A gas is kept in a container having walls which are thermally non-conducting. Initially the gas has a volume of $800 \mathrm{~cm}^3$ and temperature $27^{\circ} \mathrm{C}$. The change in temperature when the gas is adiabatically compressed to $200 \mathrm{~cm}^3$ is:

(Take $\gamma=1.5 ; \gamma$ is the ratio of specific heats at constant pressure and at constant volume)

A piston of mass $M$ is hung from a massless spring whose restoring force law goes as $F=-k x^3$, 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)