Page 174 - Advanced thermodynamics for engineers

160 CHAPTER 7 GENERAL THERMODYNAMIC RELATIONSHIPS

shows that the coefficient of thermal expansion, b, is given by
2
Rv v b

b ¼ 2
3
RTv 2aðv bÞ
and the isothermal compressibility, k, is given by
2 2
v ðv bÞ
k ¼ 2
3
RTv 2aðv bÞ
2

vp vv
Also evaluate T for the van der Waals gas. From this find c p c v for an ideal gas,
vv vT
T p
stating any assumptions made in arriving at the solution.
P7.2 Prove the general thermodynamic relationship
2
vc p v v
¼ T
vp vT 2
T p
and evaluate an expression for the variation of c p with pressure for a van der Waals gas which
obeys a law
<T a
p ¼ ;
v m b v 2 m
where the suffix, m, indicates molar quantities and < is the Universal gas constant.
It is possible to represent the properties of water by such an equation, where

m bar m
3 2 3
a ¼ 5:525 2 ;b ¼ 0:03042 ; <¼ 8:3143 kJ=kmol K:
ðkmolÞ kmol
Evaluate the change in c p as the pressure of superheated water vapour is increased from
175 bar to 200 bar at a constant temperature of 425 C. Compare this with the value you would

expect from the steam tables abstracted below.

p [ 175 bar p [ 200 bar
3
3

t ( C) v (m /kg) h (kJ/kg) v (m /kg) h (kJ/kg)
425 0.013914 3014.9 0.011458 2952.9
450 0.015174 3109.7 0.012695 3060.1