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27 February, 21:21

Suppose that a heat engine operates with a hot source at a temperature of 485 oC and a cold sink at 42 oC. What is the maximum amount of work the engine is capable of performing if 9.75 kJ of heat are extracted from the hot source?

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  1. 27 February, 23:20
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    W = - 10.5943 KJ, work is negative because it is carried out by the system towards the surroundings.

    Explanation:

    heat engine:

    ∴ Th = 485°C

    ∴ Tc = 42°C

    ∴ Qh = 9.75 KJ ... heat from hot source

    first law:

    ∴ ΔU = Q + W = 0 ... cyclic process

    ⇒ Q = - W

    ∴ Q = Qh + Qc = Qh - ( - Qc)

    ∴ Qc: heat from the cold source (-)

    ⇒ Qh - ( - Qc) = - W ... (1)

    ⇒ Qc/Qh = - Tc/Th ... (2)

    from (2):

    ⇒ Qc = - (Tc/Th) (Qh) = - (42°C/485°C) (9.75 KJ)

    ⇒ Qc = - 0.8443 KJ

    replacing in (1):

    ⇒ - W = 9.75 KJ - ( - 0.8443 KJ)

    ⇒ - W = 10.5943 KJ
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