Question

State the law of equipartition of energy.

Answer 1

Thermal Equilibrium:

1. Two systems are said to be in the state of thermal equilibrium when there is no net flow of thermal energy, that is heat, between them.
2. The thermal energy of these systems is equal to each other. Therefore, there is no heat flow.

Degree of freedom:

1. The degree of freedom can be defined as the number of ways the molecules of a gas can rotate, move or vibrate.

Law of equipartition of energy:

1. The law of equipartition of energy states that “For a system which is in thermal equilibrium, its total energy is divided equally among the degree of freedom.”

Example:

1. According to the kinetic theory of gases, the average kinetic energy of a molecule is given by the expression $KE=\frac{3}{2}kT$, where $k$ is Boltzmann's constant and $T$ is temperature.
2. Then for a monoatomic gas (for which the degree of freedom is 3), the energy associated with each degree of freedom per molecule is $\frac{1}{2}kT$, where $k$ is Boltzmann's constant and $T$ is temperature. Since, $K{E}_{perdegreeoffreedom}=\frac{{\displaystyle \frac{3}{2}}kT}{3}=\frac{1}{2}kT$.