Which of the following statements correctly describes engine efficiency?

• A. Efficiency can exceed 100% for devices that also generate energy.
• B. Efficiency is independent of the heat exchanged with reservoirs.
• C. Efficiency is 0 when no heat is transferred.
• D. Efficiency is defined as the useful work output divided by the heat input from the high-temperature reservoir.

Answer: (D)

The key idea is how we define the efficiency of a heat engine. It’s the fraction of the input heat that gets turned into useful work: η = W_out / Q_in. Since the engine also dumps some heat to the cold reservoir, W_out = Q_in − Q_out, so η = 1 − (Q_out / Q_in). This value is always ≤ 1 (and for real engines it’s less than 1), so it can’t exceed 100%.

That’s why the statement about exceeding 100% is not correct, and the claim that efficiency is independent of heat exchange is also false because efficiency depends on how much heat is transferred. Saying efficiency is zero when no heat is transferred isn’t the standard definition either, since without heat input the ratio W_out / Q_in is undefined.

The correct description matches the definition: efficiency is the useful work output divided by the heat input from the high-temperature reservoir. For example, if you input 100 J of heat and get 30 J of work, the efficiency is 0.30 (30%).