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The Carnot Cycle

The Carnot Cycle

Converting work to heat is an irreversible process, and the purpose of a heat engine is to reverse the effect partially. Heat engines aim to increase the efficiency of the reversal, that is, maximize the work retrieved from heat. If the efficiency of a heat engine were 100%, it would imply reversing the process completely without introducing any other effect. Thus, it would violate the second law of thermodynamics.
What could be the theoretical limit to the efficiency of a heat engine? The...

The Carnot Cycle and the Second Law of Thermodynamics

The Carnot Cycle and the Second Law of Thermodynamics

The Carnot engine works between two heat reservoirs of fixed temperatures. The Carnot cycle begs the following question: Is it possible to devise a heat engine that is more efficient than a Carnot engine between two fixed temperatures? The answer lies in designing a Carnot refrigerator.
Since the individual steps in a Carnot cycle can be reversed, the entire cycle is, thus, reversible. If a Carnot cycle is reversed, it becomes a Carnot refrigerator. It extracts heat Qc from a cold reservoir at...

Carnot Cycle and Efficiency

Carnot Cycle and Efficiency

The Second Law of Thermodynamics asserts that it's impossible for any heat engine to achieve 100% efficiency. While contemplating the maximum possible efficiency, Nicolas Sadi Carnot conceptualized an ideal heat engine. This engine gets its energy from a high-temperature reservoir. It then performs some work and releases the remaining energy into a low-temperature reservoir.The Carnot cycle, named after Sadi Carnot, is fully reversible. The cycle consists of four distinct stages. In the first...

Otto and Diesel Cycle

Otto and Diesel Cycle

An Otto engine is a four-stroke engine that uses a mixture of gasoline and air as the working fuel. The fuel is injected into the cylinder, and the piston is moved completely down so that the cylinder is at maximum volume. By moving the piston up, adiabatic compression takes place. The spark plug ignites the gasoline-air mixture, and the burning fuel adds heat to the system at a constant volume. The heated mixture expands adiabatically and gets further cooled by exhausting heat, and this cyclic...

Heat Engines

Heat Engines

A heat engine is a device used to extract heat from a source and then convert it into mechanical work used for various applications. For example, a steam engine on an old-style train can produce the work needed for driving the train.
Whenever we consider heat engines (and associated devices such as refrigerators and heat pumps), we do not use the standard sign convention for heat and work. For convenience, we assume that the symbols Qh, Qc, and W represent only the amounts of heat transferred...

Efficiency of The Carnot Cycle

Efficiency of The Carnot Cycle

The hypothetical Carnot cycle consists of an ideal gas subjected to two isothermal and two adiabatic processes. Since the internal energy of an ideal gas depends only on its temperature, which is the same before and after the completion of the Carnot cycle, there is no change in its internal energy. Hence, using the first law of thermodynamics, the total heat exchanged by the ideal gas equals the total work done. Thus, we can quantify the efficiency of the Carnot cycle via the heat exchanged...

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Related Experiment Video

Updated: Jun 1, 2026

A Rapid Method for Modeling a Variable Cycle Engine

A Rapid Method for Modeling a Variable Cycle Engine

Published on: August 13, 2019

Maximum-power quantum-mechanical Carnot engine.

Sumiyoshi Abe¹

¹Department of Physical Engineering, Mie University, Mie 514-8507, Japan.

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics

|May 24, 2011

Summary

This summary is machine-generated.

Researchers explored a quantum-mechanical Carnot engine analog. Maximum power output was achieved when the well width changed slowly, yielding a universal efficiency independent of model parameters.

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Last Updated: Jun 1, 2026

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Area of Science:

Quantum mechanics
Thermodynamics
Statistical mechanics

Background:

The Carnot engine is a theoretical benchmark for thermodynamic efficiency.
Quantum systems offer novel avenues for exploring thermodynamic principles.

Purpose of the Study:

To investigate the maximum power output of a quantum-mechanical Carnot engine analog.
To determine the efficiency of this engine at maximum power.

Main Methods:

Utilized a two-state model of a particle in a one-dimensional infinite potential well.
Analyzed engine performance as the well width changed at a finite speed.

Main Results:

The quantum Carnot engine analog can achieve maximum power output.
The efficiency at maximum power is universal, independent of specific model parameters.

Conclusions:

It is possible to construct and analyze quantum analogs of heat engines.
The study reveals universal properties of quantum heat engines operating at maximum power.