Efficiency of a Heat Engine

Key Formulas

	η	efficiency	[no units]
	Tc	cold temperature	K
	Th	hot temperature	K

	η	efficiency	[no units]
	Wout	work done	Joules (J)
	Qin	heat energy used	Joules (J)

	TC	Celsius temperature	°C
	TK	Kelvin temperature	K

Tips to Remember

• Though efficiency has no units, it is typically expressed as a percent rather than a pure decimal. Thus, if η = 0.4, it would typically be written as 40%.
• If the percent efficiency is given as part of a problem, be sure to convert it to a decimal. For example, if the efficiency is given to be 34%, use 0.34 for η in your calculations.
• Make sure your temperatures are in Kelvins before using them in the first equation (the one with cold and hot temperatures). If you get a really strange answer, e.g., more than 100%, this is one of the first things to check.
• While the second equation (based on the output work) can apply to any heat engine, the first (with the cold and hot temperatures) applies specifically to ideal heat engines. This equation reflects the fact that even if you had no losses due to friction, etc., you still couldn’t get 100% efficiency because of the Second Law of Thermodynamics. That is, turning heat energy into useful work would make the universe more orderly—exactly what the Second Law says can’t happen.