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