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Question

Two containers A and B contain ideal gases, helium and oxygen respectively. Volume of both containers are equal, and pressure is also equal. Container A has twice the number of molecules than container B. If VA and VB represent the rms speed of gases in containers A and B respectively, then

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Solution

The correct option is **C** VAVB=2

As we know that the ideal gas is given by : PV=nRT

For A:PV=2nRTA…(1)

For B:PV=nRTB…(2)

Given that pressure and volume are same therefore,

from equations (1) and (2)khj

TB=2TA

RMS speed of gas is given by :

Vrms=√3RTM

VAVB=√3RTA4√3RTB32

VAVB=√3RTA4√3RTA32=2

VAVB=2

As we know that the ideal gas is given by : PV=nRT

For A:PV=2nRTA…(1)

For B:PV=nRTB…(2)

Given that pressure and volume are same therefore,

from equations (1) and (2)khj

TB=2TA

RMS speed of gas is given by :

Vrms=√3RTM

VAVB=√3RTA4√3RTB32

VAVB=√3RTA4√3RTA32=2

VAVB=2

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