The Carnot Cycle Reference Page
Sadi Carnot and the Power of Fire

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Intro to The Carnot Cycle

The Carnot cycle is an idealized thermodynamic cycle that represents the maximum possible efficiency for a heat engine operating between two temperature reservoirs.

Although no real engine can achieve Carnot efficiency, the Carnot cycle provides an important benchmark for evaluating the performance of real systems and understanding the implications of the Second Law of Thermodynamics.

Sadi Carnot and the Power of Fire,
the 1824 Edition Part 1

This video introduces the Carnot cycle and explains how its efficiency depends only on the temperatures of the heat reservoirs.

Visuals

Sadi Carnot and the Power of Fire,
the 1824 Edition Part 2

This video applies the Carnot cycle concept to systems described using steam tables.

Visuals

Examples and Definitions

Definitions

Isothermal Process
A constant-temperature process, \(\Delta T = 0\).
Isentropic Process
A constant-entropy process, \(\Delta S = 0\). Clausius originally used the term to mean adiabatic and reversible, and most thermodynamics texts use the word in this sense.
Heat Engine
A (usually cyclic) system that converts thermal energy (heat) into work.
Heat-Engine or Thermal Efficiency, \(\eta\)
The ratio of the work produced by a heat engine to the heat extracted from the high-temperature reservoir powering the engine.

\[ \eta \equiv \frac{|W|}{|Q_\mathrm{hot}|} \]

Isothermal Heat Reservoir
A reservoir that can accept or reject heat at essentially constant temperature.

Any real reservoir has a finite capacity to accept or reject heat. For example, a well-mixed container of liquid water and ice at atmospheric pressure remains at \(0\ ^\circ\mathrm{C}\) while the phase change occurs.

Carnot Engine
A theoretical heat engine that operates with the maximum possible thermal efficiency:

\[ \eta = 1 - \frac{T_\mathrm{cold}}{T_\mathrm{hot}} \]

where the reservoir temperatures are expressed as absolute temperatures.

A Carnot cycle consists of four reversible processes:

  1. Adiabatic (isentropic) compression, during which the temperature increases from \(T_\mathrm{cold}\) to \(T_\mathrm{hot}\)
  2. Isothermal expansion at \(T_\mathrm{hot}\), during which heat \(Q_\mathrm{hot}\) is absorbed
  3. Adiabatic (isentropic) expansion, during which the temperature decreases from \(T_\mathrm{hot}\) to \(T_\mathrm{cold}\)
  4. Isothermal compression at \(T_\mathrm{cold}\), during which heat \(Q_\mathrm{cold}\) is rejected
Carnot Efficiency
The maximum theoretical efficiency for a heat engine operating between two reservoirs:

\[ \eta = 1 - \frac{T_\mathrm{cold}}{T_\mathrm{hot}} \]

Quality, \(x\)
The mass fraction of vapor in a saturated liquid–vapor mixture.