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
JEE MAIN 2019, Diffcult
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$n_{1}=n_{2}=n_{3}$
$\Rightarrow \quad 1-\frac{T_{2}}{T_{1}}=1-\frac{T_{3}}{T_{2}}=1-\frac{T_{4}}{T_{3}}$
$\Rightarrow \quad \frac{T_{2}}{T_{1}}=\frac{T_{3}}{T_{2}}=\frac{T_{4}}{T_{3}}$
$\Rightarrow \quad \mathrm{T}_{2} \mathrm{T}_{3}=\mathrm{T}_{1} \mathrm{T}_{4}$ and $\frac{\mathrm{T}_{3}^{2}}{\mathrm{T}_{2}}=\mathrm{T}_{4}$
Solve for $\mathrm{T}_{2}$ and $\mathrm{T}_{3}$
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