# Equations of State

The ideal gas equation Pv = RT is a consequence of Clerk Maxwells, kinetic theory of gases. The following assumptions are made in kinetic theory.

(a) The molecules are perfectly elastic and rigid. Thus there is no loss of momentum during collisions of the molecules with the walls of the container.

(b) The volume occupied by the molecules themselves is negligible as compared to the volume of the gas.

(c) There are no inter molecular forces of attraction or repulsion.

When pressure is very small or temperature is very high the real gas obeys very closely the ideal gas equation.

But as pressure increases the point (c) is no longer valid. The intermolecular forces of attraction or repulsion increases, and also the point (b) is invalid. The volume of molecules are appreciable compared to the total gas volume.

For real gas the following equations are valid.

(1)  ( p + a / u2) ( u-b) = RT à van der waal’s equation

where (a / v2 ) takes into account for intermolecular forces of attraction and b is called

covolume taking account for volumes of molecules.

(2) p = RT / u-b – a / T u2  à bethelot’s equation

(3)  Dieterici’s equation

(4)  Redlich-Kwong’s equation

(5) Saha-Bose equation

(6) p = RT ( 1-e) / u2 ( u +B) – A /u2 àBeatlie-Bridgeman equation

Where                          A = A0 ( 1- a / u) , B = B0 ( 1- b /u) , e = C / uT3

A0, B0, a, b, c are constants.

Table 9.1. Vander Waals constants