GATE ME 2023 Set 1 — Question 42
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Thermodynamics → Laws & Properties → Work & Heat in Processes
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Question
Consider a fully adiabatic piston-cylinder arrangement as shown in the figure. The piston is massless and cross-sectional area of the cylinder is . The fluid inside the cylinder is air (considered as a perfect gas), with being the ratio of the specific heat at constant pressure to the specific heat at constant volume for air. The piston is initially located at a position . The initial pressure of the air inside the cylinder is , where is the atmospheric pressure. The stop is instantaneously removed and the piston moves to the position , where the equilibrium pressure of air inside the cylinder is . What is the work done by the piston on the atmosphere during this process?
Correct answer
(B) P₀ A(L₂ - L₁)
Solution
The work done by the piston on the atmosphere is the work done against the constant external atmospheric pressure .
The volume change of the atmosphere is .
Since the atmospheric pressure is constant, the work done on the atmosphere is:Note: Option D represents the work done by the gas inside the cylinder, not the work done on the atmosphere.
The volume change of the atmosphere is .
Since the atmospheric pressure is constant, the work done on the atmosphere is:Note: Option D represents the work done by the gas inside the cylinder, not the work done on the atmosphere.
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