1. Tardigrade
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  3. Physics
  4. Two Carnot engines A and B are operated in series. The first one, A receives heat at T1(.=600K.) and rejects to a reservoir at temperature T2. The second engine B receives heat rejected by the first engine and, in turn, rejects to a heat reservoir at T3(.=400K.). Calculate the temperature T2 if the work outputs of the two engines are equal

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Q. Two Carnot engines $A$ and $B$ are operated in series. The first one, A receives heat at $T_{1}\left(\right.=600K\left.\right)$ and rejects to a reservoir at temperature $T_{2}.$ The second engine $B$ receives heat rejected by the first engine and, in turn, rejects to a heat reservoir at $T_{3}\left(\right.=400K\left.\right).$ Calculate the temperature $T_{2}$ if the work outputs of the two engines are equal

NTA AbhyasNTA Abhyas 2020

Solution:

First case, $W=Q_{1}-Q_{2}$
Second case, $W=Q_{2}-Q_{3}$
Given $Q_{1}-Q_{2}=Q_{2}-Q_{3}$
$Q_{1}+Q_{3}=2Q_{2}$
$\frac{Q_{1}}{Q_{2}}+\frac{Q_{3}}{Q_{2}}=2$
$\frac{T_{1}}{T_{2}}+\frac{T_{3}}{T_{2}}=2\Rightarrow T_{2}=\frac{T_{1} + T_{3}}{2}=500K$