---
title: "Carnot engine explanation"
chunk: 2/8
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"
---

== Preliminary outline ==
Carnot grasped that:

all heat engines work by conveying heat from a hotter to a cooler place
a heat engine may work in reverse, when it becomes a heat pump
the ideally efficient engine would be 100% reversible and it is impossible to have an engine more efficient than that
its working substance (steam, air or other fluid) is not critical; on the contrary, the ideal reversible engine's efficiency is limited by its input and output temperatures, and nothing else.
He also found the cycle by which the 100% reversible engine could work. It serves as the ideal or benchmark against which all feasible heat engines can be compared.

== His reasoning ==
For Edwin Thompson Jaynes
Carnot's reasoning is outstandingly beautiful, because it deduces so much from so little  — and with such a sweeping generality that rises above all tedious details — but at the same time with such a compelling logical force. In this respect, I think that Carnot's principle ranks with Einstein's principle of relativity. 
For historian of science D. S. L. Cardwell, "Nothing unnecessary is included and nothing essential is missed out. It is, in fact, very difficult to think of a more efficient piece of abstraction in the history of science since
Galileo taught men the basis of the procedure".

=== 1.  Heat, without a cold place, cannot generate motion ===
Carnot showed, first, that heat by itself cannot produce motion: it must also have a cooler place to go to.  The common steam engine had a hot place (the furnace) and a cool place (the condenser); but he proved the same principle must be true for all heat engines that can possibly be devised.
He did it by imagining an engine with no cool place at all i.e. engine and surroundings are uniformly hot.  Such an engine can deliver no power e.g. the piston will not retract.  (As Feynman put it, "If the whole world were at the same temperature, one could not convert any of its heat energy into work".)  "It is necessary that there should also be cold; without it, the heat would be useless", said Carnot.  (Power station cooling towers were developed to provide such cool places, as were automobile radiators; such recipients for waste heat are called cold sinks, or more directly, heat sinks.)

Carnot supplied an analogy: a waterfall.  He wroteThe motive power of a waterfall depends on its height and on the quantity of the liquid; the motive power of heat depends also on the quantity of caloric used, and on what ,,, we will call, the height of its fall, that is to say, the difference of temperature of the bodies between which the exchange of caloric is made. 
That heat engines cannot produce motion except by exploiting the difference in temperature between two places was not so obvious.
The insight was afterwards used to formulate the Second Law of Thermodynamics:- 

A ship's engine cannot extract heat from the ocean only for lack of a suitable cold sink.  A small engine for polar regions has been proposed that exploits the temperature difference between the sea (just above freezing) and the much colder winter atmosphere (—25°C).

=== 2.  A heat engine can be run in reverse and will behave as a refrigerator ===

==== Running an engine backwards ====
Next, Carnot reasoned that, like a water-mill,  the heat engine could be run backwards.  Instead of exploiting the "fall" to get useful mechanical effort, we could do the reverse: expend the mechanical effort to drive the caloric "upwards".
Specifically, by forcing the engine backwards, we can make heat go from the cool place to the hot place, contrary to what naturally happens.  The cool place will be made even cooler (as in a refrigerator) and the hot place will be made even hotter. Carnot had invented the heat pump.
(This insight - that it is possible to convey heat from a cool to a warm place, but only by the expenditure of mechanical effort, lies at the heart of another way of stating the Second Law of Thermodynamics.)

==== Reversibility as an index of efficiency ====
Carnot then went on to develop the crucial idea that, the more efficient the engine, the greater the proportion of heat that can be recovered if run backwards.
Historian of science D. S. L. Cardwell believed that Carnot was inspired by  the column-of-water engine, an early form of hydropower.  Popular in districts where coal was scarce, it was similar to a steam engine, but driven by the pressure of a head of water instead of steam. Like the steam engine, engineers strove to make it more efficient; and they expressed its efficiency in terms of the proportion of water that could be restored if run backwards, when it behaved as a pump.

=== 3.  The ideally efficient heat engine would be completely reversible ===
Carnot went on to prove that if a heat engine could be made completely reversible, its efficiency would be unsurpassable.  It is, therefore, the fundamental limit beyond which engine efficiency cannot possibly go, answering his earlier question.  Today this engine is called the Carnot engine in his honour.  When it is run in reverse, it consumes as much motive power as it generates when it is run forward.