Theory of Heat

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Theory of Heat is a textbook written by James Clerk Maxwell and published in 1871, London: Longmans, Green and Co. It was printed by Spottiswoode and Co.


  • The aim of this book is to exhibit the scientific connexion of the various steps by which our knowledge of the phenomena of heat has been extended.
    • Preface
  • The first of these steps is the invention of the thermometer... The second step is the measurement of quantities of heat, or Calorimetry. The whole science of heat is founded on Thermometry and Calorimetry, and when these operations are understood we may proceed to the third step, which is the investigation of those relations between the thermal and the mechanical properties of substances which form the subject of Thermodynamics.
    • Preface
  • The whole of [thermodynamics] depends on the consideration of the Intrinsic Energy of a system of bodies, as depending on the temperature and physical state, as well as the form, motion, and relative position of these bodies. Of this energy, however, only a part is available for the purpose of producing mechanical work, and though the energy itself is indestructible, the available part is liable to diminution by the action of certain natural processes, such as conduction and radiation of heat, friction, and viscosity. These processes, by which energy is rendered unavailable as a source of work, are classed together under the name of the Dissipation of Energy...
    • Preface
  • The last chapter is devoted to the explanation of various phenomena by means of the hypothesis that bodies consist of molecules, the motion of which constitutes the heat of those bodies.
    • Preface
  • [I]t has been found necessary to omit everything which is not an essential part of the intellectual process by which the doctrines of heat have been developed, or which does not materially assist the student in forming his own judgment on these doctrines.
    • Preface
  • A full account of the most important experiments on the effects of heat will be found in [Robert Vickers] Dixon's 'Treatise on Heat' (Hodges & Smith, 1849).
  • Professor Balfour Stewart's treatise contains all that is necessary to be known in order to make experiments on heat. The student may be also referred to [Augustin Privat-]Deschanel's ' Natural Philosophy,' Part II., translated by Professor [J. D.] Everett, who has added a chapter on Thermodynamics; to Professor Rankine's work on the Steam Engine, in which he will find the first systematic treatise on thermodynamics; to Professor Tait's 'Thermodynamics,' which contains an historical sketch of the subject, as well as the mathematical investigations; and to Professor Tyndall's work on 'Heat as a Mode of Motion,' in which the doctrines of the science are forcibly impressed on the mind by well-chosen illustrative experiments.
  • Words... 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 science.
    • Introduction
  • [W]e 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.
    • Introduction
  • Any substance in which an increase of temperature, however small, produces an increase of volume may be used to indicate changes of temperature.
  • [T]he thermo-electric properties of metals, and the variation of their electric resistance with temperature, are also employed in researches on heat.
  • Heat... 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 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... 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 a measurable quantity, and to treat it mathematically like other measurable quantities so long as it continues to exist as heat.
  • [W]e have no right to treat heat as a substance, for it may be transformed into something which is not heat, and [which] is certainly not a substance at all, namely, mechanical work.
  • [T]hough 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...
  • [E]vidence is furnished by experiments on friction, in which mechanical work, instead of being transmitted... heat is generated... 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... the word Caloric was introduced to signify heat as a measurable quantity. ...but the form of the word accommodated itself to the tendency of the chemists... to seek for new 'imponderable substances,' so that the word caloric came to connote... 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.
  • [T]he word caloric... soon came to imply the... existence of something material, though probably of a more subtle nature than the then newly discovered gases.
  • Caloric resembled... 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.
  • The instrument by which quantities of heat are measured is called a Calorimeter... 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... a Calorie.
  • We have... obtained two of the fundamental ideas... the idea of temperature, or the property of a body... 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.
  • [T]he 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... This process would go on till all bodies were brought to the same temperature if it were not for certain other processes... 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.
  • Conduction is the flow of heat through an unequally heated body from places of higher to places of lower temperature.
  • The term convection is applied to those processes by which the diffusion of heat is rendered more rapid by the motion of the hot substance from one place to another...
  • In Radiation, the hotter body loses heat, and the colder body receives heat by means of a process occurring in some intervening medium which does not itself become thereby hot.
  • [T]he amount of heat transferred from the hotter to the colder body is invariably greater than the amount, if any, transferred from the colder to the hotter.
  • When heat is passing through a body by conduction, the temperature of the body must be greater in the parts from which the heat comes than in those to which it tends, and the quantity of heat which passes through any thin layer of the substance depends on the difference of the temperatures of the opposite sides of the layer. ...[W]e may define conduction as the passage of heat through a body depending on inequality of temperature in adjacent parts of the body. ...[T]he parts of the body through which the heat comes... must be hotter... and the parts higher up the stream of heat still hotter.
  • [T]ake a thermometer with a large bulb... and dash a little hot water over the bulb. The fluid will fall in the tube before it begins to rise, showing that the bulb began to expand before the fluid expanded.
  • If we make use of a thermometer... if the sun's rays fall on it... while the air immediately surrounding the bulb is at a temperature below freezing. The heat... to which the thermometer... responds, is not conveyed... through the air, for the air is cold... The mode in which the heat reaches the body... without warming the air through which it passes, is called radiation.
  • Substances which admit of radiation taking place through them are called Diathermanous. Those which do not allow heat to pass through them without becoming themselves hot are called Athermanous. ...If the body is not perfectly diathermanous it stops more or less of the radiation, and becomes heated itself, instead of transmitting the whole radiation to bodies beyond it.
  • The distinguishing characteristic of radiant heat is, that it travels in rays like light, whence the name radiant. These rays have all the physical properties of rays of light, and are capable of reflexion, refraction, interference, and polarisation.
  • [I]t is only when the radiation is stopped that it has any effect in heating what it falls on.
  • By means of any regular concave piece of metal... pressed when hot against a clear sheet of ice, first on one side and then on the other, it is easy to make a lens of ice which may be used... as a burning glass; but this experiment... is far inferior in interest to one invented by Professor Tyndall, in which the heat, instead of being concentrated by ice, is concentrated in ice.
  • [A]ll hot bodies emit radiation.
  • When [a] body is hot enough, its radiations become visible, and the body is said to be red hot. When it is still hotter it sends forth... rays of every colour, and it is... white hot. When a body is too cold to shine visibly, it still shines with invisible heating rays... it does not appear that any body can be so cold as not to send forth radiations.
  • [O]ur eyes are sensitive only to particular kinds of rays... coming from some very hot body... directly or after reflexion or scattering at the surface of other bodies.
  • Radiation between bodies differs from heat as we have defined it—1st, in not making the body hot through which it passes; 2nd, in being of many different kinds.
  • [I]n a fluid at rest the pressure at any point must be equal in all directions.
  • There are two great classes of fluids. ...the first class, such as water... will partly fill the vessel... Fluids having this property are called liquids. If... the fluid which we put into the closed vessel be one of the second class, then... it will expand and fill the vessel... Fluids having this property are called gases. ...a gas cannot, like a liquid, be kept in an openmouthed vessel.
  • The distinction... between a gas and a liquid is that, however large the space may be into which a portion of gas is introduced, the gas will expand and exert pressure on every part of its boundary, whereas a liquid will not expand more than a very small fraction of its bulk, even when the pressure is reduced to zero; and some liquids can even sustain a hydrostatic tension, or negative pressure, without their parts being separated.
  • A great many solid bodies are constantly in a state of evaporation or transformation into the gaseous state at their free surface. Camphor, iodine, and carbonate of ammonia... if not kept in stoppered bottles, gradually disappear by evaporation, and the vapour... may be recognised by its smell and by its chemical action. Ice... is continually passing into a state of vapour... and in a dry climate during a long frost large pieces... [gradually] disappear. ...[I]ron and copper have each a well-known smell. This... may arise from chemical action at the surface, which sets free hydrogen or some other gas combined with a very small quantity of the metal.
  • The original thermometer invented by Galileo was an air thermometer. It consisted of a glass bulb with a long neck. The air in the bulb was heated and then the neck was plunged into a coloured liquid. As the air in the bulb cooled, the liquid rose in the neck, and the higher the liquid the lower the temperature of the air in the bulb. By putting the bulb into the mouth of a patient and noting the point to which the liquid was driven down in the tube, a physician might estimate whether the ailment was of the nature of a fever or not. Such a thermometer has several obvious merits. It is easily constructed, and gives larger indications for the same change of temperature than a thermometer containing any liquid as the thermometric substance. Besides this, the air requires less heat to warm it than an equal bulk of any liquid, so that the air thermometer is very rapid in its indications. The great inconvenience of the instrument as a means of measuring temperature is, that the height of the liquid in the tube depends on the pressure of the atmosphere as well as on the temperature of the air in the bulb. The air thermometer cannot therefore of itself tell us anything about temperature. We must consult the barometer at the same time, in order to correct the reading of the air thermometer. Hence the air thermometer, to be of any scientific value, must be used along with the barometer, and its readings are of no use till after a process of calculation has been gone through. This puts it at a great disadvantage compared with the mercurial thermometer... But if the researches on which we are engaged are of so important a nature that we are willing to undergo the labour of double observations and numerous calculations, than the advantages of the air thermometer may again preponderate.
    • On the Air Thermometer

See also