Law of Equi-Partition of energy

Law of Equi-partition of energy
The law of equi-partition of energy is a principle in classical statistical mechanics that relates the temperature of a system to the average kinetic energy of its particles. According to this principle, in thermal equilibrium, each degree of freedom of a particle in a system has an average energy of kT/2, where k is Boltzmann constant and T is the temperature of the system.

To understand the Law of Equipartition of Energy, first we assume that the considered gas is in thermal equilibrium and it consists of molecules of negligible size and are hard spheres.

We will consider a monatomic gas and that the molecules of the gas can move randomly in the space in all directions.

Let v x, v y and vz be the velocities of a gas molecule on the x-axis, y-axis and z-axis respectively.

Then the translational kinetic energy of a single molecule is



The number of independent terms in the expression of energy of a molecule is called its degree of freedom. In the expression of translational kinetic energy, there are three terms that can be treated independently. So the degree of freedom of a molecule in the case of a monatomic gas is three. Note that each of the translational degrees of freedom corresponds to the motion of the molecule in a particular direction.


If the molecule is moving in space, then it can move in three directions. Hence, the molecule has three degrees of freedom. If the motion of the molecule is confined to a plane, then the molecule can move in two directions. Hence, the molecule has two degrees of freedom. If the motion of the molecule is confined to a line, then the molecule can move in one direction only. Hence, the molecule has one degree of freedom.


The degrees of freedom are associated only with the translational motion of a molecule. If a molecule has other modes of motion, it will have a greater number of degrees of freedom.


This law is applies to the systems of particles that are in thermal equilibrium, meaning that have reached a state of balance where the energy is evenly distributed throughout the system. In such a system, the total energy is shared equally among all the degrees of freedom of the particles, which include their translational motion, rotational motion and vibrational motion.

The law of equi-partition of energy is important in many areas of physics and chemistry, as it allows scientists to calculate the average energy of particles in a system and predict how that energy will be distributed among the different degrees of freedom. How ever, it is important to note that this law is only valid in the classical limit, where particles are treated as classical objects and quantum effects are negligible.

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