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25 May, 14:40

One of the most efficient engines built so far has the following characteristics: combustion chamber temperature = 1900°C, exhaust temperature = 430°C, 7.0 * 109 cal of fuel produces 1.4 * 1010 J of work in one hour. (a) What is the actual efficiency of this engine? (b) What is the Carnot efficiency of the engine? (c) What is the power output, in hp, of this engine?

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  1. 25 May, 16:07
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    actual efficiency is 47.78 %

    Carnot efficiency is 67.65 %

    power output is 5.20 * 10^3 hp

    Explanation:

    given data

    temperature = 1900°C = 1900 + 273 K = 2173 K

    exhaust temperature = 430°C = 430 + 273 K = 703 K

    fuel = 7.0 * 10^9 cal

    work = 1.4 * 10^10 J

    to find out

    actual efficiency and Carnot efficiency and power output of engine

    solution

    first we find actual efficiency that is = work / heat input

    put the value and

    input energy = 7.0 * 10^9 cal (4.184 J/1 cal) = 29.29 * 10^9 J

    actual efficiency = 1.4 * 10^10 / (29.29 * 10^9)

    actual efficiency = 0.4778

    actual efficiency is 47.78 %

    and

    Carnot efficiency is = 1 - (703 / 2173)

    so Carnot efficiency is = 0.67648

    Carnot efficiency is 67.65 %

    and

    power output = work / time

    power output = 1.4 * 10^10 / 3600 sec

    power output = 3.88 * 10^6 W

    power output = 3.88 * 10^6 W / 746 hp

    so power output is 5.20 * 10^3 hp
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