Show that the efficiencies of the three Carnot engines, operating between the three reservoirs as illustrated in Figure 4-16, are related by n3 =1+n2-12 4-16 C₁ ➤ W₁ 1 Q2 Reservoir 2 Reservoir 1 Q2 W2 Q3 Reservoir 3 C3 W3 Q'3

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1 kg of a fluid expands reversibly according to a linear law from 4.5 bar to 1.6 bar; the initial and final volumes are 0.004 m3and 0.02 m3. The fluid is then cooled reversibly at constant pressure, and finally compressed reversibly according to a law pV = constant back to the initial conditions of 4.5 bar and 0.004 m3. Determine the work done in each process and the net work of the cycle. Sketch the cycle on a p-v diagram.

The efficiency of all real engines are less than that of the carnot engine. Why?