Physics Question from JEE Main 2025 · 3 April, Shift 1

A piston of mass $M$ is hung from a massless spring whose restoring force law goes as $F = -kx^3$, 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 $L_0$ to $L_1$, the total energy delivered by the filament is (Assume spring to be in its natural length before heating)