Question:
Pressure-volume relation: jar A has \(V,T\); jar B has \(V/4,2T\). Find ratio of number of molecules.
Pressure-volume relation: jar A has \(V,T\); jar B has \(V/4,2T\). Find ratio of number of molecules.
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For gases: number of molecules \(N \propto \frac{PV}{T}\).
Updated On: Apr 23, 2026
- \(1:1\)
- \(1:2\)
- \(2:1\)
- \(4:1\)
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The Correct Option is D
Solution and Explanation
Concept:
\[
PV = NkT \Rightarrow N \propto \frac{PV}{T}
\]
Step 1: Jar A
\[ N_A \propto \frac{P_0 V}{T} \]
Step 2: Jar B
\[ N_B \propto \frac{2P_0 \cdot (V/4)}{2T} = \frac{P_0 V}{4T} \]
Step 3: Ratio
\[ N_A : N_B = \frac{P_0 V}{T} : \frac{P_0 V}{4T} = 4:1 \] Conclusion: \[ {(D)} \]
Step 1: Jar A
\[ N_A \propto \frac{P_0 V}{T} \]
Step 2: Jar B
\[ N_B \propto \frac{2P_0 \cdot (V/4)}{2T} = \frac{P_0 V}{4T} \]
Step 3: Ratio
\[ N_A : N_B = \frac{P_0 V}{T} : \frac{P_0 V}{4T} = 4:1 \] Conclusion: \[ {(D)} \]
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