Carnot cycle

Carnot Cycle Figure - Step 1

Carnot Cycle Figure - Step 2

Carnot Cycle Figure - Step 3

Carnot Cycle Figure - Step 4

Carnot cycle p-V diagram

Carnot cycle is a theoretical thermodynamic cycle proposed by Nicolas Léonard Sadi Carnot in 1824. It is considered the most efficient cycle for converting a given amount of thermal energy into work or, conversely, for using work to produce a thermal gradient. The cycle is a model used to understand the limits of the second law of thermodynamics in terms of a heat engine's maximum efficiency.

Overview

The Carnot cycle consists of four reversible processes: two isothermal (constant temperature) processes and two adiabatic (no heat exchange) processes. These processes are:

1. Isothermal Expansion: The working substance (usually a gas) is placed in contact with a hot reservoir at temperature \(T_H\). It expands isothermally, doing work on the surroundings, while absorbing a quantity of heat \(Q_H\) from the hot reservoir. 2. Adiabatic Expansion: The gas continues to expand, this time without exchanging heat with its surroundings. Its temperature decreases from \(T_H\) to \(T_C\), doing work on the surroundings. 3. Isothermal Compression: The gas is then placed in contact with a cold reservoir at temperature \(T_C\). It is compressed isothermally, giving up a quantity of heat \(Q_C\) to the cold reservoir. 4. Adiabatic Compression: Finally, the gas is compressed adiabatically, increasing its temperature from \(T_C\) back to \(T_H\), without exchanging heat with its surroundings.

Efficiency

The efficiency of a Carnot engine, which is the ratio of the work done by the engine to the heat absorbed from the hot reservoir, is given by: \[ \eta = 1 - \frac{T_C}{T_H} \] where \(T_H\) and \(T_C\) are the absolute temperatures of the hot and cold reservoirs, respectively. This equation shows that the efficiency of a Carnot engine depends only on the temperatures of the hot and cold reservoirs and not on the working substance.

Significance

The Carnot cycle is significant in the field of thermodynamics because it sets an upper limit on the efficiency that any heat engine can achieve. No real engine operating between two heat reservoirs can be more efficient than a Carnot engine operating between the same two reservoirs. This principle is a cornerstone in the second law of thermodynamics and has profound implications for the design and operation of heat engines and refrigerators.

Real-World Applications

While the Carnot cycle is an idealized model, it provides a benchmark for the efficiency of real-world thermal systems. Engineers and scientists use the principles of the Carnot cycle to design more efficient heat engines, refrigerators, and heat pumps. However, due to practical limitations such as friction and heat loss, no real engine can achieve the Carnot efficiency.

See Also

• Heat engine
• Thermodynamic cycle
• Second law of thermodynamics
• Entropy

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