Question

Two identical vessels are completely filled with two ideal gases A and B. If the ratio of mass of gas A to that of gas B is 1:2 and the ratio of rms speed of molecules of gas A to that of gas B is 2:1, the ratio of pressure exerted by molecules of gas B, on the walls of vessel to that by molecules of gas A is

• A. \(4:1\)
• B. \(2:1\)
• C. \(1:2\)
• D. \(1:4\)

Hint:

Pressure is proportional to mass times the square of rms speed when the volume is the same.

Answer 1

The Correct Option is C

Step 1: Understanding the Concept
From kinetic theory \(P=\dfrac{1}{3}\dfrac{M}{V}v_{rms}^2\). The vessels are identical, so \(P\propto Mv_{rms}^2\).

Step 2: Ratio for B to A
\(\dfrac{P_B}{P_A}=\dfrac{M_B}{M_A}\left(\dfrac{v_B}{v_A}\right)^2\)

Step 3: Substitute
\(\dfrac{M_B}{M_A}=2\) and \(\dfrac{v_B}{v_A}=\dfrac{1}{2}\), so \(\dfrac{P_B}{P_A}=2\times\dfrac{1}{4}=\dfrac{1}{2}\).

Final Answer:
The pressure ratio \(P_B:P_A\) is \(1:2\). \[ \boxed{\text{(C) }1:2} \]