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27 April, 08:37

A gas within a piston-cylinder assembly executes a Carnot power cycle during which the isothermal expansion occurs at TH = 1500 K and the isothermal compression occurs at TC = 290 K. Determine: (a) the thermal efficiency. (b) the percent change in thermal efficiency if TH increases by 5% while TC remains the same. (c) the percent change in thermal efficiency if TC decreases by 5% while TH remains the same. (d) the percent change in thermal efficiency if TH increases by 5% and TC decreases by 5%.

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  1. 27 April, 10:14
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    a) 80.67%

    b) 1.14%

    c) 1.19%

    d) 0.05%

    Explanation:

    The maximum efficiency in a heat engine is expressed as;

    1-Tc/Th

    where Tc=temperature of the cold 'sink

    Th=temperature of the heat reservoir

    Given that Tc=290 K and Th = 1500 K then;

    a) thermal efficiency = 1 - 290/1500 = 0.8067 = 80.67%

    b) Increasing TH by 5% will be 105/100 * 1500 = 1575 K

    New thermal efficiency = 1 - 290/1575 = 0.8159 = 81.59%

    Change in thermal efficiency = 0.8159-0.8067 = 0.0092

    Percentage change in thermal efficiency = change in thermal efficiency/initial thermal efficiency * 100

    0.0092 / 0.8067 * 100 = 1.14%

    c) Decrease TC by 5% = 95/100 * 290 = 275.5 K

    New thermal efficiency = 1-275.5/1500 = 0.8163 = 81.63%

    change in thermal efficiency = 0. 8163-0.8067 = 0.0096

    percent change in thermal efficiency = 0.0096/0.8067 * 100 = 1.19%

    d) If TH is increased by 5%, thermal efficiency is 0.8159 as in (b) above

    if TC is decreased by 5%, thermal efficiency is 0.8163 as in (c) above

    The change in thermal efficiency = 0.8163-0.8159 = 0.0004

    percent change in thermal efficiency = 0.0004/0.8067 * 100 = 0.05%
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