Page 108 - Modern physical chemistry

98 Entropy and the Second Law

Differentiating the first of equations (5.85) with respect to T, the second with respect to
a~:T = [ ~~ l -[ ;! l· [5.86J
P, leads to

=
If we consider the entropy S to be a function of T and V, then

dS=(as) dT+[as) dV. [5.87J
aT v av T

Substituting this form into equation (5.76) yields
dE~~[:nv dT+[:a dV]-PdV [5.88J

But the coefficient of dV is
[~~l =T( ;~ l-p· [5.89J

Eliminating (aS/aV)T with relation (5.84),

( aE) = T(ap) _P, [5.90J
av T aT v
and (aPlaT)v with relation (4.86) yields

[;~lT =;T-P. [5.91 J

Substituting this result and (4.84) into (4.81) gives us

[5.92J

Example 5.6
Obtain (aElaV)T for an ideal gas. An ideal gas obeys the equation
P= nRT.

V
Differentiate this with respect to T at constant V,
nR

V'

and substitute into formula (5.90):

[ ;~ l = T n; -P = o.