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.
a. (i) Identify Path X and Path Y by naming the thermodynamic process occurring in each case.
b. (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.
c. (iii) On the same set of qualitative P–V axes, sketch both curves between the two states and label them clearly.
d. (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.