Two ideal Carnot engines operate in cascade (all heat given up by one engine is used by the other engine to…

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?
  1. T=2T1T2T1+T2
  2. T=T1+T22
  3. T=T1T2
  4. T=0

Solution

Q1: Heat input to Ist engine
Q: Heat rejected from Ist engine
Q2: Heat rejected from IInd engine
Work done by Ist engine = work done by IInd engine.
Q-Q2=Q1-Q
2Q=Q1+Q2
2=T1T+T2T
T=T1+T22

Asked in: JEE Main 2020 (07 Jan Shift 2)

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