An engine has a heat input Q_H = 200 J and a heat expelled to the cold reservoir |Q_C| = 50 J. What is the efficiency?

An engine has a heat input Q_H = 200 J and a heat expelled to the cold reservoir |Q_C| = 50 J. What is the efficiency?

• A. 25%
• B. 75%
• C. 0.75
• D. 0.50

Answer: (B)

The efficiency of a heat engine is the useful work produced per unit heat absorbed. Here the work output is the difference between heat in and heat expelled: W = Q_H − |Q_C| = 200 J − 50 J = 150 J. Then η = W / Q_H = 150 J / 200 J = 0.75, which is 75%. An equivalent form is η = 1 − |Q_C|/Q_H = 1 − 50/200 = 0.75.

The efficiency of a heat engine is the useful work produced per unit heat absorbed. Here the work output is the difference between heat in and heat expelled: W = Q_H − |Q_C| = 200 J − 50 J = 150 J. Then η = W / Q_H = 150 J / 200 J = 0.75, which is 75%. An equivalent form is η = 1 − |Q_C|/Q_H = 1 − 50/200 = 0.75.