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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
\( \mathrm{P} \) temperature \( T_{2} \) and \( T_{3} \) as shown, with \( T_{1}T_{2}T_{3}T_{4} \).

W The three engines are equally efficient if [JEE (Main) 2019]
(a) \( T_{2}=\left(T_{1} T_{4}^{2}\right)^{1 / 3} ; T_{3}=\left(T_{1}^{2} T_{4}\right)^{1 / 3} \)
(b) \( T_{2}=\left(T_{1} T_{4}\right)^{1 / 2} ; T_{3}=\left(T_{1}^{2} T_{4}\right)^{1 / 3} \)
(c) \( T_{2}=\left(T_{1}^{3} T_{4}\right)^{1 / 4} ; T_{3}=\left(T_{1} T_{4}^{3}\right)^{1 / 4} \)
(d) \( T_{2}=\left(T_{1}^{2} T_{4}\right)^{1 / 3} ; T_{3}=\left(T_{1} T_{4}^{2}\right)^{1 / 3} \)
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