Page 175 - Advanced thermodynamics for engineers

7.7 PROBLEMS 161

vc p <T
What is the value of of a gas which obeys the Clausius equation of state, p ¼ ?
vp v m b
T
P7.3 Show that if the ratio of the specific heats is 1.4, then

vp 7 vp
¼ :
vT 2 vT
s v

P7.4 Show that

!
vðf=TÞ vðg=TÞ
ðaÞ h u ¼ T 2
vT vT
v p
,
2 2
c p v g v f
ðbÞ ¼ 2 2 :
c v vT vT
p v
P7.5 Show

vv
ðaÞ Tds ¼ c p dT T dp
vT
p

vT vT
ðbÞ Tds ¼ c v dp þ c p dv
vp vv
v p

vh vv
ðcÞ ¼ v T :
vp vT
T p
P7.6 Show that, for a pure substance,

vs vs vs vv
¼ þ
vT vT vv vT
p v T p
and from this, prove that

vp vv
c p c v ¼ T :
vT vT
v p