---
title: "Carnot engine explanation"
chunk: 4/8
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"
---

For most scientists of Carnot's time the best explanation of heat was the caloric theory.  It held that heat is a material fluid that can flow from one place to another: its temperature may vary, but it can never itself be destroyed nor created.
The caloric theory was highly developed, mathematically sophisticated, and plausible.  The alternative theory, that heat consists in the agitation of a substance's particles  —  in   modern terms, energy  —   was well known, but did not command much support, mainly for lack of convincing experimental evidence.  For historian of science Thomas Kuhn, "To analyze the gas engine Carnot required a developed theory of heat, and in the 1820's the caloric theory was the only one at hand".
Several authors have speculated that without the caloric theory and his waterfall analogy Carnot would not have been led to his discovery.
Pursuant to this core idea, Carnot taught that all heat entering his engine from the hot source must fall out into the cold sink. But according to new ideas  —  that were dawning on Carnot himself, and came to be adopted overwhelmingly  — this is false.  Some of the heat will be consumed on the way: by the doing of work.

=== A new outlook ===
From 1800 new discoveries started to emerge  —  e.g. the galvanic battery, heat by electricity, electrolysis, electromagnetism, induced currents, thermoelectric cooling  —  which increasingly suggested that a single "force", nowadays called energy, was manifesting itself in different ways.  According to Thomas Kuhn,  the interconnection between previously detached branches of science was going on apace "and that is what Mary Somerville had in mind when, in 1834, she gave her famous popularization of science the title On the Connexion of the Physical Sciences".

For Kuhn, "Mrs. Somerville's remark isolates the 'new look' that physical science had acquired between 1800 and 1835. That new look, together with the discoveries that produced it, proved to be a major requisite for the emergence of 
energy conservation."

=== Energy, not heat, is conserved ===
Within the space of a few years perhaps a dozen scientists, largely working independently, became convinced that heat and work are mutually interchangeable (always at same rate of exchange, which they were able to calculate).   Four of them formally published their claims, supported by data:  Julius von Mayer (Württemberg), James Prescott Joule (England), Ludwig A. Colding (Denmark) and Hermann von Helmholtz (Prussia).  Joule's experimental proof was particularly copious.

There is "no more striking instance" of simultaneous discovery in the history of science, wrote Thomas Kuhn.  It was not heat that was conserved, but a more general thing: energy.  Heat was just one manifestation of energy.

==== Obscurity ====

One of the first to come round to the dynamical theory of heat, as it was called, had been Sadi Carnot himself.  From surviving notes it is known he started to have doubts about the caloric theory and, according to physicist Eric Mendoza, "by the time he came to correct the proofs of his book he had realized that the very basis of all his theorems and demonstrations was wrong".  He did not live to solve the problem and publish that.  It was a "sad fact that he died in a madhouse": in 1832.
His book made no discernible impact on the scientific or engineering communities of the time.  One person who did read it was his friend Émile Clapeyron who rewrote the theory in a mathematical treatment and published it in a learned journal; it was translated into English.
Sadi Carnot's book fell into such obscurity that in 1845 William Thomson (the future Lord Kelvin), then a research student in Paris, was unable to find a copy.  "He searched libraries, bookstores, and the stalls on the quays along the Seine, but no success... Sadi Carnot on heat was unknown".

== Rescuing Carnot's theory ==

=== Rudolf Clausius and William Thomson ===
Eventually Thomson did manage to get hold of a copy: in his native Scotland.  He published papers about Carnot's theory that drew it to the attention of scientists generally.  It contained some important truths.  Using it, Thomson was able to devise the Kelvin scale of temperature, and his brother James Thomson used it to make an important prediction about the freezing point of water under pressure that was verified experimentally.  Hence Thomson was extremely reluctant to give up the caloric theory, even though his friend Joule was insisting it was wrong.

Around 1850 Rudolf Clausius (Berlin, Prussia) and William Thomson (Glasgow, Scotland) independently realised that Carnot's theory could be saved by making a new assumption about the laws of physics.  Of the two, Clausius published first; Thomson conceded his priority.  Their papers can be read as external links to this article.  Their reasoning becomes increasingly mathematical but the key point is paraphrased later below.

=== Fixing the Carnot cycle: Maxwell ===