172.]

ATOMIC HEATS OF THE ELEMENTS.

357

quantity of each gas, after it had been raised to a certain known temperature, was cooled down by it to a certain other known temperature. When the specific heat of equal masses of the different gases was once known, it was easy to calculate that for equal volumes, by simply multiplying the numbers for equal weights by those representing the densities of each gas or vapour. For the details of this delicate inquiry, the reader is referred to the second volume of Regnault's great work, Relations des Expériences pour déterminer les Lois et les Données Physiques nécessaires au Calcul des Machines à Feu, 1862, 41-333.

The foregoing table, compiled from Regnault's experiments, shows how greatly the specific heat of the same liquid varies with the temperature, whilst in gases no such variation takes place. It also shows that the specific heat of a body in the gaseous state is always less than that of the same substance in the liquid state.

(172) Relation of Specific Heat to Atomic Weight.—An interesting relation has been traced between the specific heats of bodies and their combining quantities. It has already been stated (168) that the amount of heat required to raise equal masses of different substances 1° in temperature varies for each species of matter, but is always constant for the same body when it is placed under like circumstances.

By comparing together quantities of the various elementary substances in the ratio of their combining proportions, and ascertaining the amount of heat which each requires to raise it through equal intervals of temperature, Dulong and Petit made the important observation that the quantities of heat absorbed bear a very simple numerical relation to each other. In a large number of instances, the amounts of heat thus absorbed, allowing for unavoidable errors of experiment, are identical; and it was further observed, that the exceptional cases nearly always exhibit some simple multiple relation to this number. In other words, the specific heat of an elementary body is inversely as its combining proportion: consequently, the product of the specific heat of an element into its combining proportion gives, subject to slight variations due to errors of experiment, either a constant number, or some multiple of that number.

The law thus announced by Dulong and Petit has been confirmed by the subsequent researches of Regnault upon specific heat (Ann. Chim. Phys. 1840 [2], lxxiii. 61; 1841 [3], i. 129; 1843, ix. 322; 1849, xxvi. 261; 1853, xxxviii. 129; 1856, xlvi. 257; and 1861, lxiii. 5). Regnault determined the specific heats. of a great variety of bodies, both simple and compound. He

358

ATOMIC HEATS OF THE ELEMENTS.

[172.

designated the product obtained by multiplying the specific heat of a body by its atomic weight, as the atomic heat of the body. In 21 of the simple bodies which he examined, most of which were in a state of chemical purity, he found the atomic heat to range between 3'31 and 2'93, with a mean of 3'13. The elements comprised in this class are the following-viz., aluminium, cadmium, cobalt, copper, iridium, iron, lead, magnesium, manganese, mercury, molybdenum, nickel, osmium, platinum, rhodium, selenium, sulphur, tellurium, tin, tungsten, and zinc. Experiments are at present wanting upon barium, strontium, calcium, glucinum, thorinum, cerium, didymium, lanthanum, vanadium, uranium, and ruthenium; although from analogy there is reason to believe that they belong to this group of elements as regards their specific heat. No direct experiments upon the specific heat of oxygen in a form comparable with the solid elements have yet been made.

When the equivalent number formerly regarded as the atomic weight was employed as the multiplier of the specific heat, it was found that a second smaller class of elements exists which have an atomic heat double that of the elements contained in the foregoing list. This class comprises gold, silver, thallium, bismuth, antimony, arsenic, phosphorus, bromine, and iodine, as well as lithium, potassium, and sodium. From their chemical analogies, there can be little doubt that in this list should also be included chlorine, cæsium, and rubidium, although as yet the necessary experiments are wanting to decide the point. The bodies of this class gave for their atomic heat numbers ranging between 585 and 687, with a mean of 6'42; Regnault therefore proposed to divide by two the numbers usually given as the atomic weights of the elements in the second list. It was found more convenient to double the atomic weights of the first series, by which means the identity of the ratio was preserved equally well. There are chemical reasons which fully justified this alteration, startling as it at first appeared. The combining proportion of an element, it must be remembered, is not affected by this change of the number which, for various reasons, is selected as the atomic weight, and which in some cases coincides with the combining proportion, while in others it is a multiple of it.

Dulong and Petit's law may therefore be stated thus. If, instead of taking equal weights, we compare together quantities of the elementary bodies in the proportion of their atomic weights, these quantities will be found to require equal amounts of heat

172.]

ATOMIC HEATS OF THE ELEMENTS.

359

to raise them through an equal number of degrees of temperature. There are, however, still some marked exceptions to the law, particularly among the non-metallic elements.

Specific and Atomic Heats of the Elements.

The above table includes some of the principal results derived from Regnault's experiments on a large number of elementary

360

ATOMIC HEATS OF THE ELEMENTS.

[172.

bodies. He found, as has been already stated, that the same element has a different specific heat if examined in a different state of aggregation. Bodies when in the liquid form have a higher specific heat than when in the solid state, as is seen on comparing the numbers for bromine and mercury in the two conditions.

An extended table, embracing the principal results obtained on the specific heat of solids, both simple and compound, by various observers, is given by Kopp (Phil. Trans. 1865, 168).

Amongst the non-metallic elements there are, as above stated, certain striking exceptions to the law of Dulong and Petit. Carbon, for instance, as diamond, taking its atomic weight as 12, has an atomic heat of only 1-7616; the atomic heat of crystallized boron is 2725; that of fused silicon 49; that of octohedral sulphur 5.6832; and that of phosphorus 5.8497.*

Dewar (Phil. Mag. 1872 [4], xliv. 461) found the specific heat of gas carbon between 1040° and 20° to be o'32; and between 2000 and 20° it was 42, from which he estimated the true specific heat at 2000° to be at least 5.

Some experiments have recently been made by Weber (Phil. Mag. 1875 [4], xlix. 161, 276) which show that the specific heats of carbon, silicon, and boron increase rapidly as the temperature rises, and that these elements are not exceptions to the law of Dulong and Petit, when their specific heat is determined at sufficiently high temperatures.

The relation between the atomic weights and specific heats is well illustrated by the last column in the table, containing the

Kopp suggested that these exceptional cases may have their origin in the circumstance that we have as yet no absolute proof that the bodies now regarded as elements are really the simplest forms of matter; and that the metals and all the so-called elements which have the higher atomic heat 64 may possibly be compounds; whilst the diamond, which has the lowest atomic heat, 18, may be really the only elementary substance known to us-the bodies with intermediate atomic heats being truly compounds more complex than carbon, but less so than the metals.

173.]

MOLECULAR HEATS OF COMPOUND BODIES.

361

weights of the different solid elements, which, under the same conditions, exhibit the same specific heat as seven parts by weight of lithium. In most cases these numbers are the same as the atomic weights, allowance being made for errors of experiment.

(173) Molecular Heats of Compound Bodies.-The alloys, according to Regnault's experiments, yield a specific heat which is exactly the mean of that of their components; hence their specific heat is equal to the sum of that of their components; and Woestyn (Ann. Chim. Phys. 1848 [3], xxiii. 295), has shown that for the sulphides and iodides, within certain limits of error, the molecular heat may be calculated from the sum of the atomic heats of their constituents; and Garnier maintains that this is true for all bodies. The same conclusion has also been arrived

at by Kopp.

On comparing together equivalent quantities of isomorphous compounds possessed of a similar chemical composition, Neumann (Pogg. Annal. 1831, xxiii. 37) found that they likewise possess equal molecular heats. The differences from the mean are in some cases considerable, but they are of the same order as those already observed to occur in the simple bodies. The mean molecular heat of the isomorphous carbonates, such, for example, as the carbonates of calcium, barium, iron, lead, zinc, strontium, and the double carbonate of calcium and magnesium, is 20'99, varying between 2008 and 21.73. In like manner the sulphates of barium, calcium, strontium, and lead yield a mean molecular heat

of 25'57.

Regnault, from an extensive series of experiments on a great variety of compound bodies, arrived at the conclusion that, "in all compound bodies of the same atomic composition, and of similar chemical constitution, the specific heats are inversely as the atomic weights." The product obtained by multiplying the specific heat into the molecular weight in any one class of compounds may, however, differ greatly from the product of the corresponding numbers in any other class, the numbers furnished by the different classes not being connected by any very simple ratio. These facts will be rendered obvious by an examination of the subjoined summary of Regnault's results (Ann. Chim. Phys. 1841 [3], i. 172).

In the last column of the table are given the quotients obtained by dividing the molecular heat in the fourth column by the number of atoms entering into the composition of the compound.