PHYSICAL CHEMISTRY IN BRIEF

CHAP. 3: FUNDAMENTALS OF THERMODYNAMICS [CONTENTS] 96

Solution

We use equation (3.75) which at constant temperature simplifies to

H(T, p) =H◦(T) +

∫p

0



V−T

(

∂V

∂T

)

p



dp.

From the given equation of state we express the volume

V=

nRT

p

+nB ,

its derivative with respect to temperature

(

∂V

∂T

)

p

=

nR

p

+n

dB

dT

and the expression

V−T

(

∂V

∂T

)

p

=n

(

B−T

dB

dT

)

,

which we substitute into the relation for the pressure dependence of enthalpy, and integrate

H(T, p) =H◦(T) +

∫p

0

n

(

B−T

dB

dT

)

dp=H◦(T) +n

(

B−T

dB

dT

)

p.

3.5.4 Entropy

3.5.4.1 Temperature and volume dependence for a homogeneous system

By integrating the total differential (3.48) with respect to the general prescription (3.30) we
obtain

S(T, V) =S(T 1 , V 1 ) +

∫T

T 1

CV(T, V 1 )

T

dT+

∫V

V 1

(

∂p

∂T

)

V

dV. (3.79)