A heat engine is a device that converts heat into mechanical work by operating through a repeating sequence of processes. It receives energy from a higher-temperature source, produces useful work, and rejects remaining energy to a lower-temperature sink. Steam engines, piston engines, and gas turbines are examples. Their operation is governed by thermodynamics, which establishes both energy balances and fundamental limits on conversion efficiency. (openstax.org)
Operating principles
A heat engine uses a working substance, commonly a gas or vapor, whose temperature, pressure, and volume change during operation. Heating and expansion allow the substance to exert forces on a piston or turbine blades. Some of the resulting work must support compression, pumping, or other processes required to sustain operation; the useful output is the net work remaining. In a closed cycle, the working substance returns to its initial thermodynamic state. (assets.openstax.org)
An idealized engine receives heat (Q_h) from a hot reservoir and rejects heat (Q_c) to a cold reservoir. Taking both quantities as positive magnitudes, the first law of thermodynamics gives
[ W_{\mathrm{net}}=Q_h-Q_c. ]
The working substance’s internal energy has no net change over a complete cycle. Its thermal efficiency is therefore
[ \eta=\frac{W_{\mathrm{net}}}{Q_h} =1-\frac{Q_c}{Q_h}. ]
This definition measures work output relative to heat input, not simply relative to all energy circulating within the machine. (openstax.org)
For a simple compressible substance undergoing a quasistatic cycle, net boundary work is represented by (\oint p,dV), the signed area enclosed on a pressure–volume diagram. Power is work delivered per unit time: increasing cycle frequency can increase power without necessarily increasing efficiency. (www1.grc.nasa.gov)
Thermodynamic limits
The second law of thermodynamics prohibits a cyclic engine whose sole effect is to absorb heat from one reservoir and convert it entirely into work. Heat rejection is therefore not merely a consequence of imperfect engineering. Even an ideal engine operating between two reservoirs at positive absolute temperatures must reject some heat. (openstax.org)
The limit can be expressed through entropy. Although the working substance returns to its initial entropy after each cycle, the total entropy change of the engine and its surroundings cannot be negative. For two reservoirs,
[ \frac{Q_c}{T_c}-\frac{Q_h}{T_h}\geq 0. ]
Equality holds for a fully reversible process; irreversible operation generates entropy and reduces the attainable work output. (openstax.org)
The Carnot cycle, proposed by Sadi Carnot in 1824, provides the reversible benchmark. It consists of two constant-temperature processes and two reversible adiabatic processes, during which no heat is transferred. Its efficiency is
[ \eta_{\mathrm{Carnot}}=1-\frac{T_c}{T_h}, ]
with temperatures measured in kelvins. No engine operating between the same two constant-temperature reservoirs can exceed this efficiency. The result depends on reservoir temperatures, not on the working substance. (openstax.org)
For example, reservoirs at 600 K and 300 K imply a maximum efficiency of 50%. Raising the source temperature or lowering the sink temperature raises the theoretical ceiling, but does not specify the efficiency of a real engine. (openstax.org)
Principal designs and cycles
Heat engines differ in how heat reaches the working substance and how expansion produces work. A steam engine receives heat through a boiler, whereas an internal combustion engine releases fuel energy within its working gas. Idealized cycles describe their thermodynamic behavior without reproducing every detail of actual combustion or fluid flow. (openstax.org)
- Steam power systems: A steam turbine commonly operates within a Rankine cycle. A pump pressurizes liquid water, a boiler heats it into steam, the steam expands through a turbine, and a condenser returns it to liquid. This separates heat addition, expansion, heat rejection, and pumping among distinct components. (arxiv.org)
- Spark-ignition piston engines: The Otto cycle models compression and expansion with idealized constant-volume heat addition and rejection. Actual engines also require intake and exhaust processes and experience finite combustion times and mechanical losses. (www1.grc.nasa.gov)
- Gas turbines: The Brayton cycle models compression, approximately constant-pressure heat addition, expansion, and heat rejection. A gas turbine contains a compressor, combustor, and turbine; part of turbine output drives the compressor. Practical open-flow machines admit fresh air and discharge exhaust rather than recirculating the same gas. (grc.nasa.gov)
Practical performance and related devices
Real engines fall below reversible limits because of friction, imperfect compression and expansion, pressure losses, and heat transfer across finite temperature differences. Higher operating temperatures can improve efficiency, but turbine materials and cooling requirements constrain their use. Shaft output may drive machinery directly or operate an electric generator. (www1.grc.nasa.gov)
A combined-cycle power plant uses gas-turbine exhaust to generate steam for additional power production. It extracts further work from energy that would otherwise leave in the exhaust; it does not remove the thermodynamic requirement for heat rejection. (eia.gov)
A heat pump or refrigerator performs the complementary task: it consumes work to transfer heat from a colder region to a warmer one. Its coefficient of performance compares heat moved with work consumed, rather than using heat-engine efficiency. (openstax.org)
Historical development
Practical engine development helped motivate thermodynamic theory. Early steam engines wasted fuel by repeatedly heating and cooling their cylinders. James Watt developed a separate condenser in 1765 and received a patent in 1769, allowing steam condensation to occur away from the hot working cylinder. Carnot’s subsequent investigation shifted attention from particular mechanisms to the general conditions limiting heat-to-work conversion. (collection.sciencemuseumgroup.org.uk)