Question

Explain in detail the law of equipartition of energy.

Answer 1

Hint: The equipartition theorem can be otherwise called as the law of equipartition or the equipartition of energy or simply equipartition. For a dynamical system in thermal equilibrium, the total energy of the system will be distributed or shared equally by all the degrees of freedom. This will help you in answering this question.

Complete step by step solution:
The equipartition theorem can be otherwise called as the law of equipartition or the equipartition of energy or simply equipartition. This law says that every degree of freedom which is appearing only quadratically in the total energy will be having an average energy of ${\displaystyle \frac{1}{2}}kT$in thermal equilibrium and this will be contributing ${\displaystyle \frac{1}{2}}k$ to the heat capacity of the system. The law of equipartition of energy says that for a dynamical system in thermal equilibrium, the total energy of the system will be distributed or shared equally by all the degrees of freedom. The energy which is in relation with each degree of freedom per molecule will be ${\displaystyle \frac{1}{2}}kT$, where $k$ be the Boltzmann’s constant. Let us consider an example. In the case of a monatomic molecule, each molecule will have $3$ degrees of freedom. According to the kinetic theory of gases, the mean kinetic energy of a molecule can be found to be as ${\displaystyle \frac{3}{2}}kT$. Therefore the law of equipartition of energy has been explained in detail.

Note: The degrees of freedom can be defined as the number of independent parameters that can describe its configuration or the state of a mechanical system. This body will have three independent degrees of freedom which will be composed of two components of the translation and one angle of rotation.