Page 189 - Advanced thermodynamics for engineers

8.6 PROBLEMS 175

" #
8T R 3
p R ¼
3v R 1 T R v 2 R

P8.5 Show, for a gas obeying the state equation

pv ¼ð1 þ aÞ<T

where a is a function of temperature alone, that the specific heat at constant pressure is given
by

2
d ðaTÞ
c p ¼ <T ln p þ c p 0
dT 2

is the specific heat at unit pressure.
where c p 0
2

d ðaTÞ
c p ¼ <T 2 ln p þ c p 0
dT
P8.6 The virial equation of state is

b 2 b 3
pv ¼<T b 1 þ þ 2 þ :::::
v v

Compare this equation with van der Waals equation of state and determine the first two virial
coefficients, b 1 and b 2 , as a function of temperature and the van der Waals constants.
Determine the critical temperature and volume ðT c ; v c Þ for the van der Waals gas, and show that

v c 27T c
b 2 ¼ 1 :
3 8v c
½b 1 ¼ 1; b 2 ¼ðb a=<Tފ

P8.7 The equation of state for a certain gas is

pv AT
¼ 1 þ pe
<T

where A is constant.