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Question

The molecules of a given mass of gas has r.m.s speed 400 m/s at 27 C and 105 N/m2 pressure . When the absolute temperature is doubled and the pressure is halved, the r.m.s. speed of the molecules of the same gas is

A
400 m/s
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B
2002 m/s
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C
4002 m/s
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D
1200 m/s
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Solution

The correct option is C 4002 m/s
According to ideal gas equation
PV=nRT
PVT= constant
Let,
P1,V1 and T1 as initial pressure, volume and temperature of gas respectively.
P2,V2 and T2 as final pressure, volume and temperatue of gas respectively.
P1V1T1=P2V2T2......(1)

We know that,
Pressure P=13MVv2rms
PV=13Mv2rms.......(2)
Where M= Molar mass, V= Volume
Also,
P1V1=M3v2rms(1)
P2V2=M3v2rms(2)

From eqn 1.
v2rms(1)T1=v2rms(2)T2
v2rms(2)=T2T1×v2rms(1)
vrms(2)=2T1T1×vrms(1)
[T2=2 T1]
vrms(2)=vrms(1)2 m/s=4002 m/s

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