In a Carnot engine between 1000 K and 400 K, what is the maximum efficiency?

In a Carnot engine between 1000 K and 400 K, what is the maximum efficiency?

• A. 30.0%
• B. 60.0%
• C. 70.0%
• D. 40.0%

Answer: (B)

The maximum efficiency of a Carnot engine depends only on the temperatures of the hot and cold reservoirs. It’s given by ηmax = 1 − Tc/Th, and the temperatures must be in Kelvin. Plugging in Th = 1000 K and Tc = 400 K: ηmax = 1 − 400/1000 = 1 − 0.4 = 0.60, or 60%. This is the theoretical upper bound for any engine operating between those two temperatures, because a Carnot cycle is reversible and thus achieves the maximum possible conversion of heat into work. The other percentages would require different temperature ratios: for example, 30% would need Tc/Th = 0.7 (Tc = 700 K with Th = 1000 K), 40% would need Tc = 600 K, and 70% would need Tc = 300 K. These don’t match the given temperatures.

The maximum efficiency of a Carnot engine depends only on the temperatures of the hot and cold reservoirs. It’s given by ηmax = 1 − Tc/Th, and the temperatures must be in Kelvin.

Plugging in Th = 1000 K and Tc = 400 K:

ηmax = 1 − 400/1000 = 1 − 0.4 = 0.60, or 60%.

This is the theoretical upper bound for any engine operating between those two temperatures, because a Carnot cycle is reversible and thus achieves the maximum possible conversion of heat into work.

The other percentages would require different temperature ratios: for example, 30% would need Tc/Th = 0.7 (Tc = 700 K with Th = 1000 K), 40% would need Tc = 600 K, and 70% would need Tc = 300 K. These don’t match the given temperatures.