Calculate the maximum theoretical efficiency of a heat engine operating between 600 K and 300 K.

Calculate the maximum theoretical efficiency of a heat engine operating between 600 K and 300 K.

• A. 0.25
• B. 0.50
• C. 0.75
• D. 1.00

Answer: (B)

The highest possible efficiency of a heat engine between two temperatures is given by the Carnot limit: ηmax = 1 − Tc/Th, where Th is the hot reservoir temperature and Tc is the cold reservoir temperature. With Th = 600 K and Tc = 300 K, ηmax = 1 − 300/600 = 1 − 0.5 = 0.5. So the maximum theoretical efficiency is 0.50 (50%). This is the upper bound for any engine operating between these two temperatures; real engines perform below this due to irreversibilities. The other numbers don’t fit the given temperatures under the Carnot limit.

The highest possible efficiency of a heat engine between two temperatures is given by the Carnot limit: ηmax = 1 − Tc/Th, where Th is the hot reservoir temperature and Tc is the cold reservoir temperature. With Th = 600 K and Tc = 300 K, ηmax = 1 − 300/600 = 1 − 0.5 = 0.5. So the maximum theoretical efficiency is 0.50 (50%). This is the upper bound for any engine operating between these two temperatures; real engines perform below this due to irreversibilities. The other numbers don’t fit the given temperatures under the Carnot limit.