Project ForgeA fully adiabatic piston-cylinder arrangement has a massless piston of cross-sectional area A, initially restrained at position L1 with air inside at pressure P1≫P0 (atmospheric). The restraint is instantaneously removed and the piston moves to position L2, where it is caught by a second stop, with equilibrium air pressure P2≫P0 inside. What is the work done by the piston on the atmosphere during this process?
- A0
- P0·A(L2−L1)
- CP1·A·L1·ln(L1/L2)
- D(P2L2−P1L1)A/(1−γ)
Explanation
This is an irreversible (free-type) expansion where the piston pushes against a constant external atmospheric pressure P0, not against the internal gas pressure (since the process is not quasi-static). Work done on the atmosphere = external pressure × swept volume = P0·A·(L2−L1).
Source: GATE ME 2023 Official Paper (2023)
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