During which of the following thermodynamic processes represented by a $PV$ diagram can the heat energy absorbed by the system be equal to the area under the $PV$ graph?

In an isothermal process,the volume of an ideal gas is halved. One can say that:

For the $P-V$ diagram given for an ideal gas,which of the following correctly represents the $T-P$ diagram?

Write the first law of thermodynamics for an isothermal process in an ideal gas.

The specific heat of an isothermal process is:

$A$ piston of mass $M$ is hung from a massless spring whose restoring force law is given by $F = -kx^3$,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 the lower part of the chamber,so that the piston moves up from a height $L_0$ to $L_1$. Calculate the total energy delivered by the filament. (Assume the spring to be in its natural length before heating.)