When all surrounding bodies are of one temperature, then the heat attached to them is in a quiescent state; the absolute quantities of heat in any two bodies in this case are not equal, whether we take the bodies of equal weights or of equal bulks. Each kind of matter has its peculiar affinity for heat, by which it requires a certain portion of the fluid, in order to be in equilibrium with other bodies at a certain temperature. Were the whole quantities of heat in bodies of equal weight or bulk, or even the relative quantities, accurately ascertained, for any temperature, the numbers expressing those quantities would constitute a table of specific heats, analogous to a table of specific gravities, and would be an important acquisition to science. Attempts of this kind have been made with very considerable success.
Whether the specific heats, could they be thus obtained for one temperature, would express the relation at every other temperature, whilst the bodies retained their form, is an enquiry of some moment. From the experiments hitherto made there seems little doubt of its being nearly so; but it is perhaps more correct to deduce the specific heat of bodies from equal bulks than from equal weights. It is very certain that the two methods will not give precisely the same results, because the expansions of different bodies by equal increments of temperature are not the same. But before this subject can well be considered, we should first settle what is intended to be meant by the word temperature.
In speaking of the uncertainty of Crawford's results on the specific heat of elastic fluids, it must not be understood that all of them are equally implicated. The reiterated experiments on the heat given out by the combustion of hydrogen, in which it was found that 11 measures of mixed gases, when fired by electricity heated 20.5 measures of water 2°.4 (page 263) at a medium, were susceptible of very considerable accuracy, and are therefore entitled to credit. The comparative heat of atmospheric air and water, which rested on the observance of nearly 1/4 of a degree of temperature, is probably not very far from the truth; but the very small difference in the heats communicated by equal bulks of oxygen, hydrogen, carbonic acid, azotic gas and common air, together with the great importance of those differences in the calculation, render the results very uncertain. He justly observes, that if we suppose the heats imparted by equal bulks of these gases to be equal, it will not affect his doctrine. The tenor of it necessarily led him to estimate the heat of oxygen high, compared with equal weights of carbonic acid and aqueous vapour, and of azotic gas or phlogisticated air, as it was then called, under the idea of its being an opposite to oxygen or dephlogisticated air. Indeed his deductions respecting azotic gas, are not consistent with his experiments: for he makes no use of experiments 12 and 13, which are the only direct ones for the purpose, but he infers the heat of azotic gas from the observed difference between oxygen and common air. The result gives it less than half that of common air; whereas from the 13th experiment, scarcely any sensible difference was perceived between them. He has in all probability much underrated it; but his errors in this respect whatever they may be, do not affect his system.
When we consider that all elastic fluids are equally expanded by temperature, and that liquids and solids are not so, it should seem that a general law for the affection of elastic fluids for heat, ought to be more easily deducible and more simple than one for liquids, or solids. --There are three suppositions in regard to elastic fluids which merit discussion.
1. Equal weights of elastic fluids may have the same quantity of heat under like circumstances of temperature and pressure.
The truth of this supposition is disproved by several facts: oxygen and hydrogen upon their union give out much heat, though they form steam, on elastic fluid of the same weight as the elements composing it. Nitrous gas and oxygen unite under similar circumstances. Carbonic acid is formed by the union of charcoal, a substance of low specific heat, with oxygen; much heat is given out, which must be principally derived from the oxygen; if then the charcoal contain little heat, and the oxygen combining with it be reduced, the carbonic acid must be far inferior in heat to an equal weight of oxygenous gas.
2. Equal bulks of elastic fluids may have the same quantity of heat with the same pressure and temperature.
This appears much more plausible; the diminution of volume when a mixture of oxygen and hydrogen is converted into steam, may be occasioned by a proportionate diminution of the absolute heat; the same may be said of a mixture of nitrous gas and oxygen. The minute differences observed by Crawford, may have been inaccuracies occasioned by the complexity of his experiments. --But there are other considerations which render this supposition extremely improbable, if they do not altogether disprove it. Carbonic acid contains its own bulk of oxygen; the heat given out at its formation must therefore be exactly equal to the whole heat previously contained in the charcoal on this supposition; but the heat by the combustion of one pound of charcoal seems, at least, equal to the heat by the combustion of a quantity of hydrogen sufficient to produce one pound of water, and this last is equal to, or more than the heat retained by the water, because steam is nearly twice the density of the elastic mixture from which it is produced; it should therefore follow, that charcoal should be found of the same specific heat as water, whereas it is only about 1/4 of it. Were this supposition true, the specific heats of elastic fluids of equal weights would be inversely as the specific gravities. --If that of steam or aqueous vapour were represented by 1, oxygen would be .64, hydrogen 8.4, azote .72, and carbonic acid .46. --But the supposition is untenable.
3. The quantity of heat belonging to the ultimate particles of all elastic fluids, must be the same under the same pressure and temperature.
It is evident the number of ultimate particles of molecules in a given weight or volume of one gas is not the same as in another: for, if equal measures of azotic and oxygenous gases were mixed, and could be instantly united chemically, they would form nearly two measures of nitrous gas, having the same weight as the two original measures; but the number of ultimate particles could at most be one half of that before the union. No two elastic fluids, probably, therefore, have the same number of particles, either in the same volume or the same weight. Suppose, then, a given volume of any elastic fluid to be constituted of particles, each surrounded with an atmosphere of heat repelling each other through the medium of those atmospheres, and in a state of equilibrium under the pressure of a constant force, such as the earth's atmosphere, also at the temperature of the surrounding bodies; suppose further, that by some sudden change each malecule [sic] of air was endued with a stronger affinity for heat; query the change that would take place in consequence of this last supposition? The only answer that can be given, as it appears to me, is this. --The particles will condense their respective atmospheres of heat, by which their mutual repulsion will be diminished, and the external pressure will therefore effect a proportionate condensation in the volume of air: neither an increase nor diminution in the quantity of heat around each malecule, or around the whole, will take place. Hence the truth of the supposition, or as it may now be called, proposition, is demonstrated.
Corol. 1. The specific heats of equal weights of any two elastic fluids, are inversely as the weights of the atoms or molecules.
2. The specific heats of equal bulks of elastic fluids, are directly as their specific gravities, and inversely as the weights of their atoms.
3. Those elastic fluids that have their atoms the most condensed, have the strongest attraction for heat; the greater attraction is spent in accumulating more heat in a given space or volume, but does not increase the quantity around any single atom.
4. When two elastic atoms unite by chemical affinity to form one elastic atom, one half of their heat is disengaged. When three unite, then two thirds of their heat is disengaged, &c. And in general, when m elastic particles by chemical union become n; the heat given out is to the heat retained as m-n is to n.
One objection to this proposition it may be proper to obviate: it will be said, an increase in the specific attraction of each atom must produce the same effect on the system as an increase of external pressure. Now this last is known to express or give out a quantity of the absolute heat; therefore the former must do the same. This conclusion must be admitted; and it tends to establish the truth of the preceding proposition. The heat expressed by doubling the density of any elastic fluid amounts to about 50°, according to my former experiments; this heat is not so much as one hundredth part of the whole, as will be shewn hereafter, and therefore does not materially affect the specific heat: it seems to be merely the interstitial heat amongst the small globular molecules of air, and scarcely can be said to belong to them, because it is equally found in a vacuum of space devoid of air, as is proved by the increase of temperature upon admitting air into a vacuum.
Before we can apply this doctrine to find the specific heat of elastic fluids, we must first ascertain the relative weights of their ultimate particles. Assuming at present what will be proved hereafter, that if the weight of an atom of hydrogen be 1, that of oxygen will be 7, azote 5, nitrous gas 12, nitrous oxide 17, carbonic acid 19, ammoniacal gas 6, carburetted hydrogen 7, olefiant gas 6, nitric acid 19, carbonic oxide 12, sulphuretted hydrogen 16, muriatic acid 22, aqueous vapour 8, ethereal vapour 11, and alcoholic vapour 16; we shall have the specific heats of the several elastic fluids as in the following table. In order to compare them with that of water, we shall further assume the specific heat of water to that of steam as 6 to 7, or as 1 to 1.166.
|Table of the specific heats of elastic fluids.|
|Atmos. air||1.759||Sulph. hydrogen||.583|
|Nitrous gas||.777||Muriatic acid||.424|
|Nitrous oxide||.549||Aqueous vapour||1.166|
|Carbonic acid||.491||Ether. vapour||.848|
|Ammon. gas||1.555||Alcohol. vapour||.586|
Let us now see how far these results will accord with experience. It is remarkable that the heat of common air comes out nearly the same as Crawford found it by experiment; also, hydrogen excels all the rest as he determined; but oxygen is much lower and azote higher. The principles of Crawford's doctrine of animal heat and combustion, however, are not at all affected with the change. Besides the reason for thinking that azote has been rated too low, we see from the Table, page 62, that ammonia, a compound of hydrogen and azote, has a higher specific heat than water, a similar compound of hydrogen and oxygen.
Upon the whole, there is not any established fact in regard to the specific heats of bodies, whether elastic or liquid, that is repugnant to the above table as far as I know; and it is to be hoped, that some principle analogous to the one here adopted, may soon be extended to solid and liquid bodies in general.