Degree of Freedom

When a molecule can move around in three dimensions, we say that it has three degrees of freedom. If it can only move on a two-dimensional plane, it has two degrees of freedom, and if it moves in a straight line, it only has one degree of freedom.

To describe the motion of a molecule, we need to use coordinates like x and y, and velocity components like v_x and v_y. The number of coordinates or independent variables needed to fully describe the position and configuration of a system is known as its degree of freedom.

So, when a molecule has three degrees of freedom, we need three coordinates to describe its position and motion. When it has two degrees of freedom, we only need two coordinates, and when it has one degree of freedom, we only need one coordinate.

Kinetic Energy per Molecule

In this section, we will learn about Kinetic Energy Per Molecule for Triatomic and Monoatomic gaseous molecules.

Triatomic Molecule: In the case of a Triatomic Molecule the degree of freedom is 6 as given by formula 3N – k where N = 3 which number of atoms and k = 2 which is the number of independent relations between the atoms. Hence, kinetic energy per molecule for a triatomic gas molecule is given by

6 × N_a × 1/2K_bT = 3 x (R/N_a) × N_a × T = 3RT, {k_b = R/N_a}

Where,

• N – Avogadro Number,
• T – Temperature,
• R – Gas Constant, and
• K_b – Boltzman Constant.

Diatomic Molecule: From the formula 3N – k the degree of freedom for the diatomic molecule is 5 as independent relation, k is 1, and N = 2. Hence, kinetic energy per molecule for a diatomic gas molecule is given by

5 × N_a × 1/2KbT = 5/2 x (R/N_a) × N_a × T = 5/2RT

where symbols have usual meanings as mentioned above

Monoatomic Molecule: From the formula 3N – k the degree of freedom for the diatomic molecule is 3 as independent relation, k is 0, and N = 1. Hence, kinetic energy per molecule for a diatomic gas molecule is given by

3 × N_a × 1/2KbT = 3/2 x (R/N_a) × N_a × T = 3/2RT

where symbols have usual meanings as mentioned above

Law of Equipartition of Energy has many names such as Equipartition Theorem, Equipartition Principle, Law of Equipartition, or simply Equipartition and it describes the distribution of energy among the particles in a system that is at thermal equilibrium. The law of Equipartition of Energy tells us about how each degree of freedom of a particle in a system contributes to the average energy of the system. The Equipartition Theorem holds key significance in a wide range of fields of study, from thermodynamics and statistical mechanics to materials science and chemistry. This article covers the topic of the Law of Equipartition of Energy in varying detail.