Heat Engines & Carnot Efficiency

Heat Engines & the Carnot Limit

A heat engine takes in heat from a hot source, turns part of it into useful work, and dumps the rest as waste heat into a cooler place. No engine — no matter how well built — can convert all of that heat into work; some always has to be thrown away. The best possible efficiency an engine could ever reach depends only on how hot and how cold its two reservoirs are.

η = 1 − T_c / T_h

• η — efficiency (—): the fraction of the heat energy the engine converts into useful work
• T_c — cold reservoir temperature (K): the temperature of the cold place where waste heat is dumped
• T_h — hot reservoir temperature (K): the temperature of the hot source supplying heat to the engine

A power plant's hot reservoir, steam, is at 400 kelvin, and its cold reservoir, river water, is at 300 kelvin. What is the best possible efficiency for an engine working between them?

• T_h = 400 K
• T_c = 300 K

1. η = 1 − T_c / T_h
2. η = 1 − 300 K / 400 K

η = 0.25 = 25%

A heat engine runs between a hot reservoir at 800 kelvin and a cold reservoir at 200 kelvin. What is its maximum possible efficiency?

• 25%
• 75%
• 50%

Which change would raise a heat engine's maximum possible efficiency?

• Raise the cold reservoir's temperature
• Lower the hot reservoir's temperature
• Lower the cold reservoir's temperature