Isochoric Process

Work done by a gas is given by $W=\int PdV$, meaning it depends entirely on a change in volume. A rigid steel container fixes the volume, so $dV=0$ throughout the heating and the integral evaluates to zero regardless of how high the pressure climbs. Such a constant-volume process is called isochoric, and applying the First Law $$\begin{gathered} Q=\Delta \\ cup+W \end{gathered}$$ shows that all supplied heat goes directly into internal energy, $Q=\Delta U$. The option equating work to heat supplied describes an isothermal process, not this one. The option claiming negative work confuses rising pressure with compression, but no compression occurs because the walls do not move. The option $W=PV$ misapplies the constant-pressure work formula, which is invalid here since both pressure changes and volume stays fixed. A quick check confirms the result: no boundary of the gas displaces, so the gas exerts no net force through any distance, and zero displacement means zero work.