Thermodynamics and Chemistry

CHAPTER 6 THE THIRD LAW AND CRYOGENICS

6.2 MOLARENTROPIES 153

0 50 100 150 200 250 300

0

10

20

30

40

50

60

70

T=K

Cp

;m

=J K

^1

mol

^1

0 50 100 150 200 250 300

0

0:1

0:2

0:3

0:4

0:5

T=K

C

p;

=m

T


=

J K

^2

mol

^1

(^0123456)
10
20
30
40
50
60
70
ln.T=K/
Cp
;m
=J K
^1
mol
^1
(^0050100150200250300)
50
100
150
200
T=K
Sm
=J K
^1
mol
^1
Figure 6.1 Properties of hydrogen chloride (HCl): the dependence ofCp;m,Cp;m=T,
and Sm on temperature at a pressure of 1 bar. The discontinuities are at a
solid!solid phase transition, the melting temperature, and the vaporization tempera-
ture. (Condensed-phase data from Ref. [ 60 ]; gas-phase data from Ref. [ 28 ], p. 762.)
temperature,T^00 , and the temperatureT^0 at which the molar entropy is to be evaluated.
Since the integral may be written in the form
ZT 0
T^00
Cp;m
T
dTD

ZTDT 0

TDT^00

Cp;md ln.T=K/ (6.2.6)

we may also evaluate the integral from the area under a curve ofCp;mplotted as a function
of ln.T=K/.
The procedure of evaluating the entropy from the heat capacity is illustrated for the
case of hydrogen chloride in Fig.6.1. The areas under the curves ofCp;m=T versusT,
and ofCp;mversus ln.T=K/, in a given temperature range are numerically identical (Eq.
6.2.6). Either curve may be used in Eq.6.2.2to find the dependence ofSmonT. Note how