1. Tardigrade
  2. Question
  3. Physics
  4. Two ideal Carnot engines operate in cascade (all heat given up by one engine is used by the other engine to produce work) between temperatures, T1 and T2 . The temperature of the hot reservoir of the first engine is T1 and the temperature of the cold reservoir of the second engine is T2 . T is temperature of the sink of first engine which is also the source for the second engine. How is T related to T1 and T2 , if both the engines perform equal amount of work?

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Q. Two ideal Carnot engines operate in cascade (all heat given up by one engine is used by the other engine to produce work) between temperatures, $T_{1}$ and $T_{2}$ . The temperature of the hot reservoir of the first engine is $T_{1}$ and the temperature of the cold reservoir of the second engine is $T_{2}$ . $T$ is temperature of the sink of first engine which is also the source for the second engine. How is $T$ related to $T_{1}$ and $T_{2}$ , if both the engines perform equal amount of work?

NTA AbhyasNTA Abhyas 2022

Solution:

$Q_{1}:$ Heat input to $I^{s t}$ engine
$Q:$ Heat rejected from $I^{s t}$ engine
$Q_{2}:$ Heat rejected from $II^{n d}$ engine
Work done by $I^{s t}$ engine $=$ work done by $II^{n d}$ engine.
$Q_{1}-Q=Q-Q_{2}$
$2Q=Q_{1}+Q_{2}$
$2=\frac{T_{1}}{T}+\frac{T_{2}}{T}$
$\text{T}=\frac{\text{T}_{1} + \text{T}_{2}}{2}$