Heat Engines — How They Work and Their Efficiency Limit
How heat engines turn fire into motion: the four-stroke cycle, steam turbines, Carnot's efficiency limit η = 1 − Tc/Th, and why waste heat is unavoidable.
Quick answer
A heat engine converts heat into mechanical work by letting heat flow from a hot reservoir to a cold one and skimming off work along the way. Efficiency is work output divided by heat input — always below 100% because some heat must be rejected.
Unit: Efficiency is unitless (often given as %)
Example: A power plant burns fuel to make 1000 J of heat, turns 400 J into electricity, and dumps 600 J into a cooling tower. Its efficiency is 40% — excellent for a heat engine.
What you will learn
- Describe the energy flow through a heat engine: hot reservoir → work + rejected heat
- State the thermal efficiency formula η = W/QH
- Apply Carnot's limit η = 1 − TC/TH with kelvin temperatures
- Explain the four strokes of an internal combustion engine
- Distinguish heat engines from electric motors regarding efficiency limits
Fire in, motion out, waste heat away
Every car, power plant, and jet is a deal with physics: feed it heat, and it returns motion — keeping a cut for itself as waste. A heat engine is any device that turns heat flowing from hot to cold into mechanical work.
The recipe never changes: burn or concentrate heat into a hot reservoir, let a working fluid (steam, air-fuel mix) expand and push something, then dump the leftover heat into a cold reservoir (air, river water, a cooling tower). Work is skimmed off in the middle.
Measuring efficiency
Efficiency is the scorecard — useful work divided by heat paid for:
Typical efficiencies: gasoline car 25–30%, diesel truck ~40%, combined-cycle gas plant ~60% (the best in the world), old steam locomotive under 10%.
Carnot's unbreakable ceiling
In 1824, young French engineer Sadi Carnot found the absolute ceiling — no engine, however perfect, can beat:
Maximum efficiency depends only on the two reservoir temperatures — not on the engine design, the fuel, or the working fluid.
Living with the limit
The message is stark: efficiency depends only on the two temperatures. To beat the limit you must burn hotter or cool colder — metallurgy and rivers set the practical bounds. A plant with steam at 600 K rejecting heat at 300 K caps at 50%; real ones reach the low 40s after friction and imperfections take their share.
Inside a car engine: four strokes
The gasoline engine in most cars runs the Otto cycle in four piston strokes:
- Intake — the piston drops, sucking in fuel-air mixture.
- Compression — the piston rises, squeezing the mixture to a fraction of its volume.
- Power — the spark plug fires; the explosion slams the piston down. This is the only stroke that does work.
- Exhaust — the piston rises again, pushing burnt gases out.
A flywheel smooths the pulses between power strokes. Diesel engines skip the spark plug, compressing air until injected fuel ignites on its own — higher compression means higher efficiency.
The engine in reverse: refrigeration
Run the cycle backward and you get a refrigerator: spend work to pump heat from cold to hot. Your fridge is a heat engine in reverse, and a heat pump warming a house in winter is the same idea scaled up — moving existing heat rather than making it, which is why heat pumps can deliver 3–4 joules of warmth per joule of electricity.
From steam locomotives to jet turbines, the story is one: heat wants to flow downhill, and clever machines tax that flow for motion.
Variables and units
| Symbol | Name | Unit | Meaning |
|---|---|---|---|
| Thermal efficiency | unitless or % | Fraction of heat converted to work | |
| Work output | J | Work output per cycle | |
| Heat input | J | Heat absorbed from hot reservoir | |
| Heat rejected | J | Heat rejected to cold reservoir | |
| Cold temperature | K | Cold reservoir absolute temperature | |
| Hot temperature | K | Hot reservoir absolute temperature |
Common mistakes
Waste heat is legally mandated by physics. The second law forces every heat engine to reject heat to a cold reservoir; even a perfect engine keeps only the Carnot fraction. Better engineering approaches the limit — it cannot pass it.
Power is work per second; efficiency is work per unit of fuel heat. A huge truck engine can be powerful yet inefficient, while a small hybrid engine sips fuel at higher efficiency.
Electric motors convert electrical energy directly to motion without a hot-to-cold heat flow, so Carnot's limit does not apply to them — that is why EVs can exceed 85% efficiency while combustion cars cannot.
Real-world applications
Coal and gas power stations: burn fuel to make steam, expand it through turbines, condense and repeat — the Rankine cycle electrifies the world.
Car engines: the four-stroke Otto cycle turns gasoline explosions into crankshaft rotation at 25–30% efficiency.
Jet engines: the Brayton cycle compresses air, burns fuel, and expands exhaust through a turbine for thrust.
Refrigerators and heat pumps: heat engines run in reverse, using work to move heat uphill — the same physics, opposite goal.
Frequently asked questions
What is a heat engine?
A heat engine takes heat from a hot reservoir, converts part of it into mechanical work, and rejects the rest to a cold reservoir. Cars, steam turbines, and jet engines are all heat engines.
How efficient are real engines?
Efficiency is useful work out divided by heat in: η = W/QH. Real car engines manage 25–30%, modern power plants 35–45%. The rest leaves as waste heat through exhausts and cooling towers.
Can any engine be 100% efficient?
No. The second law requires rejecting some heat to a colder reservoir every cycle. Even a perfect, frictionless engine is capped by Carnot's limit: η = 1 − TC/TH. Only an infinitely hot source or absolute-zero sink would allow 100%.
What are the four strokes of a car engine?
Intake (fuel-air mix enters), compression (piston squeezes it), power (spark ignites it, explosion drives the piston), exhaust (burnt gases leave). Only the power stroke produces work — the flywheel carries the engine through the other three.