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

Question:

Three Carnot engines operate in series between a heat source at a temperature $\mathrm{T}_{1}$ and a heat sink at temperature $\mathrm{T}_{4}$ (see figure). There are two other reservoirs at temperature $\mathrm{T}_{2}^{4}$ and $\mathrm{T}_{3}$, as shown, with $\mathrm{T}_{1}>\mathrm{T}_{2}>\mathrm{T}_{3}>\mathrm{T}(4)$ The three engines are equally efficient if: 1. $\mathrm{T}_{2}=\left(\mathrm{T}_{1} \mathrm{~T}_{4}\right)^{1 / 2} ; \mathrm{T}_{3}=\left(\mathrm{T}_{1}^{2} \mathrm{~T}_{4}\right)^{1 / 3}$

2. $\mathrm{T}_{2}=\left(\mathrm{T}_{1}^{2} \mathrm{~T}_{4}\right)^{1 / 3} ; \mathrm{T}_{3}=\left(\mathrm{T}_{1} \mathrm{~T}_{4}^{2}\right)^{1 / 3}$

3. $\mathrm{T}_{2}=\left(\mathrm{T}_{1} \mathrm{~T}_{4}^{2}\right)^{1 / 3} ; \mathrm{T}_{3}=\left(\mathrm{T}_{1}^{2} \mathrm{~T}_{4}\right)^{1 / 3}$

4. $\mathrm{T}_{2}=\left(\mathrm{T}_{1}^{3} \mathrm{~T}_{4}\right)^{1 / 4} ; \mathrm{T}_{3}=\left(\mathrm{T}_{1} \mathrm{~T}_{4}^{3}\right)^{1 / 4}$

JEE Main Previous Year Single Correct Question of JEE Main from Physics Termodynamics chapter.

JEE Main Previous Year 10 Jan. 2019 I

Correct Option: 2

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