The Carnot cycle is usually represented on a pressure−volume diagram (Fig. 3A.8), but the four stages can equally well be represented on a temperature−entropy diagram, in which the horizontal axis is...

The Carnot cycle is usually represented on a pressure−volume diagram (Fig. 3A.8), but the four stages can equally well be represented on a temperature−entropy diagram, in which the horizontal axis is entropy and the vertical axis is temperature; draw such a diagram. Assume that the temperature of the hot source is Th and that of the cold sink is T_c, and that the volume of the working substance (the gas) expands from V_A
to V_B
in the first isothermal stage. (a) By considering the entropy change of each stage, derive an expression for the area enclosed by the cycle in the temperature−entropy diagram. (b) Derive an expression for the work done over the cycle.

Extracted text: Hot Stage 4 Stage 1 Cold Stage 3 Stage 2 Volume, V Figure 3A.8 The four stages which make up the Carnot cycle. In stage 1 the gas (the working substance) is in thermal contact with the hot reservoir, and in stage 3 contact is with the cold reservoir; both stages are isothermal. Stages 2 and 4 are adiabatic, with the gas isolated from both reservoirs. d 'eunssald