Heat Engine
A heat engine is a device that converts thermal energy into mechanical work by exploiting the temperature difference between a high-temperature heat source (hot reservoir) and a low-temperature heat sink (cold reservoir). The engine absorbs heat Q_H from the hot reservoir, converts part of it to useful work W, and rejects the remainder Q_C to the cold reservoir, operating in a cyclic process. The thermal efficiency of a heat engine is always less than 100% due to the Second Law of Thermodynamics, and the maximum theoretical efficiency is set by the Carnot efficiency.
Key Formula
η = W / Q_H = 1 − (Q_C / Q_H)
LaTeX: \eta = \frac{W}{Q_H} = 1 - \frac{Q_C}{Q_H}
| Symbol | Meaning | Unit |
|---|---|---|
| η | Thermal efficiency of the heat engine | dimensionless (0 to 1) |
| W | Net work output per cycle | J |
| Q_H | Heat absorbed from hot reservoir per cycle | J |
| Q_C | Heat rejected to cold reservoir per cycle | J |
Worked Example
Problem
A steam engine absorbs 800 kJ of heat from a boiler and rejects 560 kJ to a condenser per cycle. Calculate the thermal efficiency and net work output.
Solution
Step 1: Q_H = 800 kJ, Q_C = 560 kJ. Step 2: Net work output: W = Q_H − Q_C = 800 − 560 = 240 kJ. Step 3: Thermal efficiency: η = W / Q_H = 240 / 800 = 0.30 = 30%.
Answer
W = 240 kJ per cycle; Thermal efficiency η = 30%
Comparison of Common Heat Engine Types
| Engine Type | Working Fluid | Typical Efficiency (%) | Hot Reservoir | Application |
|---|---|---|---|---|
| Steam (Rankine cycle) | Water/steam | 30–40 | Boiler (~600 K) | Power plants, locomotives |
| Petrol (Otto cycle) | Air-fuel mixture | 25–35 | Combustion (~2000 K) | Cars, motorcycles |
| Diesel cycle | Air-fuel mixture | 35–45 | Combustion (~2200 K) | Trucks, ships, generators |
| Gas turbine (Brayton) | Air + fuel gas | 35–50 | Combustion (~1600 K) | Aircraft, power plants |
| Carnot engine (ideal) | Any | ~50 (theoretical) | Depends on T_H, T_C | Theoretical maximum |
Interactive Tools
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Related Terms
Carnot Cycle
The Carnot Cycle is an idealized, reversible thermodynamic cycle consisting of two isothermal and two adiabatic processes, first described by Sadi Carnot in 1824 as the most efficient possible heat engine operating between two fixed temperatures. No real engine can exceed the efficiency of a Carnot engine operating between the same hot and cold reservoirs, making it the theoretical upper bound for heat engine performance. The Carnot efficiency depends only on the absolute temperatures of the reservoirs and sets the fundamental limit imposed by the Second Law of Thermodynamics.
Second Law of Thermodynamics
The Second Law of Thermodynamics states that in any spontaneous process, the total entropy of an isolated system can only increase or remain constant, never decrease. This gives thermodynamics a preferred direction of time, explaining why heat flows from hot to cold, why mechanical energy converts irreversibly to heat, and why perpetual motion machines of the second kind are impossible. It is the thermodynamic basis for the arrow of time and sets fundamental efficiency limits on all heat engines.
Entropy
Entropy is a thermodynamic state function that quantifies the degree of disorder, randomness, or the number of microstates available to a system at a given macrostate. Macroscopically, it is defined via the Clausius inequality as the ratio of reversible heat exchange to absolute temperature; microscopically, Boltzmann's formula connects it to the number of microscopic configurations. Entropy always increases in irreversible processes in isolated systems, driving systems toward equilibrium and explaining the thermodynamic arrow of time.
The term "heat engine" arose naturally in the 19th century from the engineering study of steam engines. "Engine" derives from Latin "ingenium" (cleverness, device). Sadi Carnot's 1824 treatise "Réflexions sur la puissance motrice du feu" (Reflections on the Motive Power of Fire) laid the theoretical foundation.