Three Carnot engines operate in series between a heat source at a temperature T_{1} and a heat sink at temperature T_{4} (see figure). There are two other reservoirs at temperature T_{2} and T_{3} , as shown, with T_{1} > T_{2} > T_{3} > T_{4}. The three engines are equally efficient if :

(1) T_{2} = (T_{1} T_{4})^{1/2} ; T_{3} = (T_{1}^{2} T_{4})^{1/3}

(2) T_{2} = (T_{1} T_{4}^{2})^{1/2} ; T_{3} = (T_{1}^{2} T_{4})^{1/3}

(3) T_{2} = (T_{1}^{3}T_{4})^{1/4} ; T_{3} = (T_{1} T_{4}^{3})^{1/4}

(4) T_{2} = (T_{1}^{2} T_{4})^{1/3} ; T_{3} = (T_{1} T_{4}^{2})^{1/3}