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23 January, 20:05

A Carnot engine is operated between two heat reservoirs at temperatures of 550 K and 300 K. 1.) If the engine receives 6.70 kJ of heat energy from the reservoir at 550 K in each cycle, how many joules per cycle does it reject to the reservoir at 300 K? 2.) How much mechanical work is performed by the engine during each cycle?

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  1. 23 January, 23:24
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    a) 3654.5 joules per cycle is rejected to the reservoir at 300 K by the Carnot Engine.

    b) Mechanical work performed by the engine during each cycle = 3045.5 J = 3.046 KJ

    Explanation:

    For a Carmot engine,

    (Q꜀/T꜀) + (Qₕ/Tₕ) = 0

    (Q꜀/T꜀) = - (Qₕ/Tₕ)

    Q꜀ = - T꜀ * (Qₕ/Tₕ)

    Qₕ = 6.70 KJ

    Tₕ = 550 K

    Q꜀ = ?

    T꜀ = 300 K

    Q꜀ = - 300 (6700/550) = - 3654.5 J = - 3.65 KJ

    b) Mechanical work done by the Carnot engine is given by

    W = |Qₕ| - |Q꜀| = 6700 - 3654.5 = 3045.5 J
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