Question

The average thermal energy for a diatomic gas molecule is ($k_B$ is Boltzmann constant, $T$ is absolute temperature)

• A. $\frac{3}{2}{k}_{B}T$
• B. $2k_{B}T$
• C. $\frac{5}{2}{k}_{B}T$
• D. $k_{B}T$

Answer 1

The correct option is C $\frac{5}{2}{k}_{B}T$

Diatomic molecule has $3$ translational degrees of freedom. In addition it has $2$ rotational degrees of freedom.
Average thermal energy per degree of freedom
$=\frac{1}{2}{k}_{B}T$
Total average thermal energy
$=\text{degree of freedom}\times \frac{1}{2}{k}_{B}T$
$=5\times \frac{1}{2}{k}_{B}T$
$=\frac{5}{2}{k}_{B}T$