---
title: "Carnot engine explanation"
chunk: 3/8
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 engine is not one anyone would attempt to build.  Its point is that it represents the ideal or extreme limit which cannot be surpassed even in theory.  It is a benchmark against which all real engines can be compared.  For example, solar cells are heat engines, and "Carnot efficiency appears profusely in the numerous formulae that have been suggested for solar energy conversion".
For Carnot, a completely reversible engine has this property.  Run forwards as a motor, one cycle can lift a weight a certain distance [generate a certain amount of work] while transferring a certain amount of heat from the hot place to the cool place.  Run backwards as a refrigerator, one cycle will exactly restore the original conditions.  All real engines fall short of this ideal standard, since along the way they lose a fraction of the heat.
The proof is as follows.  Suppose there was such a thing as a 'super' engine: one even more efficient than a Carnot engine.  Then we could use it to drive a Carnot engine backwards.  The Carnot engine would restore the heat from cold to hot place.  In effect, the imaginary super engine would be delivering a margin of useful power while using the Carnot engine to feed itself an inexhaustible supply of fuel.  Wrote one commentator: "Once started, this would run forever, delivering an infinite amount of useful work without any further expenditure of fuel".  We would have perpetual motion to "drive our ships, locomotives and factories".
Since this is absurd and inadmissible, we must conclude that the supposed super engine cannot exist.  Hence

Physicist Sir Joseph Larmor thought this argument "is perhaps the most original in physical science".

=== 4.  It does not depend on finding a superlative working substance ===

It follows at once that all engines, if reversible, must have the same efficiency if operating between those temperatures, regardless of their working substances. It cannot depend on the working substance, for in the above proof none was specified: it might have been steam, air, or anything else.
(That all reversible engines working between the same heat source and cool place have the same efficiency is yet another way of stating the Second Law of Thermodynamics, and many authors have credited the law to Sadi Carnot himself.)
Therefore, advised Carnot, there was little to be gained by experimenting with exotic substances, for none was intrinsically more efficient.  As a practical matter the only promising substitute for steam was air, because  "Air could be heated directly by combustion carried on within its own mass"  — in other words, the internal combustion engine.
Rather, the guiding principle in practical engine design should be that the temperature of the working fluid should fall from as high as possible to as low as possible, acting expansively.

=== 5.  The Carnot cycle ===
To make his proof more rigorous he went on to describe an engine actually working between a hot reservoir and cold sink in a completely reversible cycle.  For this to happen each step in the cycle had itself to be reversible i.e. it must not waste any fraction of the heat.

==== Means ====

The fundamental rule for not wasting heat, deduced Carnot (see quote box), is never to allow direct thermal contact between parts which are at appreciably different temperatures.  Were that to permitted, heat would escape from hotter to cooler:  without doing any work.
Very few thermodynamic processes can be carried out without breaking that rule.  For instance, if we wanted to expand a body of gas in a cylinder to drive a piston, we would normally just heat it up: but this would require thermal contact with something hotter.
However, there are two extreme cases in which it is just possible in principle:

Completely insulate the body of gas and allow it to expand spontaneously from its own internal energy; this will lower its temperature. The jargon for this is adiabatic expansion.  (The idea was used in the Cornish engine, above.)
Apply heat to the body of gas so slowly that it has time to expand without raising its temperature.  For this to happen, the temperature gap between gas and heat source must be infinitesimal. The jargon for this is isothermal expansion.
The problem is to combine them into a working, reversible cycle.

==== Realization ====
To retract the piston and exactly restore the initial conditions, the same processes are to be used in reverse viz. isothermal compression and adiabatic compression.
Hence his cycle can be analyzed into four steps.  In the isothermal phases, more energy is produced in the (hot) expansion stroke than is consumed in the (cool) compression stoke.  The adiabatic phases exactly cancel out.  So the net balance is positive.
The Carnot Cycle is illustrated in the animation; and since it is completely reversible, by Carnot's Principle its efficiency must be the best that can be achieved.
It is usual nowadays when drawing the Carnot cycle to include a pressure–volume diagram with associated mathematics.  This was not done by Carnot himself and is not necessary for an intuitive understanding of his ideas.
For James Clerk Maxwell

The great merit of Carnot's method is that he arranges his operations in a cycle, so as to leave the working substance in precisely the same condition as he found it. We are therefore sure that the energy remaining in the working substance is the same in amount as at the beginning of the cycle.
greatly simplifying any calculations, since we only have to compare the heat taken in, the heat given out, and the work done by the engine
Maxwell also showed that a simple adjustment to the cycle can correct the flaw in Carnot's theory; see below.

== A scientific revolution seems to invalidate Carnot's work ==

=== Caloric, the established theory ===