JEE MAIN - Physics (2024 - 29th January Morning Shift - No. 15)
Two vessels $$A$$ and $$B$$ are of the same size and are at same temperature. A contains $$1 \mathrm{~g}$$ of hydrogen and $$B$$ contains $$1 \mathrm{~g}$$ of oxygen. $$\mathrm{P}_{\mathrm{A}}$$ and $$\mathrm{P}_{\mathrm{B}}$$ are the pressures of the gases in $$\mathrm{A}$$ and $$\mathrm{B}$$ respectively, then $$\frac{P_A}{P_B}$$ is:
4
32
8
16
Explanation
$$\begin{aligned}
& \frac{\mathrm{P}_{\mathrm{A}} \mathrm{V}_{\mathrm{A}}}{\mathrm{P}_{\mathrm{B}} \mathrm{V}_{\mathrm{B}}}=\frac{\mathrm{n}_{\mathrm{A}} R T_{\mathrm{A}}}{\mathrm{n}_{\mathrm{B}} \mathrm{RT}_{\mathrm{B}}} \\
& \text { Given } \mathrm{V}_{\mathrm{A}}=\mathrm{V}_{\mathrm{B}} \\
& \text { And } \mathrm{T}_{\mathrm{A}}=\mathrm{T}_{\mathrm{B}} \\
& \frac{\mathrm{P}_{\mathrm{A}}}{\mathrm{P}_{\mathrm{B}}}=\frac{\mathrm{n}_{\mathrm{A}}}{\mathrm{n}_{\mathrm{B}}} \\
& \frac{\mathrm{P}_{\mathrm{A}}}{\mathrm{P}_{\mathrm{B}}}=\frac{1 / 2}{1 / 32}=16
\end{aligned}$$
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