A sample of an ideal gas is taken quasistatically from an initial state A(1.0atm,2.0L) to a final state B(0.5atm,4.0L) by two different paths described below. In Path X the temperature of the gas remains constant, whereas in Path Y no heat enters or leaves the system during the change.
(i) Identify Path X and Path Y by naming the thermodynamic process occurring in each case.
(ii) Without performing detailed calculations, state which path involves a greater amount of work done by the gas between states A and B. Give one reason for your answer.
(iii) On the same set of qualitative P–V axes, sketch both curves between the two states and label them clearly.
(iv) At a common intermediate point (P,V) lying on both curves, which path has the larger magnitude of dVdP? Explain briefly using your sketch and the physical conditions of the processes.