Three Carnot engines operate in series between a heat source at temperature \(T_1\) and heat sink at a temperature \(T_4\). There are two other reservoirs at temperatures \(T_2\) and \(T_3\). The three engines are equally efficient, if (given that, \(\left.T_1>T_2>T_3>T_4\right)\)

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