Law of equipartition of energy

Hello dear students, we have learnt that according to the kinetic theory of gases, the kinetic energy of gas molecules is given as,

We also know that the gas molecules are constraint to move in particular axes gives raise the concept of degree of freedom.

The number of degree of freedom of a system is defined as the total number of co-ordinates or the independent quantities required for describing the position of the system in motion.

When a particle moves along a straight line its position can be specified by its displacement along this direction. Hence such particle has one translational degree of freedom.

If the particle is moving in a plane its position at any instant can be determined by knowing the displacement of the particle along X and Y axis. Hence it has two transitional degrees of freedom.

While if the is moving in space, its position at any instant can be determined by knowing the displacement of the particle along X, Y and Z-axis. Hence such particle has three translational degrees of freedom.

Let’s discuss the law of equipartition of energy……………!

Consider the motion of gas molecules along X, Y and Z-axis moving with velocities vx,vy  and vz. Then the kinetic energies of particle along these axes will be given as,

From above equation we can conclude that, kinetic energy in its translational motion along X, Y and Z axes is distributed equally in all axes. This is known as law of equipartition of energy.

Hence law of equipartition of energy can be stated as,

“For any dynamical system in thermal equilibrium, the total energy is equally distributed amongst all degrees of freedom, and the energy associated with each molecule per degree of freedom is ½ KBT where KB is Boltzmann constant and T is temperature of the system.”

Some important points to remember……!

1.) For diatomic molecules, along with translational degrees of freedom it has rotational degrees of freedom too. Then the kinetic energy of the system is sum of its translational kinetic energy and rotational kinetic energy.

2.) For polyatomic molecules along with translational and rotational degrees of freedom, vibrational degrees too taken in consideration, hence the energy will be combination of translational kinetic energy, rotational kinetic energy and vibrational kinetic energy.

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