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

Answer 1

Answer: (C)

As per Equi-partition law :
Each degree of freedom contributes
$\frac{1}{2}{k}_{B}T$ Average Energy
In monoatomic gas D.O.F. $=3$
$\Rightarrow$ Average energy $=3\times \frac{1}{2}{k}_{B}T$
$=\frac{3}{2}{k}_{B}T$