An ideally efficient airplane engine provides work as heat flows from 1200 K burned gases to 280 K air. What fraction of the heat leaving th

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An ideally efficient airplane engine provides work as heat flows from 1200 K burned gases to 280 K air. What fraction of the heat leaving the burned gases is converted into work?

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Minh Khuê 4 years 2021-08-24T12:26:45+00:00 1 Answers 10 views 0

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  1. Jezebel
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    2021-08-24T12:28:27+00:00
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    Answer:

    The fraction of heat that is converted to work is 0.7667 or 76.67% of the heat of burned gases.

    Explanation:

    Given:

    Temperature of hot burned gases is, T_H=1200\ K

    Temperature of cold air is, T_C=280\ K

    Now, the efficiency of the airplane engine in terms of temperature is given as:

    \eta=\dfrac{T_H-T_C}{T_H}

    Plug in the given values and solve for \eta. This gives,

    \eta=\frac{1200-280}{1200}\\\\\eta=\frac{920}{1200}=0.7667

    Now, efficiency in terms of work and heat input is given as:

    \eta=\frac{Work}{Heat\ in}\\\\\eta=\frac{W}{Q_H}

    As input heat is from hot burned gases. So, Heat\ in=Q_H

    Now, plug in the given value of efficiency and express “Work” in terms of input heat, Q_H. This gives,

    0.7667=\frac{Work}{Q_H}\\\\Work=0.7667Q_H

    Therefore, the fraction of heat that is converted to work is 0.7667 or 76.67% of the heat of burned gases.

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