The ideal Rankine cycle can be analyzed in the limit where the difference between the boiler pressure (P + dP) and the condenser pressure (P) is infinitesimal. The cycle is indicated on the P–v...

The ideal Rankine cycle can be analyzed in the limit where the difference between the boiler pressure (P + dP) and the condenser pressure (P) is infinitesimal. The cycle is indicated on the P–v diagram and, alternatively, on the T–s diagram. See Fig. P.13. Show that the areas enclosed by the cycle on the two diagrams are equal and from this derive dP∕dT = s_fg∕v_fg. Next, consider the reversible heating process f–g in the boiler, invoke the first law and the second law, and show that h_fg
= Ts_fg
and dP∕dT = h_fg∕(Tv_fg).