Question

Ratio of rotational kinetic energy to the total kinetic energy for diatomic gas molecule at room temperature is :

• A. $2:5$
• B. $5:2$
• C. $3:2$
• D. $2:3$

Answer 1

The correct option is A $2:5$

According to law of equipartition of energy,
Energy associated with each molecule for each degree of freedom $E=\frac{1}{2}KT$

For diatomic gas,
Rotational degree of freedom $\left(f_r\right)=2$
$\therefore$ Rotation K.E. of each molecule $=2\times \frac{1}{2}KT$
For diatomic gas,
Total degree of freedom $f=5$
$\therefore$Total kinetic energy of each molecule $=5\times \frac{1}{2}KT$

$\therefore \frac{\text{Rotational energy}}{\text{Total energy}}=\frac{KT}{\frac{5}{2}\times KT}$
$\frac{\text{Rotational energy}}{\text{Total energy}}=\frac{2}{5}$