Question:
Gas at pressure P, temperature T, and volume V is filled in jar A. Another jar B is filled with gas having parameters \(2P\), \(\frac{V}{4}\), \(2T\). The ratio of number of molecules of jar B to those of jar A is
Gas at pressure P, temperature T, and volume V is filled in jar A. Another jar B is filled with gas having parameters \(2P\), \(\frac{V}{4}\), \(2T\). The ratio of number of molecules of jar B to those of jar A is
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Number of molecules is proportional to PV/T.
Updated On: Oct 1, 2026
- \(1:2\)
- \(1:4\)
- \(2:1\)
- \(4:1\)
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The Correct Option is B
Solution and Explanation
Step 1: Understanding the Concept:
From \(PV = NkT\), the number of molecules is \(N = \frac{PV}{kT}\), so \(N \propto \frac{PV}{T}\).
Step 2: Jar A:
\(N_A \propto \frac{PV}{T}\).
Step 3: Jar B:
\(N_B \propto \frac{(2P)(V/4)}{2T} = \frac{PV}{4T}\).
Step 4: Ratio:
\[ \frac{N_B}{N_A} = \frac{PV/4T}{PV/T} = \frac14 \]
So \(N_B : N_A = 1 : 4\).
Step 5: Why the other options are wrong.
1:2 results from forgetting the extra factor of \(\frac12\) from the doubled temperature. 2:1 and 4:1 are the inverted ratios.
Final Answer:
The ratio is 1:4, option (B). \[ \boxed{1:4} \]
From \(PV = NkT\), the number of molecules is \(N = \frac{PV}{kT}\), so \(N \propto \frac{PV}{T}\).
Step 2: Jar A:
\(N_A \propto \frac{PV}{T}\).
Step 3: Jar B:
\(N_B \propto \frac{(2P)(V/4)}{2T} = \frac{PV}{4T}\).
Step 4: Ratio:
\[ \frac{N_B}{N_A} = \frac{PV/4T}{PV/T} = \frac14 \]
So \(N_B : N_A = 1 : 4\).
Step 5: Why the other options are wrong.
1:2 results from forgetting the extra factor of \(\frac12\) from the doubled temperature. 2:1 and 4:1 are the inverted ratios.
Final Answer:
The ratio is 1:4, option (B). \[ \boxed{1:4} \]
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