Heat engines are all around you. From the car you drive to the refrigerator that keeps your food cool to your house’s heating and cooling systems, they all work based on the same key principles.
The goal of any heat engine is to convert heat energy into useful work, and there are many different approaches you can use to do this. One of the simplest forms of heat engine is the Carnot engine, named after French physicist Nicolas Leonard Sadi Carnot, built around an idealized four-stage process that depends on adiabatic and isothermal stages.
But the Carnot engine is just one example of a heat engine, and many other types achieve the same basic goal. Learning about how heat engines work and how to do things like calculate the efficiency of a heat engine is important for anybody studying thermodynamics.
What Is a Heat Engine?
A heat engine is a thermodynamic system that converts heat energy into mechanical energy. Although many different designs fall under this general heading, several basic components are found in pretty much any heat engine.
Any heat engine needs a heat bath or a high-temperature heat source, which can take many different forms (for example, a nuclear reactor is the heat source in a nuclear power plant, but in many cases burning fuel is used as a heat source). Additionally, there must be a low-temperature cold reservoir, as well as the engine itself, which is usually gas that expands when heat is applied.
The engine absorbs heat from the hot reservoir and expands, and this expansion process is what does work on the environment, usually harnessed into a usable form with a piston. The system then releases heat energy back into the cold reservoir and returns to its initial state. The process then repeats, over and over in a cyclic fashion in order to continuously generate useful work.
Types of Heat Engine
Thermodynamic cycles or engine cycles are a generic way to describe many specific thermodynamic systems that work in the cyclic manner common to most heat engines. The simplest example of a heat engine working with thermodynamic cycles is the Carnot engine or an engine operating based on the Carnot cycle. This is an idealized form of heat engine that involves only reversible processes, in particular adiabatic and isothermal compression and expansion.
All internal combustion engines operate on the Otto cycle, which is another type of thermodynamic cycle that uses the ignition of fuel to do work on a piston. In the first stage, the piston drops to draw a fuel-air mixture into the engine, which is then adiabatically compressed in the second stage and ignited in the third.
There is a rapid increase in temperature and pressure, which does work on the piston through adiabatic expansion, before the exhaust valve opens, leading to a reduction in pressure. Finally, the piston rises to clear the expended gases and complete the engine cycle.
Another type of heat engine is the Stirling engine, which contains a fixed amount of gas that moves between two different cylinders at different stages of the process. The first stage involves heating the gas to raise the temperature and produce a high pressure, which moves a piston to provide useful work.
The piston then rises back up and pushes the gas into a second cylinder, where it is cooled by the cold reservoir before being compressed again, a process requiring less work than was produced in the previous stage. Finally, the gas is moved back into the original chamber, where the Stirling engine cycle repeats.
Efficiency of Heat Engines
The efficiency of a heat engine is the ratio of useful work output to heat or thermal energy input, and the result is always a value between 0 and 1, with no units because both heat energy and work output are measured in joules. This means that if you had a perfect heat engine, it would have an efficiency of 1 and convert all of the heat energy into usable work, and if it managed to convert half of it the efficiency would be 0.5. In a basic form, the formula can be written:
Of course, it’s impossible for a heat engine to have an efficiency of 1, because the second law of thermodynamics dictates that any closed system will increase in entropy over time. Although there is a precise mathematical definition of entropy that you can use to understand this, the simplest way to think about it is that inherent inefficiencies in any process lead to some loss of energy, usually in the form of waste heat. For example, an engine’s piston will undoubtedly have some friction working against its motion, which means the system will lose energy in the process of converting the heat into work.
The theoretical maximum efficiency of a heat engine is called the Carnot efficiency. The equation for this relates the temperature of the hot reservoir TH and cold reservoir TC to the efficiency (η) of the engine.
You can multiply the result of this by 100 if you want to express the answer as a percentage. It’s important to remember that this is the theoretical maximum – it’s unlikely that any real-world engine will genuinely approach the Carnot efficiency in practice.
The important thing to note is that you maximize the efficiency of heat engines by increasing the difference in temperature between the hot reservoir and the cold reservoir. For an automobile engine, TH is the temperature of the gases inside the engine when combusted, and TC is the temperature at which they are pushed out of the engine.
Real World Examples – Steam Engine
The steam engine and steam turbines are two of the most well-known examples of a heat engine, and the invention of the steam engine was an important historical event in the industrialization of society. A steam engine works in a very similar way to the other heat engines discussed so far: a boiler turns water into steam, which is sent into a cylinder containing a piston, and the high pressure of the steam moves the cylinder.
The steam transfers some of the thermal energy to the cylinder, getting cooler in the process, and then when the piston has been fully pushed out, the remaining steam is let out of the cylinder. At this point, the piston returns to its original position (sometimes the steam is routed around to the other side of the piston so it can push it back too), and the thermodynamic cycle starts over again with more steam.
This relatively simple design allows a large amount of useful work to be produced from anything capable of boiling water. The efficiency of a heat engine with this design depends on the difference between the temperature of the steam and that of the surrounding air. A steam locomotive uses the work created from this process to turn wheels and propel the train.
A steam turbine works in a very similar way, except the work goes into turning a turbine instead of moving a piston. This is a particularly useful way to generate electricity because of the rotational motion generated by the steam.
Real World Examples – Internal Combustion Engine
The internal combustion engine works based on the Otto cycle described above, with spark ignition used for gasoline engines and compression ignition used for diesel engines. The main difference between these is the way the fuel-air mixture is ignited, with the fuel-air mixture being compressed and then physically ignited in the gasoline engines and fuel being sprayed into compressed air in diesel engines, causing it to ignite from the temperature.
Aside from this, the rest of the Otto cycle is completed as described previously: Fuel is drawn into the engine (or just air for diesel), compressed, ignited (by a spark for fuel and spraying fuel into the hot, compressed air for diesel), which does usable work on the piston through adiabatic expansion, and then the exhaust valve opens to reduce the pressure, and the piston pushes out the used gas.
Real World Examples – Heat Pumps, Air Conditioners and Refrigerators
Heat pumps, air conditioners and refrigerators all work on a form of heat cycle too, although they have the different goal of using work to move the heat energy around rather than the reverse. For example, in the heating cycle of a heat pump, the refrigerant absorbs heat from the outside air because of its lower temperature (since heat always flows from hot to cold), and is then pushed through a compressor to raise its pressure and therefore its temperature.
This hotter air is then moved to the condenser, near the room to be heated, where the same process transfers heat to the room. Finally, the refrigerant is moved through into a valve that lowers the pressure and therefore the temperature, ready for another heating cycle.
In the cooling cycle (as in an air conditioning unit or a refrigerator) the process essentially runs in reverse. The refrigerant absorbs heat energy from the room (or inside the refrigerator) because it’s kept at a cold temperature, and then it’s pushed through the compressor to increase the pressure and temperature.
At this point, it moves around to the outside of the room (or at the back of the refrigerator), where the heat energy is transferred to the cooler outside air (or the surrounding room). The refrigerant is then sent through the valve to lower the pressure and temperature, reading for another heating cycle.
Since the goal of these processes is the opposite of the engine examples, the expression for the efficiency of a heat pump or refrigerator is different too. This is quite predictable in form, though. For heating:
And for cooling:
Where the Q terms are for the heat energy moved into the room (with the H subscript) and moved out of it (with the C subscript) and Win is the work input into the system in the form of electricity. Again, this value is a dimensionless number between 0 and 1, but you can multiply the result by 100 to get a percentage if you prefer.
Real World Example – Power Plants or Power Stations
Power stations or power plants are really just another form of heat engine, whether they create heat using a nuclear reactor or by burning fuel. The heat source is used to move turbines and thereby do mechanical work, often using steam from heated water to spin a steam turbine, which generates electricity in the way described above. The precise heat cycle used can vary between power plants, but the Rankine cycle is commonly used.
The Rankine cycle starts with the heat source raising the temperature of the water, then the expansion of water vapor in a turbine, followed by the condensation in the condenser (releasing waste heat in the process), before the cooled water goes to a pump. The pump increases the pressure of the water and prepares it for further heating.
- Williamson College of the Trades: Heat Engines That Power Our High-Quality Lives
- Lumen: Introduction to the Second Law of Thermodynamics: Heat Engines and Their Efficiency
- University of Calgary Energy Education: Rankine Cycle
- The Engineers Post: Air-Conditioning System: Its Working Principle and Classification of Air Conditioning System
- University of Calgary Energy Education: Heat Pump
- U.S. Department of Energy: Internal Combustion Engine Basics
- Student Energy: Steam Turbine
- University of Tennessee, Knoxville: Heat Engines
- Penn State: The Carnot Efficiency
- Chemistry LibreTexts: Carnot Cycle, Efficiency, and Entropy
- University of Calgary Energy Education: Stirling Engine
- University of Calgary Energy Education: Nuclear Power Plant
- Massachusetts Institute of Technology: The Internal Combustion Engine (Otto Cycle)
- Georgia State University HyperPhysics: Heat Engine Cycle
- Georgia State University HyperPhysics: The Otto Cycle