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Question

One mole of an ideal monoatomic gas is taken through a cycle abca 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 C 92P0V0
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,
UmaxUmin=UcUa=nCV(TcTa)
=1×3R2×(4T0T0)=92RT0
=92P0V0 [P0V0=RT0]
Thus, option (c) is the correct answer.

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