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470 13 STATISTICAL THERMODYNAMICS
200 400 600 800 1 000
0.0
0.5
1.0
1.5
2.0
T/K
C
V
,m
/R
translation
rotation
vibration
Figure 13.17
�ese three contributions are compared in Fig. 13.17.
�e translational contribution to the standard molar entropy is given by
the Sackur–Tetrode equation [13E.9b–563]
STm = R ln( kTe
5/2
p−○Λ3
) Λ = h/(2πmkT)1/2
Taking the mass of CO as 28.01 mu and inserting the values of the other
constants gives
STm/R = ln[(46.8... K−5/2)T5/2]
�e rotational contribution to the entropy is given by [13E.11a–564] with
σ = 1
SRm/R = 1 + ln
kT
hcB̃
= 1 + ln T
θR
�e vibrational contribution to the standard molar entropy is given by
[13E.12b–564] (note that there is an error in the expression in the text:
the argument of the exponential term in the ln should be negative)
SVm/R =
θV/T
eθV/T − 1
− ln(1 − e−θV/T)
�ese three contributions are compared in Fig. 13.18.
P13E.14 �e partition function for a two-level system with energy spacing ε is
q = 1 + e−βε
An expression for the internal energy is given in Brief illustration 13C.1 on page
550
Um = NAε
eβε + 1