JEE Main · 2021 · 22 Jul 2021 · Shift 2 · Heat & Thermodynamics

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

(A) $\frac{3}{2} k_{B} T$ ✓ Correct
(B) $\frac{1}{2} k_{B} T$
(C) $k_{B} T$
(D) $\frac{2}{3} K_{B} T$

Answer: (A)

Solution

For a monoatomic gas in thermal equilibrium, by the equipartition theorem, each translational degree of freedom contributes

\frac{1}{2} k_{B} T

to the average energy.

A monoatomic gas has 3 translational degrees of freedom (motion in x, y, and z directions).

Therefore, the average energy per molecule is:

E_{avg} = 3 \times \frac{1}{2} k_{B} T = \frac{3}{2} k_{B} T

JEE Main · 2021 · 22 Jul 2021 · Shift 2 · Single correct option

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