Glossary term
Thermal Efficiency
The ratio of net work output to heat input for a heat engine or thermodynamic cycle.
Definition
metricThermal efficiency is the ratio of the net work output of a heat engine or thermodynamic cycle to the heat energy supplied from the hot source, measuring how effectively the cycle converts heat into useful work.
Thermal efficiency is the primary performance metric for heat engines and power cycles — steam turbine plants operating on the Rankine cycle, gas turbines on the Brayton cycle, and reciprocating engines on the Otto or Diesel cycle. It is bounded above by the Carnot efficiency, which sets the maximum achievable efficiency for any heat engine operating between two fixed temperature reservoirs. Real cycles fall short of the Carnot limit due to irreversibilities including friction, heat transfer across finite temperature differences, and incomplete combustion.
A heat engine is a device that absorbs heat Q_\text{in} from a hot source, converts part of it into net work W_\text{net}, and rejects the remainder Q_\text{out} to a cold sink. By energy conservation:
The thermal efficiency of the cycle is the fraction of heat input that is converted to work:
Since Q_\text{out} > 0 for any real cycle (heat must be rejected to a cold sink to complete the cycle — a consequence of the second law of thermodynamics), thermal efficiency is always strictly less than 1.
The maximum possible thermal efficiency for any heat engine operating between a hot reservoir at absolute temperature T_H and a cold reservoir at T_C is the Carnot efficiency:
This limit applies regardless of the working fluid, the cycle topology, or the engineering sophistication of the machine. It is a consequence of the second law: no real irreversible engine can equal the Carnot efficiency, and any real cycle falls short by an amount determined by its internal irreversibilities. Increasing T_H or decreasing T_C raises the Carnot limit and motivates the use of high turbine inlet temperatures and low condenser pressures in power plant design.
Rankine cycle
Steam power plants operate on the Rankine cycle: water is pumped to high pressure, heated to steam in a boiler, expanded through a turbine to produce work, and condensed back to liquid in a condenser. The thermal efficiency of a simple Rankine cycle is typically 30–40%. Improvements — superheating, reheating, regenerative feedwater heating — raise efficiency by reducing heat rejection and increasing the mean temperature at which heat is added, bringing the cycle closer to the Carnot ideal between the same temperature limits.
Brayton cycle
Gas turbines — used in aircraft engines, power plants, and combined-cycle plants — operate on the Brayton cycle: air is compressed, fuel is burned at constant pressure, and the hot gas expands through a turbine. Simple Brayton cycle efficiencies are typically 35–42% for modern large gas turbines. Recuperation (using exhaust heat to preheat compressed air before combustion) and combined cycles (using exhaust heat to drive a Rankine bottoming cycle) can raise the overall system efficiency to 55–62%.
Otto and Diesel cycles
Spark-ignition reciprocating engines approximate the Otto cycle, with thermal efficiency:
where r is the compression ratio and \gamma is the ratio of specific heats of the working fluid. Higher compression ratios give higher efficiency, but are limited by knock (autoignition) in petrol engines. Compression-ignition (diesel) engines approximate the Diesel cycle and achieve higher thermal efficiencies (typically 42–50%) than equivalent petrol engines because they operate at higher compression ratios without knock limitation.
Gap between theoretical and actual efficiency
Real engines and power cycles operate below their theoretical cycle efficiency because of additional irreversibilities: friction in bearings and seals, heat transfer through cylinder walls, valve and throttling losses, incomplete combustion, turbine and compressor irreversibilities (quantified by isentropic efficiency), and parasitic power consumption by auxiliaries. The overall plant efficiency accounts for all these effects and is the quantity reported for commercial power plants.
Common mistakes
A common mistake is comparing thermal efficiency values without defining the boundary of the system. Brake thermal efficiency, indicated thermal efficiency, cycle efficiency, net plant efficiency, and combined-cycle efficiency include different losses and auxiliary loads. Another is treating the Carnot limit as a practical target without accounting for material temperature limits, finite heat-transfer area, pressure losses, emissions, cooling needs, and part-load operation. A strong review states heat-input definition, net or gross work basis, fuel lower or higher heating value, ambient condition, operating point, auxiliary loads, and whether the value is theoretical, measured, simulated, or guaranteed.