The degrees of freedom of a particle are the number of independent motions, which the particle can undergo, or the number of independent methods of gaining energy. It is denoted as `' f '`.

For an ideal gas average energy associated with its any molecule for each degree of freedom is `(KT)/2`
Where temperature T in kelvin.

Let f be the degree of freedom for a gas. Average energy associated with its any molecule `=(fKT)/2`

Total kinetic energy of a gas `= (NfKT)/2`

Kinetic energy of one mole of gas `= (fRT)/2`

For one mole `U=(fRT)/2`

`(fR)/2` is represented as `C_v`