4.3 Solutions 275
whereHis the enthalpy∴TΔS+VΔP= 0But by Problem 4.31TΔS=CPΔT−T(
∂V
∂T
)
PΔP
∴CPΔT+
[
V−T
(
∂V
∂T
)
P]
ΔP= 0
or ΔT=[
T
(∂V
∂T)
P−V
]
ΔP
CP
4.34 (a) For perfect gas
PV=RTP(
∂V
∂T
)
P=R
T
(
∂V
∂T
)
P=
TR
P
=V
orT(
∂V
∂T
)
P−V= 0
∴ΔT=0 by Problem 4.31(b) For imperfect gas
(
P+a
V^2)
(V−b)=RTorPV=RT−a
V+bP+ab
V^2
P(
∂V
∂T
)
P=R+
a
V^2(
∂V
∂T
)
P−
2 ab
V^3(
∂V
∂T
)
PRe-arranging
(
∂V
∂T)
P=
R
P−Va 2 +^2 Vab 3=
R
RT
V−b−2 a
V^2(
1 −Vb)
Multiplying both numerator and denominator of RHS by (V−b)/RT
(
∂V
∂T
)
P=(V−b)[
1 −
2 a
RT V^3(V−b)^2]− 1
=(V−b)[
1 +
2 a
RT V^3(V−b)^2