PHYSICAL CHEMISTRY IN BRIEF

CHAP. 3: FUNDAMENTALS OF THERMODYNAMICS [CONTENTS] 79

Solution

It is rather difficult to express explicitly molar volume using the van der Waals equation (it is an

algebraic equation of the third order, see the basic course on algebra). We therefore use relation

(3.28)

(

∂Vm

∂T

)

p

=−

(

∂p

∂T

)

( V

∂p

∂V

)

T

=−

R

Vm−b

−

RT

(Vm−b)^2

+

2 a

Vm^3

3.3.2 Total differential and state functions

All state functions (p, V, T, n, U, H, S, F, G, Cp, CV, f,.. .) have total differentials. Heat and
work are not state functions and they do not have any total differential.

Example

Prove that condition (3.26) holds for the pressure of an ideal gas as a function of temperature

and volume at a constant amount of substance.