N molecules of an ideal gas at temperature T1 and pressure P1 are contained in a closed box. The molecules in the box gets doubled, Keeping total kinetic energy same. If new pressure is P2 and temperature is T2, Then:
A
P2=P,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 BP2=P1,T2=T12 K.E=12NkT=constant NT=constant⇒T∝1N
Hence final temperature is halved as N is doubled.
and K.E=f2PV=constant
For a closed container, V= constant. Hence pressure is also constant.