270 4 Thermodynamics and Statistical Physics
δQ=Ldm (4)Ifν 1 andν 2 are the specific volumes (volumes per unit mass) of the liquid and
vapor respectively
δν=(ν 2 −ν 1 )dm (5)Using (4) and (5) in (3)
L
ν 2 −ν 1=T
(
∂P
∂T
)
V(6)
Here, various thermodynamic quantities refer to a mixture of the liquid and
vapor in equilibrium. In this case
(
∂P
∂T)
V=
(
∂V
∂T
)
sat
since the pressure is due to the saturated vapor and is therefore independent of
V, being only a function ofT. Thus (6) can be written as
(
∂P
∂T)
sat=
L
T(ν 2 −ν 1 )(Clapeyron’s equation) (7)4.25 L=T(ν 2 −ν 1 )
dP
dT
= 373 .2(1, 674 −1)×(
2. 71
76
)
× 1. 013 × 106
= 2. 255 × 1010 erg g−^1
= 2 .255 J/g
=2. 255
4. 18
= 539 .5 cal/g4.26
(
∂S
∂V
)
T=
(
∂P
∂T
)
V(1)
SubstitutedS=dU+PdV
T(2)
in (1)
(
∂U
∂V)
T=T
(
∂P
∂T
)
V−P (3)
Ifuis the energy density andPthe total pressure,(∂U
∂V)
=uand the total
pressureP=u/3, since the radiation is diffuse. Hence (3) reduces to