Carnot Cycle

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The Carnot cycle is a particular thermodynamic cycle proposed by Nicolas Léonard Sadi Carnot in 1824 and expanded by Benoit Paul Émile Clapeyron in the 1830s and 40s. It is the most efficient existing cycle capable of converting a given amount of thermal energy into work or, conversely, creating a temperature difference (e.g. for refrigeration) by doing a given amount of work.

Every thermodynamic system exists in a particular thermodynamic state. When a system is taken through a series of different states and finally returned to its initial state, a thermodynamic cycle is said to have occurred. In the process of going through this cycle, the system may perform work on its surroundings, thereby acting as a heat engine. A system undergoing a Carnot cycle is called a Carnot heat engine, although such a 'perfect' engine is only theoretical and cannot be built in practice.

The Carnot Cycle

The Carnot cycle when acting as a heat engine consists of the following steps:

  1. Reversible isothermal expansion of the gas at the "hot" temperature, TH (isothermal heat addition). During this step (A to B on Figure 1, 1 to 2 in Figure 2) the expanding gas makes the piston work on the surroundings. The gas expansion is propelled by absorption of quantity Q1 of heat from the high temperature reservoir.
  2. Isentropic (reversible adiabatic) expansion of the gas (isentropic work output). For this step (B to C on Figure 1, 2 to 3 in Figure 2) the piston and cylinder are assumed to be thermally insulated, thus they neither gain nor lose heat. The gas continues to expand, working on the surroundings. The gas expansion causes it to cool to the "cold" temperature, TC.
  3. Reversible isothermal compression of the gas at the "cold" temperature, TC. (isothermal heat rejection) (C to D on Figure 1, 3 to 4 on Figure 2) Now the surroundings do work on the gas, causing quantity Q2 of heat to flow out of the gas to the low temperature reservoir.
  4. Isentropic compression of the gas (isentropic work input). (D to A on Figure 1, 4 to 1 in Figure 2) Once again the piston and cylinder are assumed to be thermally insulated. During this step, the surroundings do work on the gas, compressing it and causing the temperature to rise to TH. At this point the gas is in the same state as at the start of step 1.
Figure 1: A Carnot cycle acting as a heat engine, illustrated on a temperature-entropy diagram. The cycle takes place between a hot reservoir at temperature TH and a cold reservoir at temperature TC. The vertical axis is temperature, the horizontal axis is entropy.
Figure 2: A Carnot cycle acting as a heat engine, illustrated on a pressure-volume diagram to illustrate the work done.