Carnot Cycle

Introduction

The Carnot cycle, named after Sadi Carnot who introduced it in 1824, is a theoretical thermodynamic cycle that provides the maximum possible efficiency a heat engine can achieve operating between two thermal reservoirs at different temperatures. It’s an idealized process that assumes no friction, perfectly insulated components, and other ideal conditions.

The Carnot Cycle

The Carnot cycle consists of four reversible processes: two isothermal processes (at constant temperature) and two adiabatic processes (in which no heat is exchanged).

1. Isothermal Expansion: The system, often a gas in a cylinder, expands at a constant temperature (the temperature of the hot reservoir), absorbing heat from the reservoir.
2. Adiabatic Expansion: The system continues to expand, but now without heat exchange. As the gas does work on the surroundings, its temperature drops to (the temperature of the cold reservoir).
3. Isothermal Compression: The system is compressed at a constant temperature , expelling heat to the cold reservoir.
4. Adiabatic Compression: The system is further compressed without heat exchange. As the surroundings do work on the gas, its temperature rises back to , completing the cycle.

Carnot’s Theorem and Efficiency

Carnot’s theorem states that no engine operating between two heat reservoirs can be more efficient than a Carnot engine operating between the same reservoirs. The efficiency of a Carnot engine is given by:

where is the efficiency, is the absolute temperature of the cold reservoir, and is the absolute temperature of the hot reservoir.

Relevance and Applications

While a real Carnot engine is an idealization (since it assumes reversible processes, which would take an infinite amount of time), the concept of the Carnot cycle is crucial in the second law of thermodynamics and entropy. It sets the maximum possible efficiency for heat engines and helps in understanding and designing more efficient real-world engines and refrigeration systems.

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