A heat engine operates between a hot reservoir at 500 K and a cold reservoir at 300 K. What is the maximum theoretical efficiency?

A heat engine operates between a hot reservoir at 500 K and a cold reservoir at 300 K. What is the maximum theoretical efficiency?

• A. 20%
• B. 40%
• C. 60%
• D. 80%

Answer: (B)

The maximum efficiency of any heat engine between two reservoirs is set by Carnot efficiency, which depends only on the temperatures of the hot and cold reservoirs. It’s given by eta_max = 1 − Tc/Th. Here, Th = 500 K and Tc = 300 K, so eta_max = 1 − 300/500 = 1 − 0.6 = 0.4, or 40%. That’s why the best choice is the one that shows 40%. Real engines never reach this value because of irreversibilities like friction and heat losses, but 40% is the theoretical limit for these temperatures.

The maximum efficiency of any heat engine between two reservoirs is set by Carnot efficiency, which depends only on the temperatures of the hot and cold reservoirs. It’s given by eta_max = 1 − Tc/Th.

Here, Th = 500 K and Tc = 300 K, so eta_max = 1 − 300/500 = 1 − 0.6 = 0.4, or 40%. That’s why the best choice is the one that shows 40%. Real engines never reach this value because of irreversibilities like friction and heat losses, but 40% is the theoretical limit for these temperatures.