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?

Fraction of the heat converted into work is 76.66%

Given that;

Efficient airplane engine provides work as heat TH = 1200 K

Burned gases heat TL = 280 K

Find:

Fraction of the heat converted into work

Computation:

Fraction of the heat converted into work = [(TH - TL) / TH]100

Fraction of the heat converted into work = [(1200 - 280) / 1200]100

Fraction of the heat converted into work = [(1200 - 280) / 12]

Fraction of the heat converted into work = [920 / 12]

Fraction of the heat converted into work = 76.66%

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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,

Temperature of cold air is,

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

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

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

As input heat is from hot burned gases. So,

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

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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