A piston of mass \(M\) is hung from a massless spring whose restoring force law goes as \(\mathrm{F}=-\mathrm{kx}^3\), 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 \(\mathrm{L}_0\) to \(\mathrm{L}_1\), the total energy delivered by the filament is (Assume spring to be in its natural length before heating)

1. A \(3 n R T \ln \left(\frac{L_1}{L_0}\right)+2 \mathrm{Mg}\left(L_1-L_0\right)+\frac{k}{3}\left(L_1^3-L_0^3\right)\)
2. B \(n R T \ln \left(\frac{L_1^2}{L_0^2}\right)+\frac{M g}{2}\left(L_1-L_0\right)+\frac{k}{4}\left(L_1^4-L_0^4\right)\)
3. C \(n R T \ln \left(\frac{L_1}{L_0}\right)+M g\left(L_1-L_0\right)+\frac{k}{4}\left(L_1^4-L_0^4\right)\)
4. D \(n R T \ln \left(\frac{L_1}{L_0}\right)+M g\left(L_1-L_0\right)+\frac{3 k}{4}\left(L_1^4-L_0^4\right)\)