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Related Concept Videos

The Carnot Cycle01:30

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...
Efficiency of The Carnot Cycle01:16

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...
The Carnot Cycle and the Second Law of Thermodynamics01:20

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...
Entropy Change in Reversible Processes01:10

Entropy Change in Reversible Processes

In the Carnot engine, which achieves the maximum efficiency between two reservoirs of fixed temperatures, the total change in entropy is zero. The observation can be generalized by considering any reversible cyclic process consisting of many Carnot cycles. Thus, it can be stated that the total entropy change of any ideal reversible cycle is zero.
The statement can be further generalized to prove that entropy is a state function. Take a cyclic process between any two points on a p-V diagram.
The Entropy as a State Function01:14

The Entropy as a State Function

Consider an arbitrary process that moves between two specific states (A and B) in a cyclic manner. This process is reversible and broken down into smaller parts that each follow a Carnot cycle. A Carnot cycle has two isothermal (constant temperature) processes. During these processes, the ratio of the amount of heat transferred to their respective temperature remains constant. The other two processes in the Carnot cycle are also reversible but adiabatic, which means they occur without any heat...
Path Between Thermodynamics States01:21

Path Between Thermodynamics States

Consider the two thermodynamic processes involving an ideal gas that are represented by paths AC and ABC in Figure 1:

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Related Experiment Video

Updated: May 9, 2026

An Analog Macroscopic Technique for Studying Molecular Hydrodynamic Processes in Dense Gases and Liquids
11:03

An Analog Macroscopic Technique for Studying Molecular Hydrodynamic Processes in Dense Gases and Liquids

Published on: December 4, 2017

Carnot process with a single particle.

J Hoppenau1, M Niemann, A Engel

  • 1Institut für Physik, Carl-von-Ossietzky Universität, 26111 Oldenburg, Germany. johannes.hoppenau@uni-oldenburg.de

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|July 16, 2013
PubMed
Summary
This summary is machine-generated.

This study analyzes work statistics in ideal gas volume changes and a microscopic Carnot cycle. Researchers found that while quasistatic limits yield Carnot efficiency, real-world applications show decreased efficiency with increased speed.

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Last Updated: May 9, 2026

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A Rapid Method for Modeling a Variable Cycle Engine
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Published on: August 13, 2019

Area of Science:

  • Thermodynamics
  • Statistical Mechanics
  • Non-equilibrium Physics

Background:

  • Understanding work and heat fluctuations is crucial for microscopic thermodynamic processes.
  • Previous work explored adiabatic processes, necessitating analysis of isothermal changes and combined cycles.

Purpose of the Study:

  • To determine the statistics of work during isothermal volume changes of a single-particle classical ideal gas.
  • To analyze the joint probability distribution of heat and work for a microscopic, non-equilibrium Carnot cycle.
  • To investigate the impact of piston speed on efficiency and compare it to theoretical bounds.

Main Methods:

  • Calculating work statistics for isothermal volume changes.
  • Integrating results with adiabatic process findings (Lua and Grosberg, 2005).
  • Analyzing the joint probability distribution of heat and work in a non-equilibrium Carnot cycle.

Main Results:

  • Quasistatic Carnot cycles recover Carnot efficiency but exhibit non-trivial work and heat distributions.
  • Efficiency decreases as piston speed increases.
  • Efficiency at maximum power remains within recently established theoretical bounds.

Conclusions:

  • The study provides insights into the non-equilibrium thermodynamics of microscopic systems.
  • Deviations from ideal Carnot efficiency are observed in non-static conditions.
  • The findings contribute to understanding efficiency limits in real-world thermodynamic cycles.