Two Carnot heat engines are operating in series such that the heat sink of the first engine serves as the heat source of the second on. If t

Question

Two Carnot heat engines are operating in series such that the heat sink of the first engine serves as the heat source of the second on. If the source temperature of the first engine is 1300 K and the sink temperature of the second engine is 300 K and the thermal efficiencies of both engines are the same, the temperature of the intermediate reservoir is

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Linh Đan 3 years 2021-09-05T06:22:57+00:00 1 Answers 21 views 0

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    2021-09-05T06:24:36+00:00

    Answer:

    the temperature of the intermediate reservoir is 624.5 K

    Explanation:

    Given the data in the question  

    The two Carnot heat engines are operating in series;

    [ T_H ]

      ↓

    ((1)) ⇒ W_{out

      ↓

    [ T_M ]

       ↓

     ((2)) ⇒ W_{out

    [ T_L ]

    The maximum possible efficiency for any heat engine is the Carnot efficiency;

    η_{rev = 1 – \frac{T_L}{T_H}

    the thermal efficiencies if both engines are the same will be;

    η_A = η_B

    1 –  \frac{T_M}{T_H} = 1 – \frac{T_L}{T_M}

    1 – 1 –  \frac{T_M}{T_H} = – \frac{T_L}{T_M}

    –  \frac{T_M}{T_H} = – \frac{T_L}{T_M}

    \frac{T_M}{T_H} =  \frac{T_L}{T_M}

    T_M² = T_L × T_H

    T_M = √(T_L × T_H)

    source temperature of the first engine T_H = 1300 K

    sink temperature of the second engine T_L = 300 K

    we substitute

    T_M = √(300 × 1300)

    T_M = √390000

    T_M = 624.4998 K ≈ 624.5 K

    Therefore, the temperature of the intermediate reservoir is 624.5 K

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