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82 3 THE SECOND AND THIRD LAWS
Further raising the temperature to 298 K gives an increase in the entropy of
S−○m(298 K) − S−○m(234.4 K) = 6.85 JK−1mol
−1.
Further raising the temperature to the boiling point, the entropy increases by
S−○m(343.9 K) − S−○m(234.4 K) = 10.83 JK−1mol
−1. Finally, the contribution of
the second phase transition is
∆vapS−○m(343.9 K) =
∆vapH−○
m
Tb
= 6.050 × 10
4 Jmol−1
343.9 K
= 1.75... × 102 JK−1mol−1
�e�ird-Law standard molar entropy at 298 K is the sum of the above con-
tributions.
S−○m(298 K) − S−○m(0) = (1.54... J K−1mol−1) + (57.74 JK−1mol−1)
+ (9.90... J K−1mol−1) + (10.83 JK−1mol−1)
+ (1.75... × 102 JK−1mol−1)
= 256.0 JK−1mol−1 .
P3C.4 Assuming that the Debye extrapolation is valid, the constant-pressure molar
heat capacity is of a form Cp ,m(T) = aT3.�e temperature dependence of the
entropy is given by [3C.1a–92], S(T2) = S(T1) = ∫
T2
T1 (Cp ,m/T)dT . �us for a
given (low) temperature T the change in the molar entropy from zero is
Sm(T) − Sm(0) = ∫
T
0
Cp ,m
T ′
dT ′ = ∫
T
0
aT ′3
T ′
dT ′
= a∫
T
0
T ′2dT ′ = a
3
T3 = 1
3Cp ,m(T)
Hence
S−○m(10 K) − S−○m(0) = 1
3 × (2.09 JK−1mol−1) = 0.696... J K−1mol−1
�e change in entropy is determined calorimetrically by measuring the area
under a plot of (Cp ,m/T) against T , as shown in Fig. 3.2.