A piston of mass M is hung from a massless spring whose restoring force law goes as F=-k x³, where k is the spring constant of appropriate dimension. The piston separates the vertical chamber into two parts, where the bottom part is filled with ' n ' moles of an ideal gas. An external work is done on the gas isothermally (at a constant temperature T ) with the help of a heating filament (with negligible volume) mounted in lower part of the chamber, so that the piston goes up from a height L₀ to L₁, the total energy delivered by the filament is: (Assume spring to be in its natural length before heating) [3 Apr 2025 Shift 1]

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Examsnet · Accepted Answer

Correct Answer is : nrTln⁡(L1L0)+Mg(L1−L0)+k4(L14−L04)n r T ≤ft( L₁/L₀ ) + M g (L₁ - L₀) + k/4 (L₁^4 - L₀^4)nrTln(L0​L1​​)+Mg(L1​−L0​)+4k​(L14​−L04​)

Thermodynamics Part 5