JEE Main & Advanced Physics Kinetic Theory of Gases Law of Equipartition of Energy

According to this law, for any system in thermal equilibrium, the total energy is equally distributed among its various degree of freedom. And each degree of freedom is associated with energy \[\frac{1}{2}kT\] (where \[k=1.38\times {{10}^{-23}}\,J/K\], T = absolute temperature of the system).

(1) At a given temperature T, all ideal gas molecules no  matter what their mass have the same average translational kinetic energy; namely, \[\frac{3}{2}kT.\] When measure the temperature of a gas, we are also measuring the average translational kinetic energy of it' s molecules.

(2) At same temperature gases with different degrees of freedom (e.g., He and \[{{H}_{2}}\]) will have different average energy or internal energy namely \[\frac{f}{2}kT.\] (f is different for different gases)

(3) Different energies of a system of degree of freedom f are as follows

(i) Total energy associated with each molecule  \[=\frac{f}{2}kT\]

(ii) Total energy associated with N molecules \[=\frac{f}{2}NkT\]

(iii) Total energy associated with \[\mu \] mole \[=\frac{f}{2}RT\]

(iv) Total energy associated with \[\mu \] molen \[=\frac{\,f}{2}\mu RT\]

(v) Total energy associated with each gram \[=\frac{f}{2}rT\]

(iv) Total energy associated with m gram \[=\frac{f}{2}mrT\]