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Theory of Heat

Theory of Heat

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by James Clerk Maxwell

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Though James Clerk Maxwell (1831–1879) is best remembered for his epochal achievements in electricity and magnetism, he was wide-ranging in his scientific investigations, and he came to brilliant conclusions in virtually all of them. As James R. Newman put it, Maxwell "combined a profound physical intuition, an exquisite feeling for the relationship of


Though James Clerk Maxwell (1831–1879) is best remembered for his epochal achievements in electricity and magnetism, he was wide-ranging in his scientific investigations, and he came to brilliant conclusions in virtually all of them. As James R. Newman put it, Maxwell "combined a profound physical intuition, an exquisite feeling for the relationship of objects, with a formidable mathematical capacity to establish orderly connections among diverse phenomena. This blending of the concrete and the abstract was the chief characteristic of almost all his researches."
Maxwell's work on heat and statistical physics has long been recognized as vitally important, but Theory of Heat, his own masterful presentation of his ideas, remained out of print for years before being brought back in this new edition. In this unjustly neglected classic, Maxwell sets forth the fundamentals of thermodynamics clearly and simply enough to be understood by a beginning student, yet with enough subtlety and depth of thought to appeal also to more advanced readers. He goes on to elucidate the fundamental ideas of kinetic theory, and — through the mental experiment of "Maxwell's demon" — points out how the Second Law of Thermodynamics relies on statistics.
A new Introduction and notes by Peter Pesic put Maxwell's work into context and show how it relates to the quantum ideas that emerged a few years later. Theory of Heat will serve beginners as a sound introduction to thermal physics; advanced students of physics and the history of science will find Maxwell's ideas stimulating, and will be delighted to discover this inexpensive reprint of a long-unavailable classic.

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Theory of Heat

By James Clerk Maxwell, Peter Pesic

Dover Publications, Inc.

Copyright © 2001 Peter Pesic
All rights reserved.
ISBN: 978-0-486-17406-8



THE DISTINCTION between hot bodies and cold ones is familiar to all, and is associated in our minds with the difference of the sensations which we experience in touching various substances, according as they are hot or cold. The intensity of these sensations is susceptible of degrees, so that we may estimate one body to be hotter or colder than another by the touch. The words hot, warm, cool, cold, are associated in our minds with a series of sensations which we suppose to indicate a corresponding series of states of an object with respect to heat.

We use these words, therefore, as the names of these states of the object, or, in scientific language, they are the names of Temperatures, the word hot indicating a high temperature, cold a low temperature, and the intermediate terms intermediate temperatures, while the word temperature itself is a general term intended to apply to any one of these states of the object.

Since the state of a body may vary continuously from cold to hot, we must admit the existence of an indefinite number of intermediate states, which we call intermediate temperatures. We may give names to any number of particular degrees of temperature, and express any other temperature by its relative place among these degrees.

The temperature of a body, therefore, is a quantity which indicates how hot or how cold the body is.

When we say that the temperature of one body is higher or lower than that of another, we mean that the first body is hotter or colder than the second, but we also imply that we refer the state of both bodies to a certain scale of temperatures. By the use, therefore, of the word temperature, we fix in our minds the conviction that it is possible, not only to feel, but to measure, how hot a body is.

Words of this kind, which express the same things as the words of primitive language, but express them in a way susceptible of accurate numerical statement, are called scientific terms, because they contribute to the growth of science.

We might suppose that a person who has carefully cultivated his senses would be able by simply touching an object to assign its place in a scale of temperatures, but it is found by experiment that the estimate formed of temperature by the touch depends upon a great variety of circumstances, some of these relating to the texture or consistency of the object, and some to the temperature of the hand or the state of health of the person who makes the estimate.

For instance, if the temperature of a piece of wood were the same as that of a piece of iron, and much higher than that of the hand, we should estimate the iron to be hotter than the wood, because it parts with its heat more readily to the hand, whereas if their temperatures were equal, and much lower than that of the hand, we should estimate the iron to be colder than the wood.

There is another common experiment, in which we place one hand in hot water and the other in cold for a sufficient time. If we then dip both hands in the same basin of lukewarm water alternately, or even at once, it will appear cold to the warmed hand and hot to the cooled hand.

In fact, our sensations of every kind depend upon so many variable conditions, that for all scientific purposes we prefer to form our estimate of the state of bodies from their observed action on some apparatus whose conditions are more simple and less variable than those of our own senses.

The properties of most substances vary when their temperature varies. Some of these variations are abrupt, and serve to indicate particular temperatures as points of reference; others are continuous, and serve to measure other temperatures by comparison with the temperatures of reference.

For instance, the temperature at which ice melts is found to be always the same under ordinary circumstances, though, as we shall see, it is slightly altered by change of pressure. The temperature of steam which issues from boiling water is also constant when the pressure is constant.

These two phenomena therefore—the melting of ice and the boiling of water—indicate in a visible manner two temperatures which we may use as points of reference, the position of which depends on the properties of water and not on the conditions of our senses.

Other changes of state which take place at temperatures more or less definite, such as the melting of wax or of lead, and the boiling of liquids of definite composition, are occasionally used to indicate when these temperatures are attained, but the melting of ice and the boiling of pure water at a standard pressure remain the most important temperatures of reference in modern science.

These phenomena of change of state serve to indicate only a certain number of particular temperatures. In order to measure temperatures in general, we must avail ourselves of some property of a substance which alters continuously with the temperature.

The volume of most substances increases continuously as the temperature rises, the pressure remaining constant. There are exceptions to this rule, and the dilatations of different substances are not in general in the same proportion; but any substance in which an increase of temperature, however small, produces an increase of volume may be used to indicate changes of temperature.

For instance, mercury and glass both expand when heated, but the dilatation of mercury is greater than that of glass. Hence if a cold glass vessel be filled with cold mercury, and if the vessel and the mercury in it are then equally heated, the glass vessel will expand, but the mercury will expand more, so that the vessel will no longer contain the mercury. If the vessel be provided with a long neck, the mercury forced out of the vessel will rise in the neck, and if the neck is a narrow tube finely graduated, the amount of mercury forced out of the vessel may be accurately measured.

This is the principle of the common mercurial thermometer, the construction of which will be afterwards more minutely described. At present we consider it simply as an instrument the indications of which vary when the temperature varies, but are always the same when the temperature of the instrument is the same.

The dilatation of other liquids, as well as that of solids and of gases, may be used for thermometric purposes, and the thermo-electric properties of metals, and the variation of their electric resistance with temperature, are also employed in researches on heat. We must first, however, study the theory of temperature in itself before we examine the properties of different substances as related to temperature, and for this purpose we shall use the particular mercurial thermometer just described.


This thermometer consists of a glass tube terminating in a bulb, the bulb and part of the tube being filled with mercury, and the rest of the tube being empty. We shall suppose the tube to be graduated in any manner so that the height of the mercury in the tube may be observed and recorded. We shall not, however, assume either that the tube is of uniform section or that the degrees are of equal size, so that the scale of this primitive thermometer must be regarded as completely arbitrary. By means of our thermometer we can ascertain whether one temperature is higher or lower than another, or equal to it, but we cannot assert that the difference between two temperatures, A and B, is greater or less than the difference between two other temperatures, C and D.

We shall suppose that in every observation the temperature of the mercury and the glass is equal and uniform over the whole thermometer. The reading of the scale will then depend on the temperature of the thermometer, and, since we have not yet established any more perfect thermometric scale, we shall call this reading provisionally 'the temperature by the arbitrary scale of the thermometer.'

The reading of a thermometer indicates primarily its own temperature, but if we bring the thermometer into intimate contact with another substance, as for instance if we plunge it into a liquid for a sufficient time, we find that the reading of the thermometer becomes higher or lower according as the liquid is hotter or colder than the thermometer, and that if we leave the thermometer in contact with the substance for a sufficient time the reading becomes stationary. Let us call this ultimate reading 'the temperature of the substance.' We shall find as we go on that we have a right to do so.

Let us now take a vessel of water which we shall suppose to be at the temperature of the air, so that if left to itself it would remain at the same temperature. Take another smaller vessel of thin sheet copper or tin plate, and fill it with water, oil, or any other liquid, and immerse it in the larger vessel of water for a certain time. Then, if by means of our thermometer we register the temperatures of the liquids in the two vessels before and after the immersion of the copper vessel, we find that if they are originally at the same temperature the temperature of both remains the same, but that if one is at a higher temperature than the other, that which has the higher temperature becomes colder and that which has the lower temperature becomes hotter, so that if they continue in contact for a. sufficient time they arrive at last at the same temperature, after which no change of temperature takes place.

The loss of temperature by the hot body is not in general equal to the gain of temperature by the cold body, but it is manifest that the two simultaneous phenomena are due to one cause, and this cause may be described as the passage of Heat from the hot body to the cold one.

As this is the first time we have used the word Heat, let us examine what we mean by it.

We find the cooling of a hot body and the heating of a cold body happening simultaneously as parts of the same phenomenon, and we describe this phenomenon as the passage of heat from the hot body to the cold one. Heat, then, is something which may be transferred from one body to another, so as to diminish the quantity of heat in the first and increase that in the second by the same amount. When heat is communicated to a body, the temperature of the body is generally increased, but sometimes other effects are produced, such as change of state. When heat leaves a body, there is either a fall of temperature or a change of state. If no heat enters or leaves a body, and if no changes of state or mechanical actions take place in the body, the temperature of the body will remain constant.

Heat, therefore, may pass out of one body into another just as water may be poured from one vessel into another, and it may be retained in a body for any time, just as water may be kept in a vessel. We have therefore a right to speak of heat as of ameasurable quantity, and to treat it mathematically like other measurable quantities so long as it continues to exist as heat. We shall find, however, that we have no right to treat heat as a substance, for it may be transformed into something which is not heat, and is certainly not a substance at all, namely, mechanical work.

We must remember, therefore, that though we admit heat to the title of a measurable quantity, we must not give it rank as a substance, but must hold our minds in suspense till we have further evidence as to the nature of heat.

Such evidence is furnished by experiments on friction, in which mechanical work, instead of being transmitted from one part of a machine to another, is apparently lost, while at the same time, and in the same place, heat is generated, the amount of heat being in an exact proportion to the amount of work lost. We have, therefore, reason to believe that heat is of the same nature as mechanical work, that is, it is one of the forms of Energy.

In the eighteenth century, when many new facts were being discovered relating to the action of heat on bodies, and when at the same time great progress was being made in the knowledge of the chemical action of substances, the word Caloric was introduced to signify heat as a measurable quantity. So long as the word denoted nothing more than this, it might be usefully employed, but the form of the word accommodated itself to the tendency of the chemists of that time to seek for new 'imponderable substances,' so that the word caloric came to connote not merely heat, but heat as an indestructible imponderable fluid, insinuating itself into the pores of bodies, dilating and dissolving them, and ultimately vaporising them, combining with bodies in definite quantities, and so becoming latent, and reappearing when these bodies alter their condition. In fact, the word caloric, when once introduced, soon came to imply the recognised existence of something material, though probably of a more subtle nature than the then newly discovered gases. Caloric resembled these gases in being invisible and in its property of becoming fixed in solid bodies. It differed from them because its weight could not be detected by the finest balances, but there was no doubt in the minds of many eminent men that caloric was a fluid pervading all bodies, probably the cause of all repulsion, and possibly even of the extension of bodies in space.

Since ideas of this kind have always been connected with the word caloric, and the word itself has been in no slight degree the means of embodying and propagating these ideas, and since all these ideas are now known to be false, we shall avoid as much as possible the use of the word caloric in treating of heat. We shall find it useful, however, when we wish to refer to the erroneous theory which supposes heat to be a substance, to call it the 'Caloric Theory of Heat.'

The word heat, though a primitive word and not a scientific term, will be found sufficiently free from ambiguity when we use it to express a measurable quantity, because it will be associated with words expressive of quantity, indicating how much heat we are speaking of

We have nothing to do with the word heat as an abstract term signifying the property of hot things, and when we might say a certain heat, as the heat of new milk, we shall always use the more scientific word temperature, and speak of the temperature of new milk.

We shall never use the word heat to denote the sensation of heat. In fact, it is never so used in ordinary language, which has no names for sensations, unless when the sensation itself is of more importance to us than its physical cause, as in the case of pain, &c. The only name we have for this sensation is 'the sensation of heat.'

When we require an adjective to denote that a phenomenon is related to heat we shall call it a thermal phenomenon, as, for instance, we shall speak of the thermal conductivity of a substance or of thermal radiation to distinguish the conduction and radiation of heat from the conduction of electricity or the radiation of light. The science of heat has been called (by Dr. Whewell and others) Thermotics, and the theory of heat as a form of energy is called Thermodynamics. In the same way the theory of the equilibrium of heat might be called Thermostatics, and that of the motion of heat Thermokinematics.

The instrument by which the temperature of bodies is registered is called a Thermometer or measurer of warmth, and the method of constructing and using thermometers may be called Thermometry.

The instrument by which quantities of heat are measured is called a Calorimeter, probably because it was invented at a time when heat was called Caloric. The name, however, is now well established, and is a convenient one, as its form is sufficiently distinct from that of the word Thermometer. The method of measuring heat may be called Calorimetry.

A certain quantity of heat, with which all other quantities are compared, is called a Thermal Unit. This is the quantity of heat required to produce a particular effect, such as to melt a pound of ice, or to raise a pound of water from one defined temperature to another defined temperature. A particular thermal unit has been called by some authors a Calorie.

We have now obtained two of the fundamental ideas of the science of heat—the idea of temperature, or the property of a body considered with reference to its power of heating other bodies; and the idea of heat as a measurable quantity, which may be transferred from hotter bodies to colder ones. We shall consider the further development of these ideas in the chapters on Thermometry and Calorimetry, but we must first direct our attention to the process by which heat is transferred from one body to another.

This process is called the Diffusion of Heat. The diffusion of heat invariably transfers heat from a hotter body to a colder one, so as to cool the hotter body and warm the colder body. This process would go on till all bodies were brought to the same temperature if it were not for certain other processes by which the temperatures of bodies are changed independently of any exchange of heat with other bodies, as, for instance, when combustion or any other chemical process takes place, or when any change occurs in the form, structure, or physical state of the body.


Excerpted from Theory of Heat by James Clerk Maxwell, Peter Pesic. Copyright © 2001 Peter Pesic. Excerpted by permission of Dover Publications, Inc..
All rights reserved. No part of this excerpt may be reproduced or reprinted without permission in writing from the publisher.
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Meet the Author

James Clerk Maxwell: In His Own Words — And Others
Dover reprinted Maxwell's Treatise on Electricity and Magnetism in 1954, surely one of the first classics of scientific literature over a thousand pages in length to be given new life and accessibility to students and researchers as a result of the paperback revolution of the 1950s. Matter and Motion followed in 1991 and Theory of Heat in 2001.

Some towering figures in science have to speak for themselves. Such is James Clerk Maxwell (1813–1879), the Scottish physicist and mathematician who formulated the basic equations of classical electromagnetic theory.

In the Author's Own Words:
"We may find illustrations of the highest doctrines of science in games and gymnastics, in traveling by land and by water, in storms of the air and of the sea, and wherever there is matter in motion."

"The 2nd law of thermodynamics has the same degree of truth as the statement that if you throw a tumblerful of water into the sea, you cannot get the same tumblerful of water out again." — James Clerk Maxwell

Critical Acclaim for James Clerk Maxwell:
"From a long view of the history of mankind — seen from, say, ten thousand years from now — there can be little doubt that the most significant event of the 19th century will be judged as Maxwell's discovery of the laws of electrodynamics. The American Civil War will pale into provincial insignificance in comparison with this important scientific event of the same decade." — Richard P. Feynman

"Maxwell's equations have had a greater impact on human history than any ten presidents." — Carl Sagan

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