Question

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

• A. $\frac{2}{3}{k}_{B}T$
• B. $\frac{3}{2}{k}_{B}T$
• C. $k_{B}T$
• D. $\frac{1}{2}{k}_{B}T$

Answer 1

The correct option is B $\frac{3}{2}{k}_{B}T$

As per Equi-partition law :

Each degree of freedom contributes
$\frac{1}{2}{k}_{B}T$ average energy.

In monoatomic gas, $D.O.F.=3$

$\Rightarrow \text{Average energy}=3\times \frac{1}{2}{k}_{B}T=\frac{3}{2}{k}_{B}T$

Hence, $\left(C\right)$ is the correct answer.