Question

Internal energy of $n_1$ moles of hydrogen at temperature T is equal to the internal energy of $n_2$ moles of helium at temperature $2T$. Then the ratio $n_1/n_2$ is:

• A. $\frac{3}{5}$
• B. $\frac{2}{3}$
• C. $\frac{6}{5}$
• D. $\frac{3}{7}$

Answer 1

The correct option is C $\frac{6}{5}$

We know,

Hydrogen has degree of freedom$=5$

Helium has degree of freedom$=3$

$U_H=\frac{5}{2}{n}_{1}RT$

$U_{He}=\frac{3}{2}{n}_{2}R2T$

$U_H=U_{He}$

$\frac{n_1}{n_2}=\frac{3\times 2}{5}$

$\frac{n_1}{n_2}=\frac{6}{5}$

Option $\text{C}$ is the correct answer