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8 December, 13:38

A nuclear power plant operates at 79 percent of its maximum theoretical (Carnot) efficiency between temperatures of 700° and 330°C. If the plant produces electric energy at the rate of 1.3 GW, how much exhaust heat is discharged per hour?

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  1. 8 December, 15:38
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    T₁ = 700 + 273 = 973 k

    T₂ = 330 + 273 = 603 k

    Theoretical efficiency = T₁ - T₂ / T₁

    = (973 - 603) / 973

    =.38 OR 38%

    Operating efficiency =.79 x 38

    = 30.02 %

    Heat input Q₁, Heat output to sink Q₂, conversion into power = Q₁ - Q₂

    given Q₁ - Q₂ = 1.3 x 10⁹ W

    efficiency = Q₁ - Q₂ / Q₁

    Q₁ - Q₂ / Q₁ = 30.02 / 100

    100Q₁ - 100Q₂ = 30.02Q₁

    69.98 Q₁ = 100Q₂

    Q₁ = 1.429 Q₂

    Putting this in the relation

    Q₁ - Q₂ = 1.3 x 10⁹ W

    1.429Q₂ - Q₂ = 1.3 x 10⁹ W

    .429Q₂ = 1.3 x 10⁹

    Q₂ = 3.03 x 10⁹W

    = 3.03 GW.
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