Question

The total internal energy of one mole of rigid diatomic gas is

• A. $\frac{3}{2} R T$
• B. $\frac{7}{2} R T$
• C. $\frac{5}{2} R T$.
• D. $\frac{9}{2} R T$

Answer 1

Answer: (C)

A rigid diatomic molecule has $5$ degrees of freedom:
$3$ translational and $2$ rotational.
According to the law of equipartition of energy, the total internal energy of one mole of rigid diatomic gas is
$U=\frac{5}{2} k_{B} T \times N_{A}=\frac{5}{2} R T $
$\left(\because R=k_{B} N_{A}\right)$