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Thermodynamics Part 5

Section: Physics

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Question : 16

Total: 49

A piston of mass M is hung from a massless spring whose restoring force law goes as F=−kx3, 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]

nrT‌ln(‌
L1
L0
)+Mg(L1−L0)+‌
k
4
(L14−L04)
3nrT‌ln(‌
L1
L0
)+2Mg(L1−L0)+‌
k
3
(L13−L03)
nrT‌ln(‌
L12
L02
)+‌
Mg
2
(L1−L0)+‌
k
4
(L14−L04)
nrT‌ln(‌
L1
L0
)+Mg(L1−L0)+‌
3k
4
(L14−L04)

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