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Question

A vessel contains N molecules of a gas at temperature T. Now the number of molecules is doubled, keeping the total energy in the vessel constant. The temperature of the gas is.

A
T
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B
2T
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C
T2
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D
2T
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Solution

The correct option is C T2
We know that,
E=32nRT
Now,
E1=32nRT1...(i)
E2=322nRT2...(ii)
From equation (i) and (ii)
2E1=E2
Dividing equation (i) and (ii)
E1=32nRT1E2=322nRT2
E1E2=T12T2
Energy remainig constant in the vessel,
2=T1T2
Or
T2=T12
So, if the temperature taken is T instead of T1
Then, the final temperature becomes T2





















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