A heat engine operates between a hot reservoir at 600 K and a cold reservoir at 300 K. What is its maximum theoretical efficiency?

• A. 40%
• B. 50%
• C. 25%
• D. 60%

Answer: (B)

The maximum efficiency of a heat engine between two thermal reservoirs is given by the Carnot limit: ηmax = 1 − Tc/Th. This value is reached only for a reversible cycle with no irreversibilities, meaning heat is transferred exactly at the two reservoir temperatures and there are no losses.

With Th = 600 K and Tc = 300 K, ηmax = 1 − 300/600 = 1 − 0.5 = 0.5, or 50%. So the highest possible efficiency for these reservoirs is 50%.

The other percentages would require different temperature ratios (for example, a higher Tc/Th ratio for 40% or 25%, or a lower one for 60%), which aren’t compatible with the given temperatures. In real machines, actual efficiency is lower due to irreversibilities and non-idealities.