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Q.

At a certain absolute temperature T, an ideal diatomic gas has total energy U.  Energy E is supplied to the gas and its temperature increases by t on Kelvin scale. If  an additional energy E is supplied to the gas, find the final temperature of the gas  on Kelvin scale.

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a

T+3t2

b

T+5t4

c

T+7t4

d

T+2t

answer is D.

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Detailed Solution

U=5nRT2   .....(1)U+E=5nR(T+t)2=5nRT2+5nRt2   ......(2)⇒E=5nRt2   ......(3)U+2E=5nRT+t+t′2=5nR(T+t)2+5nRt′2=U+E+5nRt′2   ......(4)⇒E=5nRt′2   ....(5)From (3) and (5),t'=tHence, final temperature of the gas is T+t+t'=T+2t .
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