Efficiency (Physics): Definition, Formula & Examples

Efficiency is a way of describing the amount of useful ​output​ a process or machine can generate as a percentage of the ​input​ required to make it go. In other words, it compares how much energy is used to do work versus how much is lost or wasted to the environment. The more efficient the machine, the less energy wasted.

For example, if a heat engine is able to turn 75 percent of the fuel it receives into motion, while 25 percent is lost as heat in the process, it would be 75 percent efficient. Out of the original 100 percent of the fuel, 75 percent was output as useful work.

In physics, the term ​heat engines​ can refer to multiple types of machines or processes. Formally, a heat engine is any thermodynamic system that converts heat energy into mechanical energy, or motion.

The basic recipe for a heat engine includes the following:

•A heat bath, or some type of high-temperature heat source
•A low-temperature cold reservoir into which the heat is let out
•The engine itself, which absorbs heat from the hot reservoir in order to create some form of system expansion that does work on the environment (such as turning a motor) and then releases heat energy into the cold reservoir as it returns to its initial state.

For example, in a car, the burning fuel is the heat source, the environment around the car is the cold reservoir and the combustion engine is what does the work transforming the heat into exhaust as it moves the pistons and rotates the crankshaft, allowing the car to drive.

The efficiency of a heat engine is the ratio of the useful work done by the system (also called the useful energy or output energy of the system) over the heat energy added to the system (the input energy).

It is a measure of how good the heat engine is at turning heat energy into mechanical work.

\(\textnormal{Efficency} = \frac {\textnormal{work done}}{\textnormal{heat added}}\)

Mathematically:

\(Eff = \frac {W}{Q}\)

Where ​W​ is work done, ​Q​ is heat added and both are given in the SI unit for energy: joules.

Because efficiency is a ratio, it is always expressed as a percentage or as a value between 0 (no efficiency) and 1 (total efficiency – all input energy converted into useful output). Efficiency can never be more than 1, or 100 percent, because it would break the law of conservation of energy if the amount of energy output was more than the energy put in! This would imply energy was being created from nothing, an impossibility in this universe.

A Carnot cycle is a thermodynamic cycle of the maximum possible efficiency. Because no processes in nature are perfectly reversible – some energy is always lost as heat thanks to the second law of thermodynamics – a Carnot cycle describes an ​ideal​ heat engine. In other words, no one could actually build one.

The value of a Carnot cycle is in setting the upper boundaries for how efficient any actual engine could be. It is expressed in terms of ​_T_h​ and ​T_c_​, the temperatures of the hot and cold energy reservoirs, respectively, both in the SI unit of Kelvins.

It can also be expressed in terms of ​_Q_h​ and ​Q_c_​, the heat added and the heat given off, respectively, both in joules.

\(\textnormal{Carnot efficiency} = \frac {Q_h – Q_c}{Q_h}\)