Law of Equipartition of Energy: Kinetic Theory of Gases.

What does the Equipartition theorem say about energy distribution?

In classical statistical mechanics, the equipartition theorem relates the temperature of a system to its average energies. The equipartition theorem is also known as the law of equipartition, equipartition of energy, or simply equipartition. The original idea of equipartition was that, in thermal equilibrium, energy is shared equally among all of its various forms; for example, the average kinetic energy per degree of freedom in the translational motion of a molecule should equal that in rotational motion.

I don’t know what “degree of freedom” means for instance.

So at relatively low temperatures, the energy of the molecules, (by hitting off of each other) will mean they eventually have the same amount of energy as they travel between the 3 different basic directions, Vx, Vy and Vz.

The energy gets shared equally, given enough time because no particular direction or no particular orientation or no particular degree of freedom has any special preference over the other.

As the temperature increases, they begin to rotate about their axis, the Vx, Vy and Vz axis. Except for diatomic molecules, like O2, which only have two axes of rotation.

Then as the temperature increases even more and the molecules bounce off of each other harder, the bonds between the atoms vibrate, like the tiny springs and masses of a harmonic oscillator.

Image Source: University of Manchester

This chart shows you how the temperature affects the way in which the internal energy of the system is divided.

The energy is distributed among all the degree of freedom equally because when millions of molecules are moving in a container randomly then there will be collisions of all the kinds among the molecules and no particular direction, or no particular orientation, or no particular degree of freedom, will have any special preference over the other, so statistically and probabilistically, it is safe to assume that energy will be same in all the degree of freedoms and if it is same then we can say the total energy will be distributed equally among all the degree of freedoms. When we assume the law of equipartition of energy then it leads to several results that match with the reality i.e. data collected in various other scientific experimentation. The predictions made by it are true, so it’s reasonable to assume “Equipartition of Energy”. It’s an assumption but it makes the right predictions.

Further Readings: Degree of Freedom: What is the need for this concept?