Two vessels A and B are of the same size and are at same temperature. A contains 1 g of hydrogen and B contains 1 g of oxygen. P A and P B are the pressures of the gases in A and B respectively, then frac P A P B is :

Physics · Kinetic Theory of Gases

JEE Main 2024 — 29 January, Shift 1 — Question 48

Two vessels $A$ and $B$ are of the same size and are at same temperature. A contains 1 g of hydrogen and B contains 1 g of oxygen. $\mathrm{P}_{\mathrm{A}}$ and $\mathrm{P}_{\mathrm{B}}$ are the pressures of the gases in $A$ and $B$ respectively, then $\frac{\mathrm{P}_{\mathrm{A}}}{\mathrm{P}_{\mathrm{B}}}$ is :

Option A:
16
Correct
Option B:
8
Option C:
4
Option D:
32

Answer: A

Step-by-step solution

$\frac{\mathrm{P}_{\mathrm{A}} \mathrm{V}_{\mathrm{A}}}{\mathrm{P}_{\mathrm{B}} \mathrm{V}_{\mathrm{B}}}=\frac{\mathrm{n}_{\mathrm{A}} \mathrm{RT}_{\mathrm{A}}}{\mathrm{n}_{\mathrm{B}} \mathrm{RT}_{\mathrm{B}}}$

Given $V_{A}=V_{B}$

And $T_{A}=T_{B}$

$\frac{\mathrm{P}_{\mathrm{A}}}{\mathrm{P}_{\mathrm{B}}}=\frac{\mathrm{n}_{\mathrm{A}}}{\mathrm{n}_{\mathrm{B}}}$

$\frac{\mathrm{P}_{\mathrm{A}}}{\mathrm{P}_{\mathrm{B}}}=\frac{1 / 2}{1 / 32}=16$

Answer key and solution verified before publishing.

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Exam: JEE Main 2024
Paper: 29 January, Shift 1
Subject: Physics
Chapter: Kinetic Theory of Gases
Topic: Pressure of Gas and Different speeds of Gas Molecules