
The Clapeyron Equation 215
11.5 Temperature dependence of latent heats
That latent heats can be temperature dependent should not come as a surprise. In
fact that is the generic thermodynamic behaviour. On noting that l = T (s
2
−s
1
),and
∂
s
∂
T
P
=
c
P
T
, one finds
∂
l
∂
T
P
=
l
T
+ c
P
2
−c
P
1
(11.27)
Likewise,
∂
l
∂
P
T
= T
∂
(s
2
−s
1
)
∂
P
T
(11.28)
We now use one of the Maxwell relations,
∂
s
∂
P
T
= −
∂
v
∂
T
P
= −v
β
,where
β
stands for the volume expansion coefficient. Therefore,
∂
l
∂
P
T
= T(v
1
β
1
−v
2
β
2
) (11.29)
The total derivative of l wrt to T is therefore given by
dl
dT
=
∂
l
∂
T
P
+
∂
l
∂
P
T
dP
dT
(11.30)
Using the earlier expressions and the Clapeyron equation we arrive at the final result
for the ...