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Question

One mole of an ideal gas is kept enclosed under a light piston (area =10−2m2) connected by a compressed spring (spring constant k=100 N/m). The volume of the gas is 0.83 m3 and its temperature is 100 K. The gas is slowly heated so that it compresses the spring further by 0.1 m. The work done by the gas in the process is
(Take R = 8.3 J/K−mole and suppose that there is no atmosphere)

A
3 J
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B
6 J
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C
9 J
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D
1.5 J
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Solution

The correct option is D 1.5 J
Work done by the gas = change in spring potential energy = 12k(x22x21)
Before heating, let the pressure of gas be P.
At equilibrium piston,
PA=kx1
x1=PAk=(nRTV)Ak=1×8.3×100×1020.83×100=101=0.1 m
Since during heating process, the spring is compressed further by 0.1 m
x2=0.2 m
work done by the gas =12.100(0.220.12)=12.100.(0.1)(0.3)=1.50=1.5 J
Since the gas is expanding, the work done by the gas is positive.

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