One mole of an ideal monoatomic gas is taken through a cycle a→b→c→a as shown in the figure. Find the difference between maximum and minimum values of internal energy of the gas during the cycle.
A
9P0V0
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B
6P0V0
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C
92P0V0
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D
3P0V0
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Solution
The correct option is C92P0V0 Let temperature in state ′a′ be T0. Temperature in state ′b′ will be 2T0. [∵PbVb=2PaVa] and temperature at state C is 4T0 [∵PcVc=4PaVa]
∵ temperature T is least at ′a′ and maximum at ′c′, Umin=Ua and Umax=Uc Thus, Umax−Umin=Uc−Ua=nCV(Tc−Ta) =1×3R2×(4T0−T0)=92RT0 =92P0V0[∵P0V0=RT0] Thus, option (c) is the correct answer.