# What will be the average value of energy along one degree

Question:

What will be the average value of energy along one degree of freedom for an ideal gas in thermal equilibrium at a temperature $\mathrm{T}\left(\mathrm{k}_{\mathrm{B}}\right.$ is Boltzmann constant)

1. (1) $\frac{1}{2} \mathrm{k}_{\mathrm{B}} \mathrm{T}$

2. (2) $\frac{2}{3} \mathrm{k}_{\mathrm{B}} \mathrm{T}$

3. (3) $\frac{3}{2} k_{\mathrm{B}} \mathrm{T}$

4. (4) $\mathrm{k}_{\mathrm{B}} \mathrm{T}$

Correct Option: 1

Solution:

(1)

Energy associated with each degree of freedom per molecule $=\frac{1}{2} \mathrm{k}_{\mathrm{B}} \mathrm{T}$.