---
title: "Carnot engine explanation"
chunk: 1/8
source: "https://en.wikipedia.org/wiki/Carnot_engine_explanation"
category: "reference"
tags: "science, encyclopedia"
date_saved: "2026-05-05T04:19:16.023719+00:00"
instance: "kb-cron"
---

In 1824 the French military engineer Sadi Carnot laid the foundations of the science of thermodynamics by describing the unsurpassably efficient Carnot engine.  His insight has been described as "real genius" and compared to Einstein's, Newton's and Galileo's.  Carnot wrote in clear and popular language and meant his theory to be easy to understand.  Yet it has been found that, as taught in many academic courses, students have difficulty intuiting his ideas.  This article is an introduction for non-specialists.
The efficiency of the ideal, or Carnot, engine is surprisingly low.  That of real heat engines is worse.

== Significance ==

=== Importance ===
Carnot's innovation has been described as "real genius" and "one of the greatest intellectual achievements of the human mind".  For Nobel laureate Richard FeynmanThe science of thermodynamics began with an analysis, by the great engineer Sadi Carnot, of the problem of how to build the best and most efficient engine.   In particular it led to the discovery of the Second Law, of which it has been claimed that "Not knowing the Second Law of Thermodynamics is equivalent to never having read a work by Shakespeare".

=== Clarity ===
Sadi Carnot died young and published only one work: Reflections on the Motive Power of Fire (1824).  A short book addressed to practical engineers in popular language, it has been described as "remarkably accessible to modern readers"; "very clearly written ... [the] mathematical arguments are consigned to footnotes".  It is known that Carnot was anxious to be understood by non-specialists.  Yet, in many university courses the Carnot cycle it is introduced in such an abstract way that students have trouble intuiting his ideas, and their implications.
Not all approve of his popular exposition.  In The Tragicomical History of Thermodynamics 1822-1854 Clifford Truesdell strongly criticised Carnot for his lack of mathematical rigour, which (he said) has affected the discipline ever since.

=== Flaw in theory, and rescue ===
Carnot's theory as published contains a serious flaw, which he increasingly came to suspect himself. Like many scientists of his time he had assumed heat was an actual substance (they called  it caloric).  This is an intuitive way to think about heat and it has been shown that children think similarly.
After Carnot's death new data led to a fundamental shift in scientific thinking.  Heat is now usually described as a form of energy, which can be converted into mechanical work, and vice versa. Carnot's theory was eventually rescued by Rudolf Clausius and (independently) William Thomson (Lord Kelvin), who made the necessary corrections.  Today most students are taught not Carnot's theory but the rescued version.  If Carnot's version is taught first it is easier to understand. This detail will be explained later.

== Context and motivation ==
Carnot's motivation was practical.  "The purpose of Reflexions was to bring to public notice the potential of the steam engine for improving the standard of living in France".

The first useful steam engines were developed in Britain and were typically employed for pumping water out of coal mines.  Since an engine could burn the mine's own coal (including waste coal, which had no commercial value) fuel economy was of little concern.  The incentive to have efficient engines arose in parts of the country where fuel was costly, such as Cornwall.
The mines of Cornwall produced useful metals like tin; but not coal.  The fuel to power their pumping engines had to be imported by sea and was expensive; users were keenly aware that "heat cost money".  They sought the engine that did the best "duty'", measured in millions of pounds of water lifted one foot high per bushel of coal burnt.  A practical business measure, it was a crude indication of the thermodynamic efficiency of an engine.
Cornish engineers were famous for the efficiency of their engines and their achievements were studied avidly, not least in France, where coal was expensive too.  Sadi Carnot's book mentioned three of them by name, Richard Trevithick, Arthur Woolf and Jonathan Hornblower.  Such men developed the Cornish engine in which high pressure steam was cut off early when the piston was at the beginning of its stroke, letting the steam's expansion complete the stroke by itself.  Today it might be called adiabatic expansion.
Their ideas were enthusiastically taken up in France, where additionally, scientists and engineers were interested in the theory of steam and other engines.

== Carnot's aim: a general theory of engines ==

"Every one knows that heat can produce motion", began Carnot. Typically it was done by steam engines.  Important to the Industrial Revolution, they had been vastly improved by practical British engineers, said Carnot, but without really understanding the theory of what they were doing.
Because of the remarkable improvements that had already been made in fuel efficiency  -  a ten-fold increase since 1775  -  it was asked whether it would go on for ever.  Or would engineers run up against a fundamental limit, impossible to exceed?  Matters such as these had attracted some of the ablest mathematicians and physicists in France.
Engineers also wondered if there could be a better working substance than steam.  In principle, anything that exerted a force when heated and cooled might work, even a solid metallic bar.  Many substances were tried or considered, for example the Stirling engine used air.  Others included alcohol, ammonia, even mercury; there were hundreds of such exotic proposals, some dangerous: there were ships and factories powered by engines that worked by boiling ether, a highly flammable liquid.

To answer questions such as these, said Carnot, one needed to think generally, to go beyond the details of this or that engine.It is necessary to establish principles applicable not only to steam-engines but to all imaginable heat-engines. 
For historian of science John D. Norton "it is important to realize just how audacious it was of Sadi to seek such a simple general theory, let alone to find it", for the practical engines of his day were already very complicated devices.