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What is the Carnot Heat Cycle?

By H.R. Childress
Updated May 17, 2024
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The Carnot heat cycle, more properly called the Carnot cycle, is an idealized thermodynamic cycle that is used to determine the maximum possible efficiency for a heat engine operating between two given temperatures. It is used for theoretical purposes, but cannot actually operate in physical systems. Although, in theory, an engine could be constructed operating near maximum efficiency, heat transfer in the cycle is too slow for it to be a practical system. The main value of the Carnot cycle lies in establishing the maximum efficiency for other types of heat engines.

Two assumptions are made in constructing the Carnot heat cycle, to give it the maximum possible efficiency — all the processes are reversible, and there is no change in entropy. A reversible process is one that can be returned to its original state with no loss of energy. Entropy is the amount of energy in a system that is unavailable to do work. According to the second law of thermodynamics, the amount of entropy in a system must increase or stay the same when a process occurs. Neither of these assumptions can be fulfilled under natural conditions, but they are useful in determining the maximum efficiency.

Four processes repeat in a Carnot heat cycle. The first is an isothermal expansion. 'Isothermal' means that the temperature remains the same throughout the process. Volume increases and pressure decreases during this, and energy is added to the system.

The next process in known as an adiabatic expansion. In adiabatic processes, no heat is gained or lost by the system. Changes in temperature occur due to changes in pressure and volume. For this particular step, pressure is decreased, and volume is increased, in order to decrease the temperature.

Third is an isothermal compression. Pressure increases and volume decreases during this process, and energy is removed from the system. Finally, an adiabatic compression is performed to return the system to its original state. Pressure is increased and volume is decreased in order to increase the temperature.

Due to the assumption that there is no change in entropy during the Carnot cycle, it could be performed endlessly and maintain the same amount of energy every time it returned to its original state. There is still some entropy even in this idealized system, however, which means that it cannot be 100% efficient. The actual efficiency of a Carnot heat cycle can be calculated using its maximum and minimum temperatures, on the absolute or Kelvin (K) temperature scale. In this equation, the minimum temperature is subtracted from the maximum, and this number is then divided by the maximum temperature.

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