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MHT CET · Physics · Kinetic Theory of Gases

We have a jar filled with gas characterized by parameters \(\mathrm{P}, \mathrm{V}, \mathrm{T}\) and another jar B filled with gas having parameters \(2 \mathrm{P}, \frac{\mathrm{V}}{4}, 2 \mathrm{~T}\), where symbols have their usual meaning. The ratio of number of molecules in jar A to those in jar B is

  1. A \(1: 1\)
  2. B \(1: 2\)
  3. C \(2: 1\)
  4. D \(4: 1\)
Verified Solution

Answer & Solution

Correct Answer

(D) \(4: 1\)

Step-by-step Solution

Detailed explanation

According to the gas equation, \(\mathrm{PV}=\mathrm{Nk}_{\mathrm{B}} \mathrm{T}\) For the first gas, we have,
\(\mathrm{PV}=\mathrm{N}_1 \mathrm{k}_{\mathrm{B}} \mathrm{T}\)
For the second gas, we have,
(2P) \(\left(\frac{\mathrm{V}}{4}\right)=\mathrm{N}_2 \mathrm{k}_{\mathrm{B}}(2 \mathrm{~T})\)
\(\mathrm{PV}=4 \mathrm{~N}_2 \mathrm{k}_{\mathrm{B}} \mathrm{T}\)
From equations (i) and (ii)
\(\mathrm{N}_1=4 \mathrm{~N}_2 \Rightarrow \frac{\mathrm{N}_1}{\mathrm{~N}_2}=4\)