Question

What will be the average value of energy for a monoatomic gas in thermal equilibrium at temperature T?

(1) \(\cfrac23\)k_B T

(2) k_B T

(3) \(\cfrac32\)k_B T

(4) \(\cfrac12\)k_B T

Answer 1

Correct option is (3) \(\cfrac32\)k_B T

As per Equi-partition law :

Each degree of freedom contributes

\(\cfrac12\)k_B T Average Energy

In monoatomic gas D.O.F. = 3

⇒ Average energy = 3 x \(\cfrac12\)k_B T