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20 November, 13:39

A Carnot engine has an efficiency of 0.610, and the temperature of its cold reservoir is376 K. (a) Determine the temperature of its hotreservoir. (b) If 5320 J of heat is rejected to thecold reservoir, what amount of heat is put into the engine?

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  1. 20 November, 15:11
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    Answer: a) Th = 935.89 K, b) Qh = 13,241.8 J

    Explanation: efficiency of a carnot engine is given below as

    E = 1 - (Tc/Th)

    Where Tc = temperature at the cold reservoir and Th = temperature the hot reservoir.

    From the question, E = 0.610, Tc = 376k, Th = ?

    By substituting parameters, we have

    0.610 = 1 - (376/Th)

    (376/Th) = 1 - 0.610

    376/Th = 0.39

    376 = 0.39 * Th

    Th = 365/0.39

    Th = 935.89 K

    Question B)

    Heat transfer in a carnot engine is defined mathematically below as

    |Qc|/|Qh| = Tc/Th

    The modulus sign beside Qc and Qh denotes that their values can not be negative

    Qc = heat rejected at cold reservoir = 5320 J

    Qh = heat put into the engine = ?

    Tc = temperature at cold reservoir = 376 K

    Th = temperature at hot reservoir = 935.89 K.

    By substituting the parameters, we have that

    5320/Qh = 376/935.89

    By cross multiplication

    Qh*376 = 5320*935.89

    Qh = 5320*935.89/376

    Qh = 4,978,934.8/376

    Qh = 13,241.8 J
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