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Question

# An ideal gas is found to obey an additional law VP2 = constant. The gas is initially at temperature T and volume V. When it expands to a volume 2V, the temperature becomes :

A
T2
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B
2T
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C
2T2
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D
4T
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Solution

## The correct option is A T√2We are given an ideal gas which is following an additional law,PV2= a constant ....................(1)As the gas is ideal, the gas law isPV=nRTTaking the value of P from the above equation, we getP=nRTVPutting this value in equation (1), we getnRT(V)2V= constantAs n and R are constant, above equation becomes,TV= a constant .....................(2)Now, the gas is expanding from initial volume V1 to final volume V2 by 2 units, it becomesV2=2V1From equation (2), we getT1V1=T2V2T1V1=T2(2V1)T2=T12So the correct answer is T2

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