Three Carnot engines operate in series between a heat source at temperature $T_1$ and a heat sink at a temperature $T_4$. There are two other reservoirs at temperatures $T_2$ and $T_3$. If the three engines are equally efficient,find the values of $T_2$ and $T_3$ in terms of $T_1$ and $T_4$,given that $T_1 > T_2 > T_3 > T_4$.

• A
  $T_2 = (T_1 \cdot T_4)^{1/2}$ and $T_3 = (T_1^2 \cdot T_4)^{1/3}$
• B
  $T_2 = (T_1^3 \cdot T_4)^{1/4}$ and $T_3 = (T_1 \cdot T_4^3)^{1/4}$
• C
  $T_2 = (T_1^2 \cdot T_4)^{1/3}$ and $T_3 = (T_1 \cdot T_4^2)^{1/3}$
• D
  $T_2 = (T_1 \cdot T_4^2)^{1/3}$ and $T_3 = (T_1^2 \cdot T_4)^{1/3}$