GATE ME 2020 Set 2 — Question 62
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Thermodynamics → Laws & Properties → Work & Heat in Processes
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Question
Air is contained in a frictionless piston-cylinder arrangement as shown in the figure.
In the figure, the piston is initially below the free end of the spring, and the free end of the spring is below the stops. The atmospheric pressure is and the initial pressure of air in the cylinder is . The area of piston is . Heat is now added and the piston moves slowly from its initial position until it reaches the stops. The spring constant of the linear spring is . Considering the air inside the cylinder as the system, the work interaction is _______ J (round off to the nearest integer).
Correct answer
543 to 545
Solution
The air pushes the piston up slowly (quasi-static), so the work done by the air is .Stage 1 – piston rises 8 cm before touching the spring. The air pressure stays at its initial value (atmosphere + piston weight).Stage 2 – piston compresses the spring by 8 cm until it reaches the stops. Now , so(with , ).Total work done by the air:Answer: 544 J
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