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See also:HEAT (0. E. haktu, which like " hot," Old Eng. See also:hat, is from the See also:Teutonic type haita, See also:hit, to be hot; cf. Ger. hitze, heiss; Dutch, hitte, heet, &c.)
, a See also:general See also:term applied to that See also:branch of See also:physical See also:science which deals with the effects produced by See also:heat on material bodies, with the See also:laws of transference of heat, and with the transformations of heat into other kinds of See also:energy
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The See also:object of the See also:present See also:article is to give a brief See also:sketch of the See also:historical development of the science of heat, and to indicate the relation of the different branches of the subject, which are discussed in greater detail with reference to the latest progress in See also:separate articles
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1
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Meanings of the Term Heat.—The term heat is employed in See also:ordinary See also:language in a number of different senses
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This makes it a convenient term to employ for the general See also:title of the science, but the different meanings must be carefully distinguished in scientific reasoning
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For the present purpose, omitting metaphorical signification, we may distinguish four See also:principal uses of the term: (a) Sensation of heat; (b) Temperature, or degree of hotness; (c) Quantity of thermal energy; (d) Radiant heat, or energy of See also:radiation
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(a) From the sense of heat, aided in the See also:case of very hot bodies by the sense of sight, we obtain our first rough notions of heat as a physical entity, which alters the See also:state of a See also:body and its See also:condition in respect of warmth, and is capable of passing from one body to another
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By touching a body we can tell whether it is warmer or colder than the See also:hand, and, by touching two similar bodies in See also:succession, we can See also:form a rough estimate, by the acuteness of the sensation experienced, of their difference in hotness or coldness over a limited range
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If a hot See also:iron is placed on a See also:cold iron See also:plate, we may observe that the plate is heated and the iron cooled until both attain appreciably the same degree of warmth; and we infer from similar cases that something which we See also:call " heat " tends to pass from hot to cold bodies, and to attain finally a state of equable See also:diffusion when all the bodies concerned are equally warm or cold
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Ideas such as these derived entirely from the sense of heat, are, so to speak, embedded in the language of every nation from the earliest times
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(b) From the sense of heat, again, we naturally derive the See also:idea of a continuous See also:scale or See also:order, expressed by such terms as summer heat, See also:blood heat, See also:fever heat, red heat, See also: Thus a large kettleful of boiling See also:water will evidently contain more heat than a teacupful, though both may be at the same temperature . The temperature does not depend on the size of the body, but on the degree of concentration of the heat in it, i.e. on the quantity of heat per unit See also:mass, other things being equal . We may regard it as axiomatic that a given body (say a See also:pound of water) in a given state (say boiling under a given pressure) must always contain the same quantity of heat, and conversely that, if it contains a given quantity of heat, and if it is under conditions in other respects, it must be at a definite temperature, which will always be the same for the same given conditions . (d) It is a See also:matter of See also:common observation that rays of the See also:sun or of a See also:fire falling on a body warm it, and it was in the first instance natural to suppose that heat itself somehow travelled across the intervening space from the sun or fire to the body warmed, in much the same way as heat may be carried by a current of hot See also:air or water . But we now know that energy of radiation is not the same thing as heat, though it is converted into heat when the rays strike an absorbing substance . The term " radiant heat," however, is generally retained, because radiation is commonly measured in terms of the heat it produces, and because the transference of energy by radiation and absorption is the most important agency in the diffusion of heat . 2 . See also:Evolution of the Thermometer.—The first step in the development of the science of heat was necessarily the invention of a thermometer, an See also:instrument for indicating temperature and measuring its changes . The first requisite in the case of such an construction . But they possess one obvious defect from a theoretical point of view, namely, that the subdivision of the temperature scale depends on the expansion of the particular liquid selected as the See also:standard . A liquid such as water, which, when continuously heated at a See also:uniform See also:rate from its freezing-pcint, first contracts and then expands, at a rapidly increasing rate, would obviously be unsuitable . But there is no a priori See also:reason why other liquids should not behave to some extent in a similar way . As a matter of fact, it was soon observed that thermometers care-fully constructed with different liquids, such as See also:alcohol, oil and See also:mercury, did not agree precisely in their indications at points of the scale intermediate between the fixed points, and diverged even more widely outside these limits . Another possible method, proposed in 1694 by Carlo Renaldeni (1615-1698), See also:professor of See also:mathematics and See also:philosophy at See also:Pisa, would be to determine the intermediate points of the scale by observing the temperatures of mixtures of See also:ice-cold and boiling water in varying proportions . On this method, the temperature of 5o° C. would be defined as that obtained by mixing equal weights of water at o° C. and oo° C.; 2o° C., that obtained by mixing 8o parts of water at o° C. with 20 parts of water at See also:roe C. and so on . Each degree rise of temperature in a mass of water would then represent the addition of the same quantity of heat . The scale thus obtained would, as a matter of fact, agree very closely with that of a mercury thermometer, but the method would be very difficult to put in practice, and would still have the disadvantage of depending on the properties of a particular liquid, namely, water, which is known to behave in an anomalous manner in other respects . At a later date, the researches of See also:Gay-Lussac (1802) and See also:Regnault (1847) showed that the laws of the expansion of gases are much simpler than those of liquids . Whereas the expansion of alcohol between o° C. and roo° C. is nearly seven times as See also:great as that of mercury, all gases (excluding easily condensible vapours) expand equally, or so nearly equally that the See also:differences between them cannot be detected without the most refined observations . This equality of expansion affords a strong a priori See also:argument for selecting the scale given by the expansion of a See also:gas as the standard scale of temperature, but there are still stronger theoretical grounds for this choice, which will be indicated in discussing the See also:absolute scale (§ 21) . Among liquids mercury is found to agree most nearly with the gas scale, and is generally employed in thermometers for scientific purposes on See also:account of its high boiling-point and for other reasons . The differences of the See also:mercurial scale from the gas scale having been carefully determined, the mercury thermometer can be used as a secondary standard to replace the gas thermometer within certain limits, as the gas thermometer would be very troublesome to employ directly in ordinary investigations . For certain purposes, and especially at temperatures beyond the range of mercury thermometers, See also:electrical thermometers, also standardized by reference to the gas thermometer, have been very generally employed in See also:recent years, while for still higher temperatures beyond the range of the gas thermometer, thermometers based on the recently established laws of{radiation are the only See also:instruments available . For a further discussion of the theory and practice of the measurement of temperature, the reader is referred to the article See also:THERMOMETRY . 4 . See also:Change of State.—Among the most important effects of heat is that of changing the state of a substance from solid to liquid, or from liquid to vapour . With very few exceptions, all substances, whether See also:simple or See also:compound, are known to be capable of existing in each of the three states under suitable conditions of temperature and pressure . The transition of any substance, from the state of liquid to that of solid or vapour under the ordinary atmospheric pressure, takes place at fixed temperatures, the freezing and boiling-points, which are very sharply defined for pure crystalline substances, and serve in fact as fixed points of the thermometric scale . A change of state cannot, however, be effected in any case without the addition or subtraction of a certain definite quantity of heat . If a piece of ice below the freezing-point is gradually heated at a uniform rate, its temperature may be observed to rise regularly till the freezing-point 5 . See also:Calorimetry by Latent Heat.—In principle, the simplest and most See also:direct method of measuring quantities of heat consists in observing the effects produced in melting a solid or vaporizing a liquid . It was, in fact, by the See also:fusion of ice that quantities of heat were first measured . If a hot body is placed in a cavity in a See also:block of ice at o° C., and is covered by a closely fitting slab of ice, the quantity of ice melted will be directly proportional to the quantity of heat lost by the body in cooling to o° C . None of the heat can possibly See also:escape through the ice, and conversely no heat can possibly get in from outside . The body must cool exactly to o° C., and every fraction of the heat it loses must melt an See also:equivalent quantity of ice . Apart from heat lost in transferring the heated body to the ice block, the method is theoretic-ally perfect .
The only difficulty consists in the See also:practical measurement of the quantity of ice melted
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See also:Black estimated this quantity by mopping out the cavity with a sponge before and after the operation
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But there is a variable film of water adhering to the walls of the cavity, which gives trouble in accurate See also:work
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In 178o See also:Laplace and See also:Lavoisier used a See also:double-walled metallic See also:vessel containing broken ice, which was in many respects more convenient than the block, but aggravated the difficulty of the.. film of water adhering to the ice
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In spite of this practical difficulty, the quantity of heat required to melt unit See also:weight of ice was for a See also:long See also:time taken as the unit of heat
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This unit possesses the great See also:advantage that it is See also:independent of the scale of temperature adopted
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At a much later date R
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See also:Bunsen (Phil
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Meg., 1871), adopting a See also:suggestion of See also:Sir See also:
Heat thus absorbed in producing a change of state without rise of temperature is called " Latent Heat," a term introduced by See also:Joseph Black, who was one of the first to study the subject of change of state from the point of view of heat absorbed, and who in many cases actually adopted the comparatively rough method described above of estimating quantities of heat by observing the time required to produce a given change when the substance was receiving heat at a steady rate from its surroundings
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For every change of state a definite quantity of heat is required, without which the change cannot take place
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Heat must be added to melt a solid, or to vaporize a solid or a liquid, and conversely, heat must be subtracted to See also:reverse the change, i.e. to condense a vapour or freeze a liquid
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The quantity required for any given change depends on the nature of the substance and the change considered, and varies to some extent with the conditions (as to pressure, &c.) under which the change is made, but is always the same for the same change under the same conditions
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A rough measurement of the latent heat of See also:steam was made as See also:early as 1764 by See also: The natural unit in this case is the quantity of heat required to evaporate unit mass of water at the boiling point under atmospheric pressure . In boilers working at a higher pressure, or supplied with water at a See also:lower temperature, appropriate corrections are applied to deduce the quantity evaporated in terms of this unit . For laboratory work on a small scale the converse method of condensation has been successfully applied by John Joly, in whose steam-calorimeter the quantity of heat required to raise the temperature of a body from the atmospheric temperature to that of steam condensing at atmospheric pressure is observed by weighing the mass of steam condensed on it . (See CALORIMETRY.) 6 . Thermometric Calorimetry.—For the See also:majority of purposes the most convenient and the most readily applicable method of measuring quantities of heat, is to observe the rise of temperature produced in a known mass of water contained in a suitable vessel or calorimeter . This method was employed from a very early date by See also:Count See also:Rumford and other investigators, and was brought to a high See also:pitch of perfection by Regnault in his extensive calorimetric researches (Memoires de l'Institut de See also:Paris, 1847); but it is only within comparatively recent years that it has really been placed on a satisfactory basis by the accurate See also:definition of the See also:units involved . The theoretical objections to the method, as compared with latent heat calorimetry, are that some heat is necessarily lost by the calorimeter when its temperature is raised above that of the surroundings, and that some heat is used in See also:heating the vessel containing the water . These are small corrections, which can be estimated with considerable accuracy in practice . A more serious difficulty, which has impaired the value of much careful work by this method, is that the quantity of heat required to raise the temperature of a given mass of water 1° C. depends on the temperature at which the water is taken. and also on the scale of the thermometer employed . It is for this reason, in many cases, impossible to say, at the present time, what was the precise value, within i or even 1% of the heat unit, in terms of which many of the older results, such as those of Regnault, were expressed . For many purposes this would not be a serious matter, but for work of scientific precision such a See also:limitation of accuracy would constitute a very serious See also:bar to progress . The unit generally adopted for scientific purposes is the quantity of heat required to raise 1 See also:gram (or kilogram) of water 1° C., and is called the calorie (or kilo-calorie) . See also:English engineers usually state results in terms of the See also:British Thermal Unit (B.Th.U.), which is the quantity of heat required to raise 1 lb of water 1° F . 7 . Watt's See also:Indicator See also:Diagram; Work of Expansion.—The rapid development of the steam-See also:engine (q.v.) in See also:England during the latter See also:part of the 18th See also:century had a marked effect on the progress of the science of heat . In the first steam-engines the working See also:cylinder served both as boiler and See also:condenser, a very wasteful method, as most of the heat was transferred directly from the fire to the condensing water without useful effect . The first improvement (about 1700) was to use a separate boiler, but the greater part of the steam supplied was still wasted in reheating the cylinder, which had been cooled by the injection of cold water to condense the steam after the previous stroke . In 1769 James Watt showed how to avoid this See also:waste by using a separate condenser and keeping the cylinder as hot as possible . In his earlier engines the steam at full boiler pressure was allowed to raise the See also:piston through nearly the whole of its stroke . Connexion with the boiler was then cut off, and the steam at full pressure was discharged into the condenser . Here again there was unnecessary waste, as the steam was still capable of doing useful work . He subsequently introduced " expansive «orking," which effected still further See also:economy . The connexion stroke had been completed, the See also:remainder of the stroke being effected by the expansion of the steam already in the cylinder with continually diminishing pressure . By the end of the stroke, when connexion was made to the condenser, the pressure was so reduced that there was comparatively little waste from this cause . Watt also devised an instrument called an indicator (see STEAM ENGINE), in which a See also:pencil, moved up and down vertically by the steam pressure, recorded the pressure in the cylinder at every point of the stroke on a See also:sheet of See also:paper moving horizontally in time with the stroke of the, piston . The diagram thus obtained made it possible to study what was happening inside the cylinder, and to deduce the work done by the steam in each stroke . The method of the indicator diagram has since proved of great utility in physics in studying the properties of gases and vapours . The work done, or the useful effect obtained from an engine or any See also:kind of See also:machine, is measured by the product of the resistance overcome and the distance through which it is overcome . The result is generally expressed in terms of the equivalent weight raised through a certain height against the force of gravity.' If, for instance, the pressure on a piston ' Units of Work, Energy and See also:Power.—In English-speaking countries work is generally measured in See also:foot-pounds . Elsewhere it is generally measured in kilogrammetres, or in terms of the work done in raising 1 kilogramme weight through the height oft See also:metre . In the See also:middle of the 19th century the terms " force " and " See also:motive power " were commonly employed in the sense of " power of doing work." The term " energy " is now employed in this sense . A quantity of energy is measured by the work it is capable of performing . A body may possess energy in virtue of its state (gas or steam,under pressure), or in virtue of its position (a raised weight), or in various other ways, when at See also:rest . In these cases it is said to possess potential energy . It may also possess energy in virtue of its See also:motion or rotation (as a See also:fly-See also:wheel or a See also:cannon-See also:ball) . In this case it is said to possess kinetic energy, or energy of motion . In many cases the energy(as in the case of a vibrating body, like a pendulum) is partly kinetic and partly potential, and changes continually from one to the other throughout the motion . For instance, the energy of a pendulum is wholly potential when it is momentarily at rest at the See also:top of its See also:swing, but is wholly kinetic when the pendulum is moving with its maximum velocity at the lowest point of its swing . The whole energy at any moment is the sum of the potential and kinetic energy, and this sum remains See also:constant so long as the See also:amplitude of the vibration remains the same . The potential energy of a weight W lb raised to a height h ft. above the See also:earth, is Wh foot-pounds . If allowed to fall freely, without doing work, its kinetic energy on reaching the earth would be Wh foot-pounds, and its velocity of motion would be such that if projected upwards with the same velocity it would rise to the height h from which it See also:fell . We have here a simple and See also:familiar case of the See also:conversion of one kind of energy into a different kind . But the two kinds of energy are mechanically equivalent, and they can both be measured in terms of the same units . The units already considered, namely foot-pounds or kilogrammetres, are gravitational units, depending on the force of gravity . This is the most obvious and natural method of measuring the potential energy of a raised weight, but it has the disadvantage of varying with the force of gravity at different places . The natural measure of the kinetic energy of a moving body is the product of its mass by See also:half the square of its velocity, which gives a measure in kinetic or absolute units independent of the force of gravity . Kinetic and gravitational units are merely different ways of measuring the same thing . Just as foot-pounds may be reduced to kilogrammetres by dividing by the number of foot-pounds in one kilogrammetre, so kinetic may be reduced to gravitational units by dividing by the kinetic measure of the intensity of gravity, namely, the work in kinetic units done by the weight of unit mass acting through unit distance . For scientific purposes, it is necessary to take account of the variation of gravity . The scientific unit of energy is called the erg . The erg is the kinetic energy of a mass of 2 gm. moving with a velocity oft cm. per sec . The work in ergs done by a force acting through a distance oft cm. is the absolute measure of the force . A force equal to the weight of s gm . (in England) acting through a distance of 1 cm. does 981 ergs of work . A force equal to the weight of moo See also:gin . (1 kilogramme) acting through a distance of r metre (See also:loo cm.) does 98.1 million ergs of work . As the erg is a very small unit, for many purposes, a unit equal to 10 million ergs, called a See also:joule, is employed . In England, where the weight of 1 gm. is 981 ergs per cm., a foot-pound is equal to 1.356 joules, and a kilograinmetre is equal to 9.81 joules . The term power is now generally restricted to mean " rate of working." Watt estimated that an See also:average See also:horse was capable of raising 550 lb r ft. in each second, or doing work at the rate of 55o foot-pounds per second, or 33,000 foot-pounds per See also:minute . This conventional horse-power is the unit commonly employed fcrestimating is 5o lb per sq. in., and the See also:area of the piston is loo sq. in., the force on the piston is 5000 lb weight . If the stroke of the piston is 1 ft., the work done per stroke is capable of raising a weight of 5000 lb through a height of 1 ft., or 50 lb through a height of See also:ioo ft. and so on . Fig . 3 represents an imaginary indicator diagram for a steam-engine, taken from one of Watt's See also:patents . Steam is admitted to the cylinder when the piston is at the beginning of its stroke, at S . ST represents the length of the stroke or the limit of See also:horizontal See also:movement of the paper on which the diagram is See also:drawn . The indicating pencil rises to the point A, representing the absolute pressure of 6o lb per sq. in . As the piston moves outwards' the pencil traces 2.50 d a –a0 tL 030 O W 20 W 0 . a m 10 N,"8 1 2 F 3 4 5 6 7 8T the horizontal See also:line AB, the pressure remaining constant till the point B is reached, at which connexion to the boiler is cut off . The work done so far is represented by the area of the rectangle ABSF, namely AS X SF, multiplied by the area of the piston in sq. in . The result is in foot-pounds if the fraction of the stroke SF is taken in feet . After cut-off at B the steam expands under diminishing pressure, and the pencil falls gradually from B to C, following the steam pressure until the exhaust See also:valve opens at the end of the stroke . The pressure then falls rapidly to that of the condenser, which for an ideal case may be taken as zero, following Watt . The work done during expansion is found by dividing the remainder of the stroke FT into a number of equal parts (say 8, Watt takes 2o) and measuring the pressure at the points 1, 2, 3, 4, &c., corresponding to the middle of each . We thus obtain a number of small rectangles, the sum of which is evidently very nearly equal to the whole area BCTF under the expansion See also:curve, or to the remainder of the stroke FT multiplied by the average or mean value of the pressure . The whole work done in the forward stroke is represented by the area ABCTSA, or by the average value of the pressure P over the whole stroke multiplied by the stroke L . This area must be multiplied by the area of the piston A in sq. in. as before, to get the work done per stroke in foot-pounds, which is PLA . If the engine repeats this See also:cycle N times per minute, the work done per minute is See also:PLAN foot-pounds, which is reduced to horse-power by dividing by 33,000 . If the steam is ejected by the piston at atmospheric pressure (15 lb per sq. in.) instead of being condensed at zero pressure, the area CDST under the atmospheric line CD, representing work done against back-pressure on the return stroke must be subtracted . If the engine repeats the same cycle or series of operations continuously, the indicator diagram will be a closed curve, and the nett work done per cycle will be represented by the included area, what-ever the form of the curve . 8 . Thermal Efficiency.—The thermal efficiency of an engine is the ratio of the work done by the engine to the heat supplied to it . According to Watt's observations, confirmed later by See also:Clement and Desormes, the See also:total heat required to produce r lb of saturated steam at any temperature from water at o° C. was approximately 65o times the quantity of heat required to raise 1 lb of water 1° C . Since 1 lb of steam represented on this See also:assumption a certain quantity of heat, the efficiency could be measured naturally in foot-pounds of work obtainable per lb of steam, or conversely in pounds of steam consumed per horse-power-See also:hour . In his patent of 1782 Watt gives the following example of the improvement in thermal efficiency obtained by expansive work- the power of engines . The horse-power-hour, or the work done by one horse-power in one hour, is nearly 2 million foot-pounds . For electrical and scientific purposes the unit of power employed is called the watt . The watt is the work per second done by an electromotive force of 1 volt in See also:driving a current of 1 See also:ampere, and is equal to 10 million ergs or 1 joule per second . One horse-power is 746 See also:watts or nearly of a kilowatt . The kilowatt-hour, which is the unit by which electrical energy is sold, is 3.6 million joules or 2.65 million foot-pounds, or 366,000 kilogrammetres, and is capable of raising nearly 19 lb of water from the freezing to the boiling point.See also:ing . Taking the diagram already given, if the quantity of steam represented by AB, or 300 cub. in. at 6o lb pressure, were employed without expansion, the work realized, represented by the area ABSF, would be 6000/4=1500 foot-pounds . With expansion to 4 times its See also:original volume, as shown in the diagram by the whole area ABCTSA, the mean pressure (as calculated by Watt, assuming See also:Boyle's See also:law) would be o•58 of the original pressure, and the work done would be 6000Xo•58=348o foot-pounds for the same quantity of steam, or the thermal efficiency would be 2.32 times greater . The advantage actually obtained would not be so great as this, on account of losses by condensation, back-pressure, &c., which are neglected in Watt's calculation, but the margin would still be very considerable . Three See also:hundred cub. in. of steam at 6o lb pressure would represent about •0245 of r lb of steam, or 28.7 B.Th.U., so that, neglecting all losses, the possible thermal efficiency attainable with steam at this pressure and four expansions (; cut-off) would be 3480/28.7, or 121 foot-pounds per B.Th.U . At a later date, about 182o, it was usual to include the efficiency of the boiler with that of the engine, and to reckon the efficiency or " See also:duty " in foot-pounds per See also:bushel or cwt. of See also:coal . The best Cornish pumping-engines of that date achieved about 70 million foot-pounds per cwt., or consumed about 3.2 lb per horse-power-hour, which is roughly equivalent to 43 foot-pounds per B.Th.U . The efficiency gradually increased as higher pressures were used, with more See also:complete expansion, but the conditions upon which the efficiency depended were not fully worked out till a much later date . Much additional knowledge with regard to the nature of heat, and the properties of gases and vapours, was required before the problem could be attacked theoretically . 9 . Of the Nature of Heat.—In the early days of the science it was natural to ascribe the manifestations of heat to the See also:action of a subtle imponderable fluid called " caloric," with the power of penetrating, expanding and dissolving bodies, or dissipating them in vapour . The fluid was imponderable, because the most careful experiments failed to show that heat produced any in-crease in weight . The opposite See also:property of levitation was often ascribed to heat, but it was shown by more cautious investigators that the apparent loss of weight due to heating was to be attributed to evaporation or to upward air currents . The fundamental idea of an imaginary fluid to represent heat was useful as helping the mind to a conception of something remaining invariable in quantity through many transformations, but in some respects the See also:analogy was misleading, and tended greatly to retard the progress of science . The caloric theory was very simple in its application to the majority of calorimetric experiments, and gave a See also:fair account of the elementary phenomena of change of state, but it encountered serious difficulties in explaining the See also:production of heat by See also:friction, or the changes of temperature accompanying the See also:compression or expansion of a gas . The explanation which the calorists offered of the production of heat by friction or compression was that some of the latent caloric was squeezed or ground out of the bodies concerned and became " sensible." In the case of heat See also:developed by friction, they supposed that the abraded portions of the material were capable of holding a smaller quantity of heat, . or had less " capacity for heat," than the original material . From a logical point of view, this was a perfectly tenable See also:hypothesis, and one difficult to refute . It was easy to account in this way for the heat produced in See also:boring cannon and similar operations, where the amount of abraded material was large . To refute this explanation, Rumford (Phil . Trans., 1798) made his celebrated experiments with a See also:blunt borer, in one of which he succeeded in boiling by friction 26.5 lb of cold water in 22 See also:hours, with the production of only 4145 grains of metallic See also:powder . He then showed by experiment that the metallic powder required the same amount of heat to raise its temperature 1°, as an equal weight of the original See also:metal, or that its " capacity for heat " (in this ense) was unaltered by reducing it to powder; and he argued that " in any case so small a quantity of powder could not possibly account for all the heat generated, that the See also:supply of heat appeared to be inexhaustible, and that heat could not be a material substance, but must be more exact generalization . The way was paved in the first instance by a more complete study of the laws of gases, to which Laplace, See also:Dalton, Gay-Lussac, See also:Dulong and many others contributed both on the experimental and theoretical See also:side . Although the develojlment proceeded simultaneously along many parallel lines, it is interesting and instructive to take the investigation of the properties of gases, and to endeavour to trace the steps by which the true theory was finally attained . ro . Thermal Properties of Gases.—The most characteristic property of a gaseous or elastic fluid, namely, the See also:elasticity, or resistance to compression, was first investigated scientifically by See also:Robert Boyle (1662), who showed that the pressure p of a given mass of gas varied inversely as the volume v, provided that the temperature remained constant . This is generally expressed by the See also:formula pv = C, where C is a constant for any given temperature, and v is taken to represent the specific volume, or the volume of unit mass, of the gas at the given pressure and temperature . Boyle was well aware of the effect of heat in expanding a gas, but he was unable to investigate this properly as no thermometric scale had been defined at that date . According to Boyle's law, when a mass of gas is compressed by a small amount at constant temperature, the percentage increase of pressure is equal to the percentage diminution of volume (if the compression is v/roo, the increase of pressure is very nearly p/roo) . Adopting this law, See also:Newton showed, by a most ingenious piece of reasoning (Principia, ii., See also:sect . 8), that the velocity of See also:sound in air should be equal to the velocity acquired by a body falling under gravity through a distance equal to half the height of the See also:atmosphere, considered as being of uniform See also:density equal to that at the See also:surface of the earth . This gave the result 918 ft. per sec . (28o metres per sec.) for the velocity at the freezing point . Newton was aware that the actual velocity of sound was somewhat greater than this, but supposed that the difference might be due in some way to the size of the air particles, of which no account could be taken in the calculation . The first accurate measurement of the velocity of sound by the See also:French Academie See also:des Sciences in 1738 gave the value 332 metres per sec. as the velocity at o° C . The true explanation of the discrepancy was not discovered till nearly Too years later . The law of expansion of gases with change of temperature was investigated by Dalton and Gay-Lussac (1802), who found that the volume of a gas under constant pressure increased by 1/267th part of ,its volume at o° C. for each 1° C. rise in temperature . This value was generally assumed in all calculations for nearly 50 years . More exact researches, especially those of Regnault, at a later date, showed that the law was very nearly correct for all permanent gases, but that the value of the coefficient should be T7rd . According to this law the volume of a gas at any temperature t° C. should be proportional to 273+1, i.e. to the temperature reckoned from a zero 273° below that of the Centigrade scale, which was called the absolute zero of the gas thermometer . If T= 273+1, denotes the temperature measured from this zero, the law of expansion of a gas may be combined with Boyle's law in the simple formula pv=RT . . (I) something of the nature of motion." Unfortunately Rumford's argument was not quite conclusive . The supporters of the caloric theory appear, whether consciously or unconsciously, to have used the phrase " capacity for heat" in two entirely distinct senses without any clear definition of the difference . The phrase " capacity for heat " might very naturally denote the total quantity of heat contained in a body, which we have no means of measuring, but it was generally used to signify the quantity of heat required to raise the temperature of a body one degree, which is quite a different thing, and has no necessary relation to the total heat . In proving that the powder and the solid metal required the same quantity of heat to raise the temperature of equal masses of either one degree, Rumford did not prove that they contained equal quantities of heat, which was the real point at issue in this instance . The metal See also:tin actually changes into powder below a certain temperature, and in so doing evolves a measurable quantity of heat . A mixture of the gases See also:oxygen and See also:hydrogen, in the proportions in which they combine to form water, evolves when burnt sufficient heat to raise more than See also:thirty times its weight of water from the freezing to the boiling point; and the mixture of gases may, in this sense, be said to contain so much more heat than the water, although its capacity for heat in the ordinary sense is only about half that of the water produced . To complete the refutation of the calorists' explanation of the heat produced by friction, it would have been necessary for Rumford to show that the powder when reconverted into the same state as the solid metal did not absorb a quantity of heat equivalent to that evolved in the grinding; in other words that the heat produced by friction was not simply that due to the change of state of the metal from solid to powder . Shortly afterwards, in 1799, See also:Davy' described an experiment in which he melted ice by rubbing two blocks together . This experiment afforded a very direct refutation of the calorists' view, because it was a well-known fact that ice required to have a quantity of heat added to it to convert it into water, so that the water produced by the friction contained more heat than the ice . In stating as the conclusion to be drawn from this experiment that " friction consequently does not diminish the capacity of bodies for heat," Davy apparently uses the phrase capacity for heat in the sense of total heat contained in a body, because in a later See also:section of the same See also:essay he definitely gives the phrase this meaning, and uses the term " capability of temperature " to denote what we now term capacity for heat . The delay in the overthrow of the caloric theory, and in the See also:acceptance of the view that heat is a mode of motion, was no doubt partly due to some fundamental confusion of ideas in the use of the term " capacity for heat " and similar phrases . A still greater obstacle See also:lay in the See also:comparative vagueness of the motion or vibration theory . Davy speaks of heat as being " repulsive motion," and distinguishes it from See also:light, which is " projective motion "; though heat is certainly not a substance—according to Davy in the essay under discussion—and may not even be treated as an imponderable fluid, light as certainly is a material substance, and is capable of forming chemical compounds with ordinary matter, such as oxygen gas, which is not a simple substance, but a compound, termed phosoxygen, of light and oxygen . Accepting the conclusions of Davy and Rumford that heat is not a material substance but a mode of motion, there still remains the question, what definite conception is to be attached to a quantity of heat ? What do we mean by a quantity of vibratory motion, how is the quantity of motion to be estimated, and why should it remain invariable in many trans-formations ? The idea that heat was a " mode of motion " was applicable as a qualitative explanation of many of the effects of heat, but it lacked the quantitative precision of a scientific statement, anc%could not be applied to the calculation and prediction of definite results . The state of science at the time of Rumford's and Davy's experiments did not admit of a ' In an essay on " Heat, Light, and Combinations of Light," republished in Sir H . Davy's Collected See also:Works, ii . (See also:London, 1836) . which is generally taken as the expression of the gaseous laws . If equal volumes of different gases are taken at the same temperature and pressure, it follows that the constant R is the same for all gases . If equal masses are taken, the value of the constant R for different gases varies inversely as the molecular weight or as the density relative to hydrogen . - Dalton also investigated the laws of vapours, and of mixtures of gases and vapours . He found that condensible vapours approximately followed Boyle's law when compressed, until the condensation pressure was reached, at which the vapour liquefied without further increase of pressure . He found that when a liquid was introduced into a closed space, and allowed to evaporate until the space was saturated with the vapour and evaporation ceased, the increase of pressure in the space was equal to the condensation pressure of the vapour, and did not depend on the volume of the space or the presence of any other gas or vapour provided that there was no solution or chemical action . He showed that the condensation or saturation-pressure of a vapour depended only on the temperature, and increased by nearly the same fraction of itself per degree rise of temperature, and that the pressures of different vapours were nearly the See also:sake at equal distances from their boiling points . The increase of pressure per degree C. at the boiling point was about See also:Ath of 76o mm. or 27.2 mm., but increased in geometrical progression with rise of temperature . These results of Dalton's were confirmed, and in part corrected, as regards increase of vapour-pressure, by Gay-Lussac, Dulong, Regnault and other investigators, but were found to be as See also:close an approximation to the truth as could be obtained with such simple expressions . 
More accurate empirical expressions for the increase of vapour-pressure of a liquid with temperature were soon obtained by See also: |