Law of Equipartition of Energy: Overview, Questions, Preparation

The law of equipartition of energy is defined as the equal distribution of energy among the degrees of freedom for any dynamic system in thermal equilibrium.

Let us see the kinetic energy divided equally in a single molecule along the x-axis, y-axis, and z-axis.

1. X – Axis = ½ mvx2
2. Y-Axis = ½ mvy2
3. Z-Axis = ½ mvz2

The average kinetic energy when gas is at thermal equilibrium is represented as

1. X-Axis = (½ mvx2)
2. Y-Axis = (½ mvy2)
3. Z-Axis = (½ mvz2)

The average kinetic energy according to the kinetic theory of gases is represented as

= ½ mvrms2 = 3/2 KbT

Here, vrms is the square root of the velocity of the molecules,

The Boltzmann constant is denoted as Kb

And the T is the temperature of the gas.

Every molecule has three translational degrees of freedom for the molecule to move freely in space. Every molecule has three coordinates to specify the location in orbit. Likewise, if it is needed to move in a place, the molecule requires two translational degrees of freedom, and in the case of a straight line, it requires one translational degree of freedom. It varied from one molecule to another.

Similarly, if we talk about the triatomic molecule, it needs to possess 6 degrees of freedom. So, the per molecule kinetic energy of the gas is:

6 x N x ½ KbT = 3 x R / N N KbT = 3RT

Let us now take a different example to understand the concept of the degree of freedom deeper. The gases like helium and argon possess only one translational degree of freedom, so let us take a look at the equation of per molecule kinetic energy of the gas, which is as follows:

3 x N x ½ KbT = 3 x R / N N KbT = 3 / 2 RT

Similarly, some gases like oxygen (O2) and nitrogen (N2) have three translational degrees of freedom, but due to the 2-dimensional structure, only two translational degrees of freedom are considered.

The chapter 'Thermodynamics' holds a weightage of 8 marks as per the new CBSE pattern. It includes 3 questions, consisting of one objective type question of 1 mark, one very short question of 2 marks, and one long question of 5 marks.

Example 1: Write the value of gamma for polyatomic gas.

Answer: The value of gamma is y>1.

Example 2: Write the full form of kb

Answer: kb is the Boltzmann constant.

Example 3: State the meaning of vrms

Answer: The vrms is the square root of the velocity of the molecules.

Q: What do you mean by equipartition of energy?

Q: How can we find the degree of freedom?

Q: What is the formula of degree freedom?

Q: Explain the 3 degrees of freedom?

Q: What is the value of energy according to the law of equipartition of energy?