PHYSICAL CHEMISTRY IN BRIEF

CHAP. 3: FUNDAMENTALS OF THERMODYNAMICS [CONTENTS] 98

3.5.4.3 Ideal gas.

For an ideal gas equation (3.79) simplifies to

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

∫T

T 1

CV◦(T)

T

dT+nRln

V

V 1

. (3.87)

Equation (3.83) becomes

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

∫T

T 1

Cp◦(T)

T

dT−nRln

p

p 1

. (3.88)

3.5.4.4 Changes at phase transitions

Entropy changes at a crystalline transformation, melting and boiling, ∆crystS ,∆fusSand ∆vapS
at reversible phase transitions are calculated using the relation

∆S=

∆H

T

, [T, p, reversible phase transition] (3.89)

where ∆His the enthalpy change at the given phase transition. For irreversible phase transi-
tions, we have the inequality

∆S >

∆H

T

, [T, p, irreversible phase transition] (3.90)

In this case the entropy change is calculated using the procedure described in3.5.9.

Example

Derive the relation for the dependence of entropy of a gas on temperature, volume and amount

of substance. Assume that the gas obeys the van der Waals equation of state [see2.2.6]

(

p+

a

Vm^2

)

(Vm−b) =RT ,

and that the temperature dependence of the molar isochoric heat capacity of an ideal gas can be

approximated using the relation

CV◦m=A+BT.