Two different quasi-static processes, X and Y, take an ideal gas from the same initial state I to the same final state F.
• Process X first decreases the pressure at constant volume, then expands at low pressure to the final volume.
• Process Y first expands at the initial high pressure to the final volume, then decreases the pressure at constant volume to reach the final state.
On a PV diagram the two paths form the adjacent sides of a right-angled "L" shape, enclosing a finite area between them.
(a) Without performing a numerical calculation, state which process, X or Y, involves the greater magnitude of work done by the gas. Justify your answer in terms of the geometrical area under each path.
(b) Both processes start and end at the same thermodynamic states. Using that fact, compare the amounts of thermal energy transferred to the gas (heating) during processes X and Y. Provide a qualitative explanation grounded in the first law of thermodynamics and your result from part (a).