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Thermodynamics · Quick Reference
Heat Engines Cheat Sheet
In one line: a heat engine converts thermal energy into useful mechanical work — the foundational technology behind everything from steam locomotives to modern car engines.
Key Ideas
1How a Heat Engine Works. Absorbs heat from a hot reservoir, converts part of it into useful work, and expels the remaining heat to a cold reservoir, typically operating in a repeating cycle.
2Efficiency of a Heat Engine. Efficiency = (useful work output) / (heat input) = W/Qh, often expressed as a percentage.
3The Carnot Engine. An idealized, theoretically perfect heat engine that sets the maximum possible efficiency for any engine operating between two temperatures: efficiency_max = 1 - (Tc/Th), with temperatures in Kelvin.
4Why Real Engines Are Less Efficient. Friction, heat loss to the environment, and non-ideal gas behavior all reduce real engines below the theoretical Carnot efficiency limit.
5The Four-Stroke Engine Cycle. A common real-world heat engine cycle: intake, compression, power (combustion), and exhaust -- repeating continuously to produce mechanical work.
Worked Examples
A heat engine absorbs 1000 J of heat and produces 300 J of useful work. Find its efficiency.
0.3, or 30%
Find the maximum possible (Carnot) efficiency of an engine operating between a hot reservoir at 500K and a cold reservoir at 300K.
0.4, or 40%
Why can no real engine achieve 100% Carnot efficiency, even in theory?
Because a cold reservoir at absolute zero (Tc=0) is physically unattainable
Formulas
Efficiency = W/Qh
Carnot max efficiency = 1 - (Tc/Th)
Practice Yourself
A heat engine absorbs 500 J and produces 150 J of work. Find its efficiency.
0.3 or 30%
Find the Carnot efficiency between Th=600K and Tc=300K.
1-(300/600)=0.5 or 50%
What does a heat engine's efficiency measure?
The fraction of absorbed heat converted into useful work