Question

Two vessels of the same volume contain the same ideal gas at the same temperature. If the pressure in the vessels are in the ratio of 1 : 2, then

• A. The ratio of the average kinetic energies is 1 : 2
• B. The ratio of the root mean square velocities is 1 : 1
• C. The ratio of the average velocities is 1 : 2
• D. The ratio of the number of molecules is 1 : 2

Answer 1

Answer: (A), (B), (D)

The ratio of the number of molecules is 1 : 2

From ideal gas law, $PV=nRT$
Given, $V$ & $T$ are the same in both vessels.
$\Rightarrow \frac{P_1}{P_2}=\frac{n_1}{n_2}=\frac{1}{2}$ [given]

Ratio of rms velocities, $\frac{V_{rm{s}_1}}{V_{rm{s}_2}}=\sqrt{\frac{T_1}{T_2}}=1$

Ratio of average velocities, $\frac{V_{a{v}_1}}{V_{a{v}_2}}=\sqrt{\frac{T_1}{T_2}}=1$

& Ratio of average kinetic energies, $\frac{K_{a{v}_1}}{K_{a{v}_2}}=\frac{\frac{3}{2}{n}_{1}R{T}_1}{\frac{3}{2}{n}_{2}R{T}_2}=\frac{n_1}{n_2}\frac{T_1}{T_2}=\frac{1}{2}$

Therefore, options (a), (b) & (d) are correct.