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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 is P2 and temperature is T2, 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=T12P1V=NkT1 ....(1)P2V=2NkT2 .....(2)Dividing (2) by (1)P2P1=2T2T1 ....(3)Since KE remains same, N×32kT1=2N×32kT2 ⇒T2=T12 ....(4)Substituting (4) in (3)P2P1=1⇒P2=P1

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