Problem # p038

Carnot efficiency, 2-step heating

A reversible power cycle, shown in the p-v diagram below, receives heat Q1 and Q2 from two different hot reservoirs at temperatures T1 and T2, respectively. Heat Q3 is discharged to a cold reservoir at temperature T3. The process 1-2 is an adiabatic, reversible compression while the processes 3-4 and 5-6 are adiabatic, reversible expansions.

  1. Derive an equation for the efficiency of this power cycle in terms of the temperature ratio T3/T1 and T3/T2 and the ratio of heats q = Q2/Q1.

  2. For the equation derived under 1) consider the limits of q=0, q = infinity and finally T1 = infinity