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4 November, 17:00

A completely reversible heat engine operates with a source at 1500 R and a sink at 500 R. If the entropy of the sink increases by 10 Btu/R, how much will the entropy of the source decrease? How much heat, in Btu, is transferred from the source?

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  1. 4 November, 17:20
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    Efficiency of reversible engine

    = (T₁ - T₂) / T₁, T₁ and T₂ be temperature of source and sink respectively

    = (1500 - 500) R / 1500R

    = 1000 / 1500

    = 2 / 3

    If Q₁ be heat extracted and Q₂ be heat dumped into sink

    efficiency = (Q₁ - Q₂) / Q₁

    given Q₂ / T₂ = 10

    Q₂ = 10 T₂ = 10 x 500R = 5000BTu

    Q₁ - 5000R / Q₁ = 2/3

    3Q₁ - 15000R = 2Q₁

    Q₁ = 15000BTu

    Q₂ = 5000 BTu

    Q₁ / T₁ = 15000R / 1500R

    = 10R

    Decrease in entropy of source = 10R.

    Heat transferred = Q₁ - Q₂

    = 15000 - 5000 BTu

    = 10000BTu

    =
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