36),
and the two are allowed to come
to thermal equilibrium, with no
heat lost to the surroundings. The
sphere just passes through the
ring at the equilibrium tempera-
ture. What is the mass of the
sphere?
Module 18-5 The First Law of
Thermodynamics
•43 In Fig. 18-37, a gas sample ex-
pands from V0 to 4.0V0 while itspressure decreases from p0 to
p0/4.0. If V0$ 1.0 m3 and p0$ 40
Pa, how much work is done by the
gas if its pressure changes with vol-
ume via (a) path A, (b) path B, and
(c) path C?
•44 A thermodynamic system
is taken from state A to state B to
#
#
Pr
es
su
re
 (
N
/m
2 )
40
30
20
10
Vs
C B
Volume (m3)
0
A
Figure 18-39 Problem 45.
a
i
f
b
Pr
es
su
re
Volume 0
Figure 18-40 Problem 47.
••48 As a gas is held within a
closed chamber, it passes through the
cycle shown in Fig. 18-41. Determine
the energy transferred by the system
as heat during constant-pressure
process CA if the energy added as heat
QAB during constant-volume process
AB is 20.0 J, no energy is transferred
as heat during adiabatic process BC,
and the net work done during the cycle
is 15.0 J.
A C 
B
0 Volume 
Pr
es
su
re
Figure 18-41 Problem 48.
2
13. A figura mostra um ciclo fechado de um ga´s. A variac¸a˜o da energia interna do ga´s no
processo abc e´ -200J. Quando o ga´s passa de c para d recebe 180J na forma de calor. Mais
80 J sa˜o recebidos quando o ga´s passa de d para a. Qual e´ o trabalho realizado sobre o ga´s
quando ele passa de c para d?
Resp.: 60J.
544 CHAPTER 18 TEMPERATURE, HEAT, AND THE FIRST LAW OF THERMODYNAMICS
••49 Figure 18-42 represents a
closed cycle for a gas (the figure is not
drawn to scale).The change in the inter-
nal energy of the gas as it moves from a
to c along the path abc is !200 J.
As it moves from c to d, 180 J must be
transferred to it as heat. An additional
transfer of 80 J to it as heat is needed as
it moves from d to a. How much work is
done on the gas as it moves from c to d?
••50 A lab sample of gas is taken
through cycle abca shown in the p-V
diagram of Fig. 18-43. The net work
done is "1.2 J. Along path ab, the
change in the internal energy is "3.0 J
and the magnitude of the work done
is 5.0 J. Along path ca, the energy
transferred to the gas as heat is "2.5
J. How much energy is transferred as
heat along (a) path ab and (b) path bc?
a beehive, several hundred of the bees quickly form a compact
ball around the hornet to stop it. They don’t sting, bite, crush, or
suffocate it. Rather they overheat it by quickly raising their body
temperatures from the normal 35 C to 47 C or 48 C, which is
lethal to the hornet but not to the bees (Fig. 18-44). Assume the
following: 500 bees form a ball of radius R# 2.0 cm for a time t#
20 min, the primary loss of energy by the ball is by thermal radia-
tion, the ball’s surface has emissivity ´# 0.80, and the ball has a
uniform temperature. On average, how much additional energy
must each bee produce during the 20 min to maintain 47 C?
••57 (a) What is the rate of energy loss in watts per square meter
through a glass window 3.0 mm thick if the outside temperature is
!20 F and the inside temperature is "72 F? (b) A storm window
having the same thickness of glass is installed parallel to the first
window, with an air gap of 7.5 cm between the two windows. What
now is the rate of energy loss if conduction is the only important
energy-loss mechanism?
••58 A solid cylinder of radius r1 # 2.5 cm, length h1 # 5.0 cm,
emissivity 0.85, and temperature 30 C is suspended in an environ-
ment of temperature 50 C. (a) What is the cylinder’s net thermal
radiation transfer rate P1? (b) If the cylinder is stretched until its
radius is r2 # 0.50 cm, its net thermal radiation transfer rate be-
comes P2.What is the ratio P2 /P1?
$
$
$$
$
$$$
p
V
c
ba
Figure 18-43 Problem 50.
(a)
(b)
T1
T1
T2
T2
Figure 18-45 Problem 59.
Figure 18-44
Problem 56. © Dr. Masato Ono, Tamagawa University
Module 18-6 Heat Transfer Mechanisms
•51 A sphere of radius 0.500 m, temperature 27.0 C, and emissiv-
ity 0.850 is located in an environment of temperature 77.0 C. At
what rate does the sphere (a) emit and (b) absorb thermal radia-
tion? (c) What is the sphere’s net rate of energy exchange?
•52 The ceiling of a single-family dwelling in a cold climate
should have an R-value of 30. To give such insulation, how thick
would a layer of (a) polyurethane foam and (b) silver have to be?
•53 Consider the slab shown in Fig. 18-18. Suppose thatSSM
$
$
p
V
b
c d 
a
Figure 18-42 Problem 49.
TH TC
k1 k2 k3
L1 L2 L3
Figure 18-46 Problem 60.
Air
Ice
Water
Figure 18-47 Problem 61.
L # 25.0 cm, A # 90.0 cm2, and the material is copper. If TH #
125 C, TC # 10.0 C, and a steady state is reached, find the conduc-
tion rate through the slab.
•54 If you were to walk briefly in space without a spacesuit
while far from the Sun (as an astronaut does in the movie 2001, A
Space Odyssey), you would feel the cold of space—while you radi-
ated energy, you would absorb almost none from your environ-
ment. (a) At what rate would you lose energy? (b) How much en-
ergy would you lose in 30 s? Assume that your emissivity is 0.90,
and estimate other data needed in the calculations.
•55 A cylindrical copper rod of length 1.2 m and cross-sectional
area 4.8 cm2 is insulated along its side.The ends are held at a temper-
ature difference of 100 C by having one end in a water–ice mixture
and the other in a mixture of boiling water and steam. At what rate
(a) is energy conducted by the rod and (b) does the ice melt?
••56 The giant hornet Vespa mandarinia japonica preys on
Japanese bees. However, if one of the hornets attempts to invade
$
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••59 In Fig. 18-45a, two identical rec-
tangular rods of metal are welded end
to end, with a temperature of T1 # 0 C
on the left side and a temperature 
of T2 # 100 C on the right side. In 
2.0 min, 10 J is conducted at a constant
rate from the right side to the left side.
How much time would be required to
conduct 10 J if the rods were welded
side to side as in Fig. 18-45b?
••60 Figure 18-46 shows the cross
section of a wall made of three layers.
The layer thicknesses are L1, L2 #
0.700L1, and L3 # 0.350L1. The ther-
mal conductivities are k1, k2 #
0.900k1, and k3 0.800k1. The temper-
atures at the left side and right side of
the wall are TH # 30.0 C and TC #$
#
$
$
!15.0 C, respectively. Thermal
conduction is steady. (a) What is
the temperature difference %T2
across layer 2 (between the left and
right sides of the layer)? If k2 were,
instead, equal to 1.1k1, (b) would
the rate at which energy is con-
ducted through the wall be greater
than, less than, or the same as pre-
viously, and (c) what would be the
value of %T2?
••61 A 5.0 cm slab has formed
on an outdoor tank of water (Fig.
18-47). The air is at !10$C. Find the
rate of ice formation (centimeters
per hour). The ice has thermal con-
ductivity 0.0040 cal/s &cm &C and
density 0.92 g/cm3. Assume there is
$
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$
no energy transfer through the walls or bottom.
14. Quando se leva um sistema do estado i ao estado f ao longo do trajeto iaf da figura,
descobre-se que Q = 50 J e W = 20J. Ao longo do trajeto ibf , Q = 36J . (a) Qual o
valor de W ao longo do trajeto ibf? (b) Se W = −13J para o trajeto curvo fi de retorno,
quanto vale Q para este trajeto? (c) Tome Ui = 10 J. Quanto vale Uf? (d) Se Ub = 22J ,
encontre Q para o processo ib e o processo bf .
Resp.:
543PROBLEMS
point of !114 C, a heat of vaporization of 879 kJ/kg, a heat of fu-
sion of 109 kJ/kg, and a specific heat of 2.43 kJ/kg"K. How much
energy must be removed from 0.510 kg of ethyl alcohol that is ini-
tially a gas at 78.0 C so that it becomes a solid at !114 C?
••40 Calculate the specific heat of a metal from the following
data. A container made of the metal has a mass of 3.6 kg and con-
tains 14 kg of water. A 1.8 kg piece of the metal initially at a tem-
perature of 180 C is dropped into the water. The container and
water initially have a temperature of 16.0 C, and the final tempera-ture of the entire (insulated) system is 18.0 C.
•••41 (a) Two 50 g ice cubes are dropped into 200 g
of water in a thermally insulated container. If the water is initially
at 25 C, and the ice comes directly from a freezer at !15 C, what is
the final temperature at thermal equilibrium? (b) What is the final
temperature if only one ice cube is used?
##
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#
#
#
##
#
reached. The temperatures T of the liquid water and the ice are
given in Fig. 18-35 as functions of time t; the horizontal scale is set
by ts$ 80.0 min. (a) What is rate P? (b) What is the initial mass of
the ice in the container? (c) When thermal equilibrium is
reached, what is the mass of the ice produced in this process?
state C, and then back to A, as shown in the p-V diagram of Fig. 18-
38a. The vertical scale is set by ps$ 40 Pa, and the horizontal scale
is set by Vs$ 4.0 m3. (a)–(g) Complete the table in Fig. 18-38b by
inserting a plus sign, a minus sign, or a zero in each indicated cell.
(h) What is the net work done by the system as it moves once
through the cycle ABCA?
Pr
es
su
re
 (
Pa
) 
ps
Vs
C
BA
Volume (m3)
0
BA
CB
AC
Q W ∆ Eint 
+
(e) (f) 
(a) (b) 
(g) 
(c) (d) 
+
(a) (b)
Figure 18-36 Problem 42.
Al
d
D
Cu
Pr
es
su
re
 (
Pa
)
p0
V0 4.0V0
C B
A
Volume (m3)
0
Figure 18-37 Problem 43.
Figure 18-38 Problem 44.••39 Ethyl alcohol has a boiling point of 78.0 C, a freezing#
•45 A gas within a
closed chamber undergoes the
cycle shown in the p-V diagram
of Fig. 18-39. The horizontal
scale is set by Vs $ 4.0 m3.
Calculate the net energy added
to the system as heat during
one complete cycle.
•46 Suppose 200 J of work is
done on a system and 70.0 cal is
extracted from the system as
heat. In the sense of the first law
of thermodynamics, what are
the values (including algebraic signs) of (a) W, (b) Q, and (c) %Eint?
••47 When a system is taken from state i to state fWWWSSM
ILWSSM
along path iaf in Fig. 18-40,Q$ 50 cal and W$ 20 cal. Along path 
ibf, Q$ 36 cal. (a) What is W along path ibf? (b) If W $!13 cal
for the return path fi, what is Q for this path? (c) If Eint,i $ 10 cal,
what is Eint, f? If Eint,b $ 22 cal, what is Q for (d) path ib and (e)
path bf ?
40
20
0
–20
0
t (min)
ts
T
 (
°
C
)
Figure 18-35 Problem 38.
•••42 A 20.0 g copper ring at
0.000 C has an inner diameter of 
D $ 2.54000 cm. An aluminum
sphere at 100.0 C has a diameter
of d $ 2.545 08 cm. The sphere is
put on top of the ring (Fig. 18-36),
and the two are allowed to come
to thermal equilibrium, with no
heat lost to the surroundings. The
sphere just passes through the
ring at the equilibrium tempera-
ture. What is the mass of the
sphere?
Module 18-5 The First Law of
Thermodynamics
•43 In Fig. 18-37, a gas sample ex-
pands from V0 to 4.0V0 while its
pressure decreases from p0 to
p0/4.0. If V0$ 1.0 m3 and p0$ 40
Pa, how much work is done by the
gas if its pressure changes with vol-
ume via (a) path A, (b) path B, and
(c) path C?
•44 A thermodynamic system
is taken from state A to state B to
#
#
Pr
es
su
re
 (
N
/m
2 )
40
30
20
10
Vs
C B
Volume (m3)
0
A
Figure 18-39 Problem 45.
a
i
f
b
Pr
es
su
re
Volume 0
Figure 18-40 Problem 47.
••48 As a gas is held within a
closed chamber, it passes through the
cycle shown in Fig. 18-41. Determine
the energy transferred by the system
as heat during constant-pressure
process CA if the energy added as heat
QAB during constant-volume process
AB is 20.0 J, no energy is transferred
as heat during adiabatic process BC,
and the net work done during the cycle
is 15.0 J.
A C 
B
0 Volume 
Pr
es
su
re
Figure 18-41 Problem 48.
15. O ga´s dentro de uma caˆmara sofre os processos mostrados no diagrama pV da figura.
Calcule o calor resultante que entra no sistema durante um ciclo completo.
Resp.: Q = 35J saindo do sistema.
Problemas Resolvidos de Física Prof. Anderson Coser Gaudio – Depto. Física – UFES 
________________________________________________________________________________________________________ 
Resnick, Halliday, Krane - Física 2 - 4a Ed. - LTC - 1996. Cap. 25 – Calor e Primeira Lei da Termodinâmica 
1 
 
 
RESNICK, HALLIDAY, KRANE, FÍSICA, 4.ED., LTC, RIO DE JANEIRO, 1996. 
 
 
FÍSICA 2 
 
 
CAPÍTULO 25 - CALOR E PRIMEIRA LEI DA TERMODINÂMICA 
 
40. O gás dentro de uma câmara sofre os processos mostrados no diagrama pV da Fig. 27. Calcule o 
calor resultante adicionado ao sistema durante um ciclo completo. 
 
 (Pág. 237) 
Solução. 
Durante um ciclo termodinâmico a variação da energia interna (∆Eint) do sistema é zero, 
 int 0E Q W∆ = + = 
 WQ −= (1) 
Nesta equação, Q é o calor resultante transferido durante o ciclo e W é o trabalho resultante 
executado sobre o sistema. De acordo com a convenção adotada neste livro, num ciclo 
termodinâmico anti-horário o sinal do trabalho é positivo. Portanto, no presente ciclo, o trabalho e o 
calor apresentam os seguintes sinais: 
 0W > 
 0Q < 
O trabalho realizado sobre o sistema corresponde à área do semicírculo mostrado na figura (pela 
convenção adotada neste livro, o trabalho num ciclo anti-horário é positivo). Embora seja tentador 
calcular essa área diretamente a partir da figura, este procedimento não é possível porque as escalas 
da ordenada e da abscissa são diferentes. No entanto, se as escalas dos eixos forem ignoradas é 
possível contornar essa dificuldade. 
Admitindo-se que cada quadrado do diagrama tenha uma unidade de comprimento (1 uc) de aresta, 
implica em que cada quadrado tenha uma unidade de área (1 ua). O semicírculo possui raio R = 1,5 
uc e sua área vale: 
 ua 534291,35,1
2
1
2
1 22 === ππRA 
Pode-se calcular a quantidade de trabalho que corresponde a cada quadrado no diagrama (Wq), 
multiplicando-se os valores da pressão (1 Mpa) e do volume (1 l = 1×10-3 m3) correspondentes a um 
quadrado. 
 kJ/ua 10)m 101).(MPa 10( 33 =×= −qW 
3
16. Uma amostra de um ga´s ideal e´ submetida ao processo mostrado na figura. A escala e´
definida por pb = 7, 5kPa e pac = 2, 5 kPa. No ponto a, T = 200 K. (a) Quantos mols
do ga´s esta˜o presentes na amostra? (b) Qual a temperatura no ponto b? (c) Qual a
temperatura no ponto c (d) Qual e´ a energia adicionada ao sistema na forma de calor?
Resp.: (a)1,5 mol; (b) 1, 8 × 103K (c) 6, 0 × 102K (d) 5,0kJ.
•••16 An air bubble of volume 20 cm3 is at the bottom of a lake
40 m deep, where the temperature is 4.0!C. The bubble rises to the
surface, which is at a temperature of 20!C.Take the temperature of
the bubble’s air to be the same as that of the surrounding water.
Just as the bubble reaches the surface, what is its volume?
•••17 Container A in Fig. 19-22
holds an ideal gas at a pressure of
5.0 " 105 Pa and a temperature of
300 K. It is connected by a thin tube
(and a closed valve) to container B,
with four times the volume of A.
Container B holds the same ideal
gas at a pressure of 1.0 " 105 Pa and
a temperature of 400 K. The valve is
opened to allow the pressures to equalize, but the temperature of
each container is maintained.What then is the pressure?
Module 19-3 Pressure, Temperature, and RMS Speed
•18 The temperature and pressure in the Sun’s atmosphere are
2.00 " 106 K and 0.0300 Pa. Calculate the rms speed of free elec-
trons (mass 9.11 " 10#31 kg) there, assuming they are an ideal gas.
•19 (a) Compute the rms speed of a nitrogen molecule at 20.0!C.
The molar mass of nitrogen molecules (N2) is given in Table 19-1.
At what temperatures will the rms speed be (b) half that value and
(c) twice that value?
•20 Calculate the rms speed of helium atoms at 1000 K. See
Appendix F for the molar mass of helium atoms.
•21 The lowestpossible temperature in outer space is 2.7 K.
What is the rms speed of hydrogen molecules at this temperature?
(The molar mass is given in Table 19-1.)
•22 Find the rms speed of argon atoms at 313 K. See Appendix F
for the molar mass of argon atoms.
••23 A beam of hydrogen molecules (H2) is directed toward a wall,
at an angle of 55! with the normal to the wall. Each molecule in the
beam has a speed of 1.0 km/s and a mass of 3.3" 10#24 g. The beam
strikes the wall over an area of 2.0 cm2, at the rate of 1023 molecules
per second.What is the beam’s pressure on the wall?
••24 At 273 K and 1.00" 10#2 atm, the density of a gas is 1.24"
10#5 g/cm3. (a) Find vrms for the gas molecules. (b) Find the molar
mass of the gas and (c) identify the gas. See Table 19-1.
Module 19-4 Translational Kinetic Energy
•25 Determine the average value of the translational kinetic en-
ergy of the molecules of an ideal gas at temperatures (a) 0.00!C
SSM
578 CHAPTER 19 THE KINETIC THEORY OF GASES
pressure of the air in the tires when its temperature rises to 27.0!C
and its volume increases to 1.67 " 10#2 m3? Assume atmospheric
pressure is 1.01 " 105 Pa.
•10 A container encloses 2 mol of an ideal gas that has molar
mass M1 and 0.5 mol of a second ideal gas that has molar mass 
M2 $ 3M1. What fraction of the total pressure on the container
wall is attributable to the second gas? (The kinetic theory explana-
tion of pressure leads to the experimentally discovered law of par-
tial pressures for a mixture of gases that do not react chemically:
The total pressure exerted by the mixture is equal to the sum of the
pressures that the several gases would exert separately if each were
to occupy the vessel alone. The molecule–vessel collisions of one
type would not be altered by the presence of another type.)
••11 Air that initially occupies 0.140 m3 at a
gauge pressure of 103.0 kPa is expanded isothermally to a pressure
of 101.3 kPa and then cooled at constant pressure until it reaches
its initial volume. Compute the work done by the air. (Gauge pres-
sure is the difference between the actual pressure and atmospheric
pressure.)
••12 Submarine rescue. When the U.S. submarine
Squalus became disabled at a depth of 80 m, a cylindrical cham-
ber was lowered from a ship to rescue the crew. The chamber
had a radius of 1.00 m and a height of 4.00 m, was open at the
bottom, and held two rescuers. It slid along a guide cable that a
diver had attached to a hatch on the submarine. Once the cham-
ber reached the hatch and clamped to the hull, the crew could es-
cape into the chamber. During the descent, air was released from
tanks to prevent water from flooding the chamber. Assume that
the interior air pressure matched the water pressure at depth h
as given by p0 % rgh, where p0$ 1.000 atm is the surface pres-
sure and r$ 1024 kg/m3 is the density of seawater. Assume a sur-
face temperature of 20.0!C and a submerged water temperature
of #30.0!C. (a) What is the air volume in the chamber at the sur-
face? (b) If air had not been released from the tanks, what would
have been the air volume in the chamber at depth h$ 80.0 m?
(c) How many moles of air were needed to be released to main-
tain the original air volume in the
chamber?
••13 A sample of an ideal gas is
taken through the cyclic process abca
shown in Fig. 19-20. The scale of the
vertical axis is set by pb$ 7.5 kPa and
pac$ 2.5 kPa. At point a, T $ 200 K.
(a) How many moles of gas are in the
sample? What are (b) the temperature
of the gas at point b, (c) the tempera-
ture of the gas at point c, and (d) the
net energy added to the gas as heat
during the cycle?
••14 In the temperature range 310 K to 330 K, the pressure p of a
certain nonideal gas is related to volume V and temperature T by
How much work is done by the gas if its temperature is raised from
315 K to 325 K while the pressure is held constant?
••15 Suppose 0.825 mol of an ideal gas undergoes an isothermal
expansion as energy is added to it as heat Q. If Fig. 19-21 shows the
final volume Vf versus Q, what is the gas temperature? The scale of
p $ (24.9 J/K) 
T
V
# (0.00662 J/K2)
T 2
V
.
WWWILWSSM
the vertical axis is set by Vfs$ 0.30 m3, and the scale of the horizon-
tal axis is set by Qs$ 1200 J.
Figure 19-21 Problem 15.
Vfs
0
Q (J)
Qs
V f
(m
3 )
pb
pac
1.0 3.0 
Volume (m3)
Pr
es
su
re
 (
kP
a)
 b
ca
Figure 19-22 Problem 17.
A
B
Figure 19-20 Problem 13.
17. O ar que inicialmente ocupa 0, 140m3 a` pressa˜o manome´trica de 103,0 kPa se expande
isotermicamente para uma pressa˜o de 101,3 kPa e em seguida e´ resfriado a pressa˜o constante
ate´ atingir o volume inicial. Calcule o trabalho realizado pelo ar.
Resp.: 5,60 kJ.
18. Suponha que 4,00 mols de um ga´s ideal diatoˆmico, com rotac¸a˜o molecular, mas sem os-
cilac¸a˜o, sofrem um aumento de temperatura de 60,0K em condic¸o˜es de pressa˜o constante.
Qual sa˜o (a) a energia transferida como calor; (b) A variac¸a˜o da energia interna do ga´s ;
(c) O trabalho realizado pelo ga´s (d) A variac¸a˜o da energia cine´tica de translac¸a˜o do ga´s?
Resp.: (a) 6,98 kJ; (b) 4,99 kJ; (c) 1,99 kJ; (d) 2,99 kJ.
19. Um certo g˚as ocupa um volume de 4,3 litros a uma pressa˜o de 1,2 atm e uma temperatura
de 310 K. Ele e´ comprimido adiabaticamente para um volume de 0,76 litros. Determine
(a) a pressa˜o final e (b) a temperatura final, supondo que γ = 1, 4.
Res.: 14 atm.
20. Um ga´s pode ser expandido de um estado inicial i para um estado final f ao longo de
duas poss´ıvel trajeto´rias 1 ou 2. A trajeto´ria 1 e´ composta de treˆs etapas: uma expansa˜o
isote´rmica com o mo´dulo do trabalho 40 J, uma expansa˜o adiaba´tica o mo´dulo do trabalho
de 20 J e outra expansa˜o isote´rmica de 30 J. A trajeto´ria 2 e´ composta de duas etapas:
uma reduc¸a˜o na pressa˜o a volume constante e uma expansa˜o a pressa˜o constante. Qual e´
a variac¸a˜o da energia interna do ga´s ao longo da trajeto´ria 2?
Resp.: -20 J.
21. O volume de um ga´s ideal e´ reduzido adiaba´ticamente de 200 litros para 74,3 litros. A
pressa˜o e o volume iniciais sa˜o 1,20 atm e 0, 200m3. A pressa˜o e temperatura iniciais sa˜o
1,00 atm e 300 K. A pressa˜o final e´ 4,00 atm. (a) o ga´s e´ monoatoˆmico, diatoˆmico ou
poliatoˆmico? (b) Qual e´ a temperatura final do ga´s? (c) Quantos moles existem no ga´s?
(d) Qual o trabalho realizado pelo ga´s?
Resp.: (a) diatoˆmico (b) 446 K (c) 8,10 mol.
22. Um ga´s ideal diatoˆmico, com rotac¸a˜o, mas sem oscilac¸o˜es, sofre uma compressa˜o adiaba´tica.
A pressa˜o e o volume iniciais sa˜o 1,20 atm e 0,200 m3. A pressa˜o final e´ 2,40 atm. Qual e´
o trabalho realizado pelo ga´s?
4
Problemas abrangentes
23. Um motor faz com que 1,00 mol de um ga´s ideal monoatoˆmico percorra o ciclo mostrado na
figura. O processo AB ocorre a volume constante, o processo BC e´ adiaba´tico e o processo
CA ocorre a pressa˜o constante. (a) Calcule o calor Q, a variac¸a˜o de energia interna e o
trabalho para cada um dos treˆs processos e para o ciclo como um todo. (b) Se a pressa˜o
inicial no 5 ponto A e´ 1,00 atm, encontre a pressa˜o e o volume nos pontos B e C. Considere
T1 = 300K, T2 = 600K e T3 = 455K.
Resp.:
581PROBLEMS
1.20 atm and 0.200 m3. Its final pressure
is 2.40 atm. How much work is done by
the gas?
•••63 Figure 19-27 shows a cycle un-
dergone by 1.00 mol of an ideal
monatomic gas. The temperatures are
T1! 300 K, T2! 600 K, and T3! 455
K. For 1: 2, what are (a) heat Q,
(b) the change in internal energy "Eint,
and (c) the work done W? For 2 : 3,
what are (d) Q, (e) "Eint, and (f) W?
For 3 : 1, what are (g) Q, (h) "Eint,
and (i) W? For the full cycle, what are (j) Q, (k) "Eint, and (l) W? The
initial pressure at point 1 is 1.00 atm (! 1.013# 105 Pa).What are the
(m) volume and (n) pressure at point 2 and the (o) volume and (p)
pressure at point 3?
Additional Problems64 Calculate the work done by an external agent during an
isothermal compression of 1.00 mol of oxygen from a volume of
22.4 L at 0$C and 1.00 atm to a volume of 16.8 L.
65 An ideal gas undergoes an adiabatic compression from 
p! 1.0 atm, V! 1.0# 106 L, T! 0.0$C to p! 1.0# 105 atm,
V! 1.0# 103 L. (a) Is the gas monatomic, diatomic, or polyatomic?
(b) What is its final temperature? (c) How many moles of gas are
present? What is the total translational kinetic energy per mole
(d) before and (e) after the compression? (f) What is the ratio of
the squares of the rms speeds before and after the compression?
66 An ideal gas consists of 1.50 mol of diatomic molecules that ro-
tate but do not oscillate. The molecular diameter is 250 pm. The gas is
expanded at a constant pressure of 1.50# 105 Pa,with a transfer of 200
J as heat.What is the change in the mean free path of the molecules?
67 An ideal monatomic gas initially has a temperature of 330 K
and a pressure of 6.00 atm. It is to expand from volume 500 cm3
to volume 1500 cm3. If the expansion is isothermal, what are (a) the
final pressure and (b) the work done by the gas? If, instead, the ex-
pansion is adiabatic, what are (c) the final pressure and (d) the
work done by the gas?
68 In an interstellar gas cloud at 50.0 K, the pressure is 
1.00 # 10%8 Pa. Assuming that the molecular diameters of the
gases in the cloud are all 20.0 nm, what is their mean free path?
69 The envelope and basket of a hot-air balloon have a
combined weight of 2.45 kN, and the envelope has a capacity (vol-
ume) of 2.18 # 103 m3. When it is fully inflated, what should be
the temperature of the enclosed air to give the balloon a lifting
capacity (force) of 2.67 kN (in addition to the balloon’s weight)?
Assume that the surrounding air, at 20.0$C, has a weight per unit
volume of 11.9 N/m3 and a molecular mass of 0.028 kg/mol, and is
at a pressure of 1.0 atm.
70 An ideal gas, at initial temperature T1 and initial volume
2.0 m3, is expanded adiabatically to a volume of 4.0 m3, then ex-
panded isothermally to a volume of 10 m3, and then compressed
adiabatically back to T1.What is its final volume?
71 The temperature of 2.00 mol of an ideal monatomic gas
is raised 15.0 K in an adiabatic process. What are (a) the work W
done by the gas, (b) the energy transferred as heat Q, (c) the
change "Eint in internal energy of the gas, and (d) the change "K in
the average kinetic energy per atom?
SSM
SSM
72 At what temperature do atoms of helium gas have the same
rms speed as molecules of hydrogen gas at 20.0$C? (The molar
masses are given in Table 19-1.)
73 At what frequency do molecules (diameter 290 pm) col-
lide in (an ideal) oxygen gas (O2) at temperature 400 K and pres-
sure 2.00 atm?
74 (a) What is the number of molecules per cubic meter in air at
20$C and at a pressure of 1.0 atm (! 1.01 # 105 Pa)? (b) What is
the mass of 1.0 m3 of this air? Assume that 75% of the molecules
are nitrogen (N2) and 25% are oxygen (O2).
75 The temperature of 3.00 mol of a gas with CV ! 6.00 cal/mol &K
is to be raised 50.0 K. If the process is at constant volume, what are
(a) the energy transferred as heat Q, (b) the work W done by
the gas, (c) the change "Eint in internal energy of the gas, and
(d) the change "K in the total translational kinetic energy? If the
process is at constant pressure, what are (e) Q, (f) W, (g) Eint,
and (h) "K? If the process is adiabatic, what are (i) Q, ( j) W,
(k) "Eint, and (l) "K?
76 During a compression at a constant pressure of 250 Pa, the
volume of an ideal gas decreases from 0.80 m3 to 0.20 m3. The ini-
tial temperature is 360 K, and the gas loses 210 J as heat. What are
(a) the change in the internal energy of the gas and (b) the final
temperature of the gas?
77 Figure 19-28 shows a hy-
pothetical speed distribution for
particles of a certain gas: P(v)! Cv2
for 0' v( v0 and P(v)! 0 for v)
v0. Find (a) an expression for C in
terms of v0, (b) the average speed of
the particles, and (c) their rms speed.
78 (a) An ideal gas initially at pressure p0 undergoes a free ex-
pansion until its volume is 3.00 times its initial volume. What then
is the ratio of its pressure to p0? (b) The gas is next slowly and adia-
batically compressed back to its original volume. The pressure af-
ter compression is (3.00)1/3p0. Is the gas monatomic, diatomic, or
polyatomic? (c) What is the ratio of the average kinetic energy per
molecule in this final state to that in the initial state?
79 An ideal gas undergoes isothermal compression from
an initial volume of 4.00 m3 to a final volume of 3.00 m3. There is
3.50 mol of the gas, and its temperature is 10.0$C. (a) How much
work is done by the gas? (b) How much energy is transferred as
heat between the gas and its environment?
80 Oxygen (O2) gas at 273 K and 1.0 atm is confined to a cubical
container 10 cm on a side. Calculate "Ug/Kavg, where "Ug is the
change in the gravitational potential energy of an oxygen molecule
falling the height of the box and Kavg is the molecule’s average
translational kinetic energy.
81 An ideal gas is taken through a complete cycle in three steps:
adiabatic expansion with work equal to 125 J, isothermal contraction
at 325 K, and increase in pressure at constant volume. (a) Draw a p-V
diagram for the three steps. (b) How much energy is transferred as
heat in step 3, and (c) is it transferred to or from the gas?
82 (a) What is the volume occupied by 1.00 mol of an ideal gas
at standard conditions — that is, 1.00 atm (! 1.01 # 10 5 Pa) and
273 K? (b) Show that the number of molecules per cubic centime-
ter (the Loschmidt number) at standard conditions is 2.69 # 109.
83 A sample of ideal gas expands from an initial pressureSSM
SSM
SSM
"
SSM
P(
v)
Speed
v00
Figure 19-28 Problem 77.
Volume
Pr
es
su
re
2
Adiabatic
31
Figure 19-27 Problem 63.
24. A figura mostra um cilindro que conte´m ga´s, fechado por um pista˜o mo´vel e submerso em
uma mistura de gelo-a´gua. Empurra-se o pista˜o para baixo rapidamente da posic¸a˜o 1 para
a posic¸a˜o 2. Mante´m-se o pista˜o na posic¸a˜o 2 ate´ que o ga´s esteja novamente a 0oC e, enta˜o,
ele e´ levantado lentamente de volta a` posic¸a˜o 1. A figura mostra tambe´m e´ um diagrama
pV para o processo. Se 122 g de gelo sa˜o derretidos durante o ciclo, quanto trabalho se
realizou sobre o ga´s?
Resp.: 9,71 kcal.
546 CHAPTER 18 TEMPERATURE, HEAT, AND THE FIRST LAW OF THERMODYNAMICS
there? The thermal conductivity of ice is 0.400 W/m!K, and the
density of liquid water is 1000 kg/m3.
79 A sample of gas expands from an initial pressure and
volume of 10 Pa and 1.0 m3 to a final volume of 2.0 m3. During the
expansion, the pressure and volume are related by the equation 
p " aV 2, where a " 10 N/m8. Determine the work done by the gas
during this expansion.
80 Figure 18-56a shows a cylinder containing gas and closed by a
movable piston.The cylinder is kept submerged in an ice–water mix-
ture.The piston is quickly pushed down from position 1 to position 2
and then held at position 2 until the gas is again at the temperature of
the ice–water mixture; it then is slowly raised back to position 1.
Figure 18-56b is a p-V diagram for the process. If 100 g of ice is
melted during the cycle, how much work has been done on the gas?
SSM
ple versus time t. The temperature scale is set by Ts"30 C and the
time scale is set by ts"20 min.What is the specific heat of the sample?
72 The average rate at which energy is conducted outward
through the ground surface in North America is 54.0 mW/m2, and
the average thermal conductivity of the near-surface rocks is 2.50
W/m !K. Assuming a surface temperature of 10.0 C, find the tem-
perature at a depth of 35.0 km (near the base of the crust). Ignore
the heat generated by the presence of radioactive elements.
73 What is the volume increase of an aluminumcube 5.00 cm on
an edge when heated from 10.0 C to 60.0 C?
74 In a series of experiments,
block B is to be placed in a ther-
mally insulated container with
block A, which has the same mass as
block B. In each experiment, block
B is initially at a certain tempera-
ture TB, but temperature TA of
block A is changed from experi-
ment to experiment. Let Tf repre-
sent the final temperature of the
two blocks when they reach thermal
equilibrium in any of the experi-
ments. Figure 18-53 gives temperature Tf versus the initial tem-
perature TA for a range of possible values of TA, from TA1" 0 K
to TA2" 500 K. The vertical axis scale is set by Tfs" 400 K. What
are (a) temperature TB and (b) the ratio cB/cA of the specific
heats of the blocks?
75 Figure 18-54 displays a closed
cycle for a gas. From c to b, 40 J is
transferred from the gas as heat.
From b to a, 130 J is transferred
from the gas as heat, and the mag-
nitude of the work done by the gas
is 80 J. From a to c, 400 J is trans-
ferred to the gas as heat. What is
the work done by the gas from a to
c? (Hint: You need to supply the
plus and minus signs for the given data.)
76 Three equal-length straight rods, of aluminum, Invar, and
steel, all at 20.0 C, form an equilateral triangle with hinge pins at
the vertices. At what temperature will the angle opposite the Invar
rod be 59.95 ? See Appendix E for needed trigonometric formulas
and Table 18-2 for needed data.
#
#
##
#
# sides of the icicle or down through the tip because there is no tem-
perature change in those directions. It can lose energy and freeze
only by sending energy up (through distance L) to the top of the
icicle, where the temperature Tr can be below 0 C.Take L" 0.12 m
and Tr"$5 C. Assume that the central tube and the upward con-
duction path both have cross-sectional area A. In terms of A, what
rate is (a) energy conducted upward and (b) mass converted from
liquid to ice at the top of the central tube? (c) At what rate does
the top of the tube move downward because of water freezing
#
#
Figure 18-53 Problem 74.
Tfs
0
TA1
TA (K)
TA2
T f
(K
)
c
p
V
ba
Figure 18-54 Problem 75.
Ice and 
water
(a)
V1V2
Volume
Pr
es
su
re
Start
(b)
1
2
Figure 18-56 Problem 80.
77 The temperature of a 0.700 kg cube of ice is decreasedSSM
81 A sample of gas under-
goes a transition from an initial state
a to a final state b by three different
paths (processes), as shown in the p-
V diagram in Fig. 18-57, where Vb"
5.00Vi. The energy transferred to
the gas as heat in process 1 is 10piVi.
In terms of piVi, what are (a) the en-
ergy transferred to the gas as heat in
process 2 and (b) the change in in-
ternal energy that the gas undergoes
in process 3?
82 A copper rod, an aluminum rod, and a brass rod, each of
6.00 m length and 1.00 cm diameter, are placed end to end with the
aluminum rod between the other two. The free end of the copper
rod is maintained at water’s boiling point, and the free end of the
brass rod is maintained at water’s freezing point. What is the
steady-state temperature of (a) the copper–aluminum junction
and (b) the aluminum–brass junction?
83 The temperature of a Pyrex disk is changed from 10.0 C
to 60.0 C. Its initial radius is 8.00 cm; its initial thickness is
0.500 cm. Take these data as being exact. What is the change in the
volume of the disk? (See Table 18-2.)
#
#SSM
SSM
pi/2
pi
3pi/2
Vi Vb
V
a
b
2
1
3
p
Figure 18-57 Problem 81.
Energy transfer 
Liquid coating 
(0°C)
Liquid water 
(0°C)
Tr
L
Figure 18-55 Problem 78.
to $150 C. Then energy is gradually transferred to the cube as#
heat while it is otherwise thermally
isolated from its environment. The
total transfer is 0.6993 MJ. Assume
the value of cice given in Table 18-3
is valid for temperatures from
$150 C to 0 C. What is the final
temperature of the water?
78 Icicles. Liquid water
coats an active (growing) icicle and
extends up a short, narrow tube along
the central axis (Fig. 18-55). Because
the water–ice interface must have a
temperature of 0 C, the water in the
tube cannot lose energy through the
#
##
25. Um ga´s ideal sofre uma compressa˜o isote´rmica de um volume inicial de 4,00 m3 para um
volume final de 3,00 m3. Existem 3,50 mol do ga´s e a sua temperatura e´ de 10,0 oC. (a)
Qual e´ o trabalho realizado pelo ga´s? Qual e´ a energia trocada como calo entre o ga´s e o
ambeinte?
Resp.: (a) -2,37 kJ
26. A figura mostra um ciclo composto de cinco trajeto´rias; AB e´ isote´rmica a 300 K, BC
e´ adiaba´tica com um trabalho 5,0 J, CD e´ uma compressa˜o isoba´rica de 5,0 atm, DE
e´ isote´rmica e EA e´ adiaba´tica com uma variac¸a˜o da energia interna de 8,0 J. Qual e´ a
variac¸a˜o da energia interna do ga´s ao longo da trajeto´ria CD?
Resp.: -3,0 J
5