Page 187 - Advanced Thermodynamics for Engineers, Second Edition

174 CHAPTER 8 EQUATIONS OF STATE

8.6 PROBLEMS

P8.1 The Dieterici equation for a pure substance is given by
<T a
p ¼ e <Tv
v b

Determine
(a) the constants a and b in terms of the critical pressure and temperature;
(b) the compressibility factor at the critical condition;
(c) the law of corresponding states.
2 2
4< T c <T c T R 1
a ¼ 2 ; b ¼ 2 ; z c ¼ 0:2707; p R ¼ exp 2 1
p c e p c e ð2v R 1Þ v R T R

vc v
P8.2 Derive expressions for for substances obeying the following laws:
vv T
a
<T
(a) p ¼ e <Tv
v b
<T a
(b) p ¼ 2
v b Tv
<T a c
(c) p ¼ þ 3 :
v b vðv bÞ v
Discuss the physical implication of the results.

2
pa 2a
; ;0
2 2
2 2 3
< v T v T
P8.3 The difference of specific heats for an ideal gas, c p;m c v;m ¼<. Evaluate the difference in
specific heats for gases obeying (1) the van der Waals and (2) the Dieterici equations of state.
Comment on the results for the difference in specific heat for these gases compared with the
ideal gas.
" , !#
2
2aðv bÞ
< 1 3
<Tv

P8.4 Derive an expression for the law of corresponding states for a gas represented by the following
expression:
<T a
p ¼ 2 :
v b Tv