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Question

# A gas container as shown in figure has a piston-spring arrangement. The initial volume of gas is 0.5 m3. Pressure inside the cylinder is 200 kPa. Initially there is no spring force gas is heated to increase the volume by 2 times and final pressure is 600 kPa. Take extension to be linear. What percentage of work is done against the spring?

A
75%
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B
100%
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C
25%
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D
50%
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Solution

## The correct option is D 50%For linear relationship the p−V diagram for process in given Area (1) = work done against spring Area (2) = work done against atmosphere and weight of piston. ⇒Area (1) =12×(1−0.5)×400=100 kJ Area (2) = 200×(1−0.5)=100 kJ ⇒% of work against spring = Area(1)Area(1)+Area(2)×100=50%

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