Question

A jar 'P' is filled with gas having pressure, volume and temperature P, V, T respectively. Another gas jar Q filled with a gas having pressure 2P, volume $\frac{V}{4}$ and temperature 2T. The ratio of the number of molecules in jar P to those in jar Q is

• A. 1:1
• B. 1:2
• C. 2:1
• D. 4:1

Hint:

Logic Tip: The proportionality $N \propto \frac{PV}{T}$ provides a rapid shortcut. For jar Q, $P$ is doubled ($\times 2$), $V$ is quartered ($\times \frac{1}{4}$), and $T$ is doubled ($\div 2$). So the modifier for $N_Q$ is $2 \times \frac{1}{4} \times \frac{1}{2} = \frac{1}{4}$. Therefore $N_P$ is 4 times larger than $N_Q$.

Answer 1

The Correct Option is D