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Kinetic Theory

JEE Main level, single correct, medium

43 of 168

Question 43 of 168

Same gas is filled in two vessels of the same volume at the same temperature. If the ratio of the number of molecules is $1:4$ , then
$A$ . The r.m.s. velocity of gas molecules in two vessels will be the same.
$B$ . The ratio of pressure in these vessels will be $1:4$ .
$C$ . The ratio of pressure will be $1:1$ .
$D$ . The r.m.s. velocity of gas molecules in two vessels will be in the ratio of $1:4$ .

Show answer and solution

Answer: (C) $A$ and $B$ only

The rms velocity of a gas is given by

{V}_{rms}=\sqrt{\dfrac{3RT}{M}}

. Therefore,

{V}_{rms}

is independent of number of moles, Hence, statement A is correct and D is incorrect.
According to the ideal gas equation

PV=nRT\Rightarrow P\propto n

\Rightarrow \dfrac{{P}_{1}}{{P}_{2}}=\dfrac{{n}_{1}}{{n}_{2}}=\dfrac{1}{4}

Hence, statement B is correct and C is incorrect.
Ans [

A&B

only are correct]

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