Three Carnot engines operate in series between a heat source at a temperature T1 and a heat sink at temperature T4 (see figure). There are two other reservoirs at temperature T2 and T3 , as shown, with T1 > T2 > T3 > T4. The three engines are equally efficient if :
(1) T2 = (T1 T4)1/2 ; T3 = (T12 T4)1/3
(2) T2 = (T1 T42)1/2 ; T3 = (T12 T4)1/3
(3) T2 = (T13T4)1/4 ; T3 = (T1 T43)1/4
(4) T2 = (T12 T4)1/3 ; T3 = (T1 T42)1/3