QJEEM22Ph1e50: JEE Main 2022 Physics - Class 11 JEEM22Ph1e50 Solution: Same gas is filled in two vessels of the same volume at the…

Question

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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 $1 : 4$ .

Choose the correct answer from the options given below :

Accepted Answer

$v_{r m s} = \sqrt{\frac{3 R T}{M_{0}}}$ because T is same

v_rms will be same so, A is correct D is incorrect

$\frac{P_{1}}{P_{2}} = \frac{n_{1} R T_{1} / V_{1}}{n_{2} R T_{2} / V_{2}} = \frac{n_{1}}{n_{2}} = \frac{1}{4}$

B is correct

C is incorrect

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