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 .