What is the degree of freedom? And what about the power-sharing principle?

If some molecules of gas are released into a closed container, surely the molecules will move around inside that container. Molecules can run along the length, width, or height of the container. That is, the molecule can move along three dimensions. The number of degrees along which molecules of an ideal gas can move is called its degrees of freedom.

Since the molecules of an atomic gas such as helium, neon, argon, etc. have only one molecule, we can think of them as a ball. These balls can move freely along three dimensions. So we say, an atomic gas has three degrees of freedom.

Now diatomic gases such as nitrogen, oxygen, etc. are joined by two atoms in one molecule. As we can imagine, two balls are connected by a rod. Since two atoms are connected here, we can think that their degrees of freedom will be three and six in total. But it is not. Due to being connected through bonds, a degree will be reduced between them both. That’s why two atoms individually two by two give a total of four and a common one together will give them a total of five dimensions. So the degrees of freedom of a diatomic gas will be five.

Similarly, triatomic gases will have seven degrees of freedom instead of nine. The energy along one degree of freedom of any molecule or atom is 1/2.KT. then,

The total energy of one atomic gas molecule = 3.1/2.KT
The total energy of molecules of diatomic gas = 5.1/2.KT
The total energy of molecules of tri-atomic gas = 7.1/2.KT

Thus the total energy of gas molecules is distributed equally along their degrees of freedom. It is called the principle of power-sharing.