We have a jar filled with gas characterized by parameters P, V, T and another jar B filled with gas having parameters 2 P, V 4 , 2 ~T , where symbols have their usual meaning. The ratio of number of molecules in jar A

Correct answer: D. 4: 1 According to the gas equation, PV=Nk_ B T For the first gas, we have, PV=N_1 k_ B T For the second gas, we have, (2P) ( V 4 )=N_2 k_ B (2 ~T)PV=4 ~N_2 k_ B T From equations (i) and (ii) N_1=4 ~N_2 N_1 ~N_2 =4

JEE Main

Exam: JEE Main
Subject: Physics
Chapter: Kinetic Theory of Gases

JEE Main · Physics · Kinetic Theory of Gases

We have a jar filled with gas characterized by parameters P, V, T...

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

Options

A $1: 1$
B $1: 2$
C $2: 1$
D $4: 1$

Correct answer

D. $4: 1$

Step-by-step solution

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

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