A heat engine operating according to the second law of thermodynamics rejects one fourth of the heat taken from a high temperature reservoir. What is the percentage efficiency of a heat engine?
Correct answer: D. 75%
- A. 100%
- B. 25%
- C. 50%
- D. 75%
Explanation
The percentage efficiency of a heat engine is given by:Efficiency = (Useful work output / Heat input) x 100%According to the second law of thermodynamics, some heat must be rejected to a low temperature reservoir during the operation of a heat engine. Let Qh be the heat taken from a high temperature reservoir, and Qc be the heat rejected to a low temperature reservoir. The net work output of the engine is given by:W = Qh - QcGiven that the engine rejects one-fourth of the heat taken from the high temperature reservoir, we can write:Qc = Qh/4Substituting this in the above equation for W, we get:W = Qh - Qh/4 = 3Qh/4The efficiency of the engine is therefore:Efficiency = (W / Qh) x 100%Efficiency = [(3Qh/4) / Qh] x 100%Efficiency = 75%Therefore, the correct option is D) 75%.
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About First Law of Thermodynamics
The first law relates heat supplied, work done and the change in internal energy through energy conservation. Problems use sign conventions and apply the law to isothermal, adiabatic, isobaric and isochoric processes. Internal energy is a state function, while heat and work depend on the path followed.
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