The specific heats of bodies, it is well known, are determined by means of the relative quantities of heat necessary to raise the temperature of those bodies a certain number of degrees. They are expressed by the ratios of those quantities. If the capacities of the same bodies for heat were permanent at all temperatures, then these ratios would also express those of the whole quantities of heat in bodies. In fact, most authors represent the specific heats as expressing both the ratio of the total quantities of heat in bodies, and of the relative quantities to raise their temperature a given number of degrees; but it is the latter only which they accurately represent, and the former only hypothetically.
In regard to bodies in the solid and liquid forms, all experience shews that their capacities for heat are nearly if not accurately constant within the common range of temperature; it seems therefore not unreasonable to infer that the whole quantity of heat in each is proportional to their increments. When, however, a solid body by an increase of temperature assumes a fluid form, and absorbs heat without any increase of its temperature, its total quantity of heat is thus increased; and it is contended by the writers on capacity, that the increments of heat afterwards are increased in the same proportion as the total quantities. This is probable enough; but it ought to be proved in several instances by direct experiment before it can safely be admitted as a general principle; more especially now since the analogy in the case of a liquid becoming an elastic fluid is found to fail in this particular. As an instance of uncertainty, the capacity of ice to water has been found as 9 to 10 by one person, and as 7.2 to 10 by others; such wide difference in the results shows there must be a difficulty in determining the specific heat of ice, and that it may even be doubted whether the specific heat of ice or water is greatest.
From the foregoing detail of experiments on elastic fluids, it appears evident that such fluids exhibit matter under a form in which it has the greatest possible capacity for heat, when capacity is understood to denote the total quantity of heat connected with the fluid; but if the capacity or specific heat is meant to denote the quantity of heat necessary to raise the body a given number of degrees of temperature, then the elastic fluid form of matter is that which has the least capacity for heat of any known form of the same matter. When therefore we use the terms specific heat as applied to elastic fluids we should henceforward carefully distinguish in what sense they are used; but the terms may still be indifferently used in the one or the other sense as applied to liquids and solids, till some more decisive experiments shew that a distinction is required. Probably the anomalies that have occurred in investigations of the zero of cold, or point of total privation of heat, are in part due to the want of accordance between the ratio of the total quantities of heat in bodies, and the ratio of the quantities producing equal increments of temperature.
The greatest possible quantity of heat which a given weight of elastic fluid can contain is when the dilatation of the fluid is extreme. For, condensation, whether arising from mechanical pressure or from increased attraction of the atoms of matter for each other, tends to dissipate the heat, by increasing its elasticity. Hence increase of temperature, at the same time that on one account it increases the absolute quantity of heat in an elastic fluid, diminishes the quantity on another account by an increase of pressure, if the fluid be not suffered to dilate. This is well known from the fact that condensation produces increase of temperature in elastic fluids.
When it is considered that all elastic fluids expand the same quantity by the same increase of temperature, it might be imagined that all of them would have the same capacity, or require the same quantity of heat to produce that expansion. The results of De la Roche and Berard do not seem to admit of this supposition, though the differences of the capacities of elastic fluids of equal volumes are not very great. There is a remarkable difference too between their results and those of Clement and Desormes, in regard to hydrogen gas: namely, .9033 and .6640; also in carbonic acid gas, 1.2583 and 1.5. The subject deserves further investigation.
In reference to the experiments of Dulong and Petit, on the relative expansions of air and mercury by heat, I have no doubt their results are good approximations to the truth. My former experiments were chiefly made in temperatures between 32° and 212°, and I found, as General Roi had done, the expansion of air to be somewhat greater in the lower half than in the upper half of that interval, compared with mercury. On a repetition of the experiments, I think the difference is less than I concluded it to be, and I find that the like coincidence of the air scale and mercurial, continues down to near freezing mercury; at least the difference will not be so great as my new table of temperature makes it at [page 14]. I have made some experiments on the expansions of air above 212°, which lead me to adopt the results of Dulong. On a comparison of the air and mercurial thermometer upon the laws which I pointed out, namely, the former expanding in geometrical progression to equal intervals of temperature, and the latter expanding as the square of the temperature reckoned from its freezing point, it appears that in the long range of 600° from freezing water to boiling mercury, the greatest deviation of the two thermometers does not exceed 22°. However, the great deviation of the scales between the temperatures of freezing water and freezing mercury, is sufficient to shew, as Dulong and Petit have observed, that their coincidence is only partial. Like the scales of air and mercury, which are so nearly coincident from -40° to 212° that scarcely any difference is sensible, though no one doubts of its existence; yet afterwards the differences become obvious enough, and the greater the farther we advance.
Expansion of Mercury. See page 34, vol. I. I have overrated the expansion of glass bulbs (as will be seen presently,) and hence that of mercury; my expansion of mercury corrected on account of the glass, will be ¹/₅₃ nearly, which leaves it still greater than Dulong’s. The 2nd table of Dulong is valuable, on account of its affording us information of the rate of expansion in the higher degrees of temperature, from a given or standard air thermometer.
Iron, Copper, and Platina.
Expansion of Glass.—By the 3rd Table of Dulong and Petit, it appears these ingenious chemists found the expansion of glass for 180°, or from 32° to 212°, very nearly the same as had been determined previously by Smeaton and others. It also expands increasingly with the temperature, whether it is estimated by the air or mercurial standard. This was observed by Deluc, but more extensively by the present authors. The expansions of iron, copper, and platina, from 32° to 212° as detailed in the 4th table, agree nearly with the results of others; but the expansions in the higher part of the scale manifest some remarkable facts not before known. Platina not only expands the least of the above bodies, but its expansion is almost equable; iron expands more than glass and less than copper, but the most unequally of any one, the expansion increasing rapidly as the temperature advances. These facts explain some others which have fallen under my observation. I was formerly surprised to find glass and iron expand so nearly alike (see vol. I. page 31); but it now appears that iron increases more slowly in proportion than glass about the freezing point. More recently I procured a small thermometrical vessel of platina to contain water like those described at page 31, vol. I, and having filled it and treated it as the other metallic vessels, I was again surprised to find that the apparent greatest density of water in this vessel was at 43°, whereas I expected to have found it below 42°, the point for glass vessels. This observation, in conjunction with Dulong’s, shews, that platina expands more than iron at low temperatures, though for a range of 300° the whole expansion of the platina is to that of the iron as 2 to 3 nearly. Hence the error (for I now consider it as such) which I was led into with respect to the expansion of glass bulbs, (see vol. I. page 32) and subsequently into that of the expansion of mercury abovementioned. It is not the expansion of glass which approaches that of iron, but it is the reverse, which occasions the two bodies to meet so nearly in the table, page 31. This consideration will affect the point of greatest density of water also; for, the less the expansion of iron and glass, the nearer will be the points of real and apparent greatest density of water, contained in vessels of those materials. My observations on brown earthenware are scarcely to be relied upon from the difficulty of making such vessels water tight: but the common white ware I have verified repeatedly since the publication of that table, and am satisfied the point of apparent greatest density, is at or near 40° in such vessels; hence the real maximum density of water must be below 40°. I am inclined to adopt 38° as the most proximate degree.
Capacities of bodies for heat. In the 5th table of Dulong, we have the specific heats of glass and of six metals, determined between freezing and boiling water: that of iron is given before. So far the question does not involve that of the measure of temperature. Their results afford no striking differences from those previously determined; however, it is desirable to find a greater accordance amongst philosophers in this respect. The experiments which give the specific heats between 0° and 300° centigrade, are original and interesting. The results go to shew that the capacities of bodies increase in a small degree with the temperature. But supposing that these results may be relied upon as accurate (which can scarcely be affirmed of any former ones) still the character of them may be changed by adopting a different measure of temperature.