---
title: "Carnot engine explanation"
chunk: 5/8
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"
---

The Carnot cycle as published cannot work since it is wrongly assumed that as much heat should be expelled to the cold sink as came in from the hot source.  That is too much: not enough will be left in the engine to complete the cycle.  A simple way to correct the mistake was described by James Clerk Maxwell in his Theory of Heat (1871).  This was a book meant for "artisans and students" but Maxwell "did not hesitate to include discussions of the latest work in thermodynamics".
By that date French engineer Gustave-Adolphe Hirn had confirmed by experiment that, whenever an engine performs mechanical work, less heat emerges from it than goes in.  The missing heat is changing into work.
But it was easy to see that the quantities (heat in vs. heat out) could not have been equal, said Maxwell.  For, supposing they were, how could we explain that the engine, by doing work, can produce yet more heat  —  e.g. by stirring a liquid to raise its temperature?  In that case the engine must somehow be producing more heat than it consumes, contrary to the doctrine that caloric cannot be created.
To fix the Carnot cycle, therefore, one must terminate the isothermal compression phase at just the right point, before too much heat has passed to the cold sink.  It is easy to do this by calculation, said Maxwell, "but is still easier" by removing the sink as soon as the fluid pressure rises to its original cold-temperature value.

=== Fixing the proof ===
A deeper problem was that Carnot's proof of his central Principle was not valid either.  Granted the conservation of heat, he had reasoned (above) that there could not be such a thing as a 'super' engine more efficient than a Carnot engine, or else perpetual motion would be possible.  However, as Ted Jacobson noted
While Carnot's conclusion was correct, his argument contained a single deep flaw: heat is not by itself conserved! More heat flows out of the hot reservoir than flows into the colder reservoir, the difference being the work extracted.
This means that, since the 'super' engine is the more efficient of the two, it extracts more work and so passes less waste heat into the cold reservoir.  Hence, when the Carnot engine is run backwards, "the cold reservoir is no longer restored to its initial state: more heat is drawn out than went in".

The leftover work, then, is not produced from nothing, but rather from the heat drawn out of the colder reservoir. While not as inadmissable [i.e. intentionally absurd] as Carnot's result, this is nevertheless inadmissable. Its impossibility is Kelvin's version of the second law of thermodynamics. 
There is another way of looking at it:
Alternatively, all of the work from the more efficient engine could be used to run the less efficient engine backwards, in which case the net result would be spontaneous (but engineered) heat flow from the colder reservoir to the hotter one, in violation of Clausius' version of the second law.

== Aftermath ==

=== The Second Law ===

Hence, Kelvin and Clausius saved the Carnot Principle by formally identifying and stating new laws of nature.  The First Law of Thermodynamics is the conservation of energy.  The Second Law can be encapsulated thus:

Heat cannot flow spontaneously from cold to hot (Clausius).
An engine cannot be run from a single heat reservoir (Kelvin)
Those are similar formulations; were long believed to be completely equivalent; but turn out not to be quite the same. A disquieting feature, which has still not been explained, is that there is no universally agreed way of stating this law, despite attempts at consensus.  There have been many formulations.  "And even today, the Second Law remains so obscure that it continues to attract new efforts at clarification".

==== Engineering in spite of the Second Law ====

Only slowly did the new theory diffuse into engineering practice, and reputable technologists continued to conceive engines that were thermodynamically impossible.  John Ericsson built a hot air ship's engine that (it was claimed) saved fuel by continually recycling waste heat.  Called the Caloric Engine, its cylinders were 14 foot (4.3 metres) thick. According to one who believed in it:
The principle of this new engine consists in this, that the heat which is required to give motion to the engine at the commencement, is returned by a peculiar process of transfer, and thereby made to act over and over again, instead of being, as in the steam engine, thrown into a condenser, or into the atmosphere as so much waste fuel.To which Scientific American riposted: "Let us point out its fallacious principles: it is stated that it only uses so much coal to make up the loss of radiation, therefore, if there were no loss of heat by radiation, it would use no coai at all, after the first fire; it would go on for ever  —  a perpetual motion surely".

==== Entropy ====

Sadi Carnot's most important single idea may have been the completely reversible thermodynamic process.  It led to the concept of entropy, whose meaning is indicated below.
The word entropy ("transformational energy") was coined by Clausius in 1865 to refer to a variable in his mathematical reasoning. It stands for something  that is expressed in units of energy divided by temperature,  is not directly apprehended by the human senses, and is difficult to measure experimentally, Generally, there exists a rather hazy understanding of entropy, even amongst those who have to use the concept professionally.  Also the word is much misused by some scientists, educators and popular writers, if not abused by charlatans.
In the same paper Clausius summarised the laws of thermodynamics as follows:

The energy of the universe is constant.
The entropy of the universe tends to a maximum.
One way of understanding 2. is as follows: