quantity

efficiency

The ratio of useful work output to total energy input in a thermodynamic process.
36 related articles · 1 formulas

Description

Efficiency in thermodynamics is the ratio of useful work output to the total energy input in a process, often expressed as a percentage. It quantifies how well a system converts heat or other energy forms into useful work, and it is bounded by the second law of thermodynamics. The maximum possible efficiency for a heat engine operating between two temperatures is given by the Carnot limit, which depends only on the temperature difference and is always less than 100%.

History

The concept was formalized by Sadi Carnot in 1824, who introduced the ideal engine cycle and its efficiency limit, later refined by Rudolf Clausius and William Thomson (Lord Kelvin) in the 1850s.

How it works

In a heat engine, energy is extracted from a hot reservoir, some is converted to work, and the rest is rejected to a cold reservoir. Efficiency is the work divided by the heat input. The Carnot efficiency sets the upper limit: 1 - (T_cold / T_hot), where temperatures are in kelvin. Real engines fall short due to friction, heat losses, and irreversible processes. In quantum systems, efficiency can be analyzed similarly, but with quantum effects like coherence and entanglement potentially altering the trade-offs.

In practice

Efficiency is central to designing power plants, engines, refrigerators, and heat pumps, as well as in emerging fields like quantum thermodynamics for optimizing quantum heat engines and refrigerators.

Fun fact

A typical coal-fired power plant operates at about 33% efficiency, meaning two-thirds of the fuel's energy is wasted as heat — a modern combined-cycle gas plant can reach over 60%.

Concept graph →

Formulas

$$\eta = 1 - \frac{T_c}{T_h}$$
Maximum efficiency of a heat engine between two reservoirs.
What is in the formula
ηvariableThermodynamic efficiency — efficiency
T_cvariableTemperature of the cold reservoir — temperature kelvin
T_hvariableTemperature of the hot reservoir — temperature kelvin

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