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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 ,

Options

  1. AT = 2 T 1 T 2 T 1 + T 2
  2. BT = T 1 + T 2 2
  3. CT = T 1 T 2
  4. DT = 0

Correct answer

B. T = T 1 + T 2 2

Step-by-step solution

Q 1 : Heat input to I s t engine Q : Heat rejected from I s t engine Q 2 : Heat rejected from I I n d engine Work done by I s t engine = work done by I I n d engine. Q - Q 2 = Q 1 - Q 2 Q = Q 1 + Q 2 2 = T 1 T + T 2 T T = T 1 + T 2 2

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