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b c

Figure 2.2.1

The theorem of equipartition of energy states that molecules in thermal
equilibrium have the same average energy associated with each

independent degree of freedom of their motion and that the energy is
equal to

1
E  kT (2.2.1)
2

This principle was assumed to be exact in classical physics, but
quantum theory shows that it is true only in certain special cases.

Therefore, in classical physics average kinetic energy of molecule is
associated with f-degree of freedom. So, we may write it as

i
E  kT (2.2.2)
2

One mole of any substance consists of N (Avogadro number) molecules
A
,so internal energy of one mole of ideal gas is equal to

i
U  N A kT (2.2.3)
2

m
For ideal gas containing  moles
M

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