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Question

A box contains N molecules of a perfect gas at temperature T1 and pressure P1. The number of molecules in the box is doubled keeping the total kinetic energy of the gas same as before. If the new pressure and temperature are P2 are T2 respectively, then

A
P2=P1,T2=T1
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B
P2=P1,T2=T12
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C
P2=2P1,T2=T1
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D
P2=2P1,T2=T12
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Solution

The correct option is B P2=P1,T2=T12
Initial and final conditions

Ui=Uf

N | 2N
T1 | T2
P1 | P2
v0 | v0

Ui=Uf (Given KE remains constant)

Nf2KT1=2Nf2KT2

T2=0.5T1

Pv=nRTNANA=NkT

PV is constant.

so P1v1=P2v2

P2=P1



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