Two reversible heat engines are connected in a series (looks like a hot reservoi

Question

Two reversible heat engines are connected in a series (looks like a hot reservoir at the top, heat engine 1 directly under, then heat engine 2 directly under that, then a cold reservoir at the bottom) These engines operate between a hot and cold reservoir as shown. The efficiencies of engines 1 and 2 are 0.75 and 0.5 respectively. Considering the two engines as one power system, what is the efficiency of the system?
also: the word "reversible" is underlined.

Explanation / Answer

For any reversible engine operating between hot source =Th and cold sink = Tc efficiency (eta, say e) is given by e= 1 - Tc/Th Assume that the 1st engine operates between hot side T1 and cold side Ti e1 = 1 - (Ti/T1) = 0.75 solving for T1 in terms of Ti=> T1 = 4* Ti (Solve the equation and check) second engine operates between hot side Ti and cold side T2. Important to note that cold side of first engine is the hot side for the second. e2= 1 - (T2/Ti) =0.5 Solve for T2 in terms of Ti=> T2 = 0.5 * Ti Now for an equivalent engine operating between hot side T1 and cold side T2 efficiency (net) => enet= 1 - (T2/T1) but T2 = 0.5 * Ti and T1 = 4*Ti Substituting in relationship for enet-> enet = 1 - (0.5 * Ti/ 4* Ti) => = 1 - (0.5/4) => = 1 - 0.125 => enet = net efficiency = 0.875 Note - 'Reversible' is underlined so that you can use the relationship for the carnot efficiency of an engine operating between given temperatures.

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