CHAPTER VI. The Properties of Argon

THE PROPERTIES OF ARGON

The density of a gas is one of its most characteristic and important properties. Avogadro’s law, which postulates that equal volumes of gases, at equal temperature and pressure, contain equal numbers of molecules, renders it possible to compare the weights of the molecules by determining the relative weights of the gases. Thus, as the ratio between the densities of nitrogen and oxygen is 7 to 8, a single molecule of nitrogen, the smallest portion which can exist in freedom, uncombined with other elements, is ⅞ths of the weight of a single molecule of oxygen. Hence a determination of the density of argon leads directly to a knowledge of the relative weight of a single molecule of this gas.

But with what should the density of argon be compared? What gas must serve as the standard of density? To answer this question, it is necessary to give a short sketch of the development of chemical theory regarding the atomic weights of elements and their relative volumes.

Dalton proposed to adopt as the unit of atomic weight the weight of the lightest atom, namely, that of hydrogen. Taking, for example, water as one substance containing hydrogen, its percentage composition by weight is--

Hydrogen 11·11 per cent Oxygen 88·88 "

If the smallest portion of water capable of free existence contains one atom of hydrogen and one of oxygen, then placing the weight of an atom of hydrogen as unity, the weight of an atom of oxygen is eight times as great. And although we do not know the absolute weight of any single atom, we are justified in supposing that an atom of oxygen is eight times as heavy as an atom of hydrogen. But have we any right to make the assumption that a molecule of water contains one atom of each element? Dalton came to the conclusion that this supposition was a justifiable one; but there are strong reasons against it. We have already seen that Cavendish discovered approximately, and that Gay-Lussac and Humboldt determined accurately, that when hydrogen and oxygen unite to form water, two volumes of the former combine with one of the latter. Now it appears improbable on the face of it that any given volume of hydrogen should contain only half as many particles as an equal volume of oxygen; and it is still more improbable, when we take into consideration (1) Boyle’s discovery that if the pressure on a gas be increased, the volume of the gas, whatever it may be, diminishes in like proportion; and (2) Gay-Lussac’s and Dalton’s discovery, that all gases, when equally raised in temperature, expand equally. It would be very remarkable if one gas, containing twice as many particles in unit volume as another, should show exactly similar behaviour towards pressure and temperature. Hence it appeared not unreasonable to suppose that the composition of water was expressed by one particle of oxygen in union with two particles of hydrogen. (The word “particle” is here used in the meaning of “small portion”; such particles may be molecules or they may be atoms.)

When steam is formed by the union of hydrogen with oxygen, it has a volume equal not to the sum of the volumes of the hydrogen and the oxygen, but to two-thirds of the sum, or equal to that of the hydrogen alone, or twice that of the oxygen. And as steam, like hydrogen and oxygen, follows Boyle’s and Gay-Lussac’s laws, it must be supposed that in the steam there are as many particles as in the hydrogen from which it was formed. But the particles of steam must necessarily be more complex than those of the hydrogen, inasmuch as the steam contains oxygen as well as hydrogen.

These difficulties may, however, be easily overcome by the following supposition, which was first formulated by Avogadro in 1811. The ordinary particles of hydrogen and of oxygen are complex, each containing at least two atoms, or smaller particles, which usually exist in combination with each other, or with atoms of some other element. Two volumes of hydrogen, therefore, contain twice as many particles as one volume of oxygen; to such particles the name “molecules” is now universally applied. And as these molecules are themselves each made up of two smaller particles, now termed “atoms,” there exist in two volumes of hydrogen twice as many atoms as in one volume of oxygen. On combination, the atoms in the molecules of hydrogen and oxygen rearrange themselves, so that two atoms of hydrogen and one atom of oxygen combine to form a molecule of water-vapour, containing three atoms. The steam now contains as many molecules as did the hydrogen before combination; but whereas the molecules of hydrogen originally consisted of two atoms each, the molecules of steam contain three atoms. It is this which causes the contraction from three volumes to two when hydrogen and oxygen molecules exchange partners in forming water molecules.

Of course the difficulty would meet with an equally good explanation if it were supposed that the hydrogen molecules and the oxygen molecules each contained four atoms, or eight atoms; but there is no need to increase the complexity of the molecule, and the assumption that these molecules are “diatomic” completely serves the purpose. The composition of water is therefore believed to be two atoms of hydrogen in combination with one atom of oxygen; and when hydrogen and oxygen unite to form water, a transaction similar to an exchange of partners is supposed to occur; the atoms of hydrogen and oxygen are imagined to leave their partners of like kind, and to rearrange themselves so that groups of atoms, or molecules, each containing two atoms of hydrogen and one of oxygen, are formed. To such an arrangement the formula H{2}O is applied, while ordinary hydrogen molecules may be represented as H{2}, and molecules of oxygen as O_{2}.

It has been shown already (p. 150) how Lord Rayleigh obtained the number 15·882 for the density of oxygen compared with that of hydrogen. To determine the atomic weights of elements, the usual process has been to analyse their oxides, for only a few elements form compounds with hydrogen. Thus the analysis of copper oxide yields the numbers--

Copper 79·96 per cent Oxygen 20·04 "

And as no compound of copper and hydrogen is known which lends itself to analysis, the atomic weight of copper is necessarily referred to that of oxygen. If the atomic weight of hydrogen be taken as unity, that of oxygen, from Lord Rayleigh’s determination, must be 15·882, because, in comparing the weights of equal volumes of the gases, a comparison is made of the weights of equal numbers of molecules; and as it is reasonable to suppose that each molecule of hydrogen and of oxygen contains two atoms, the number 15·882 represents the weight of an atom of oxygen compared with that of an atom of hydrogen taken as 1. But this number has not been regarded as sufficiently established by experiment. Other observers (for the importance of this ratio has been acknowledged since the beginning of the century) have obtained results differing from that given above, although not to any great extent. And as it is a matter of indifference what basis or standard be taken for atomic weights, which represent only relative numbers, it is common to accept the atomic weight of oxygen as 16, in which case that of hydrogen, if Lord Rayleigh’s determination of its density be regarded as accurate, would be 1·0074. Hence if we place the atomic weight of oxygen as 16, that of copper would be 63·34. And as with copper, so with most other elements. It is very seldom that the atomic weight of an element has been directly compared with that of hydrogen; it is, in fact, almost always ascertained by analysis of its chloride, bromide, or oxide; and the atomic weights of chlorine and bromine have been very carefully compared with that of oxygen. There is, besides, another convenience in accepting 16 as the atomic weight of oxygen: it is that many atomic weights are then represented by whole numbers instead of by fractions; thus, sulphur has the atomic weight 32, if oxygen be made 16, whereas, if it were 15·882, the atomic weight of sulphur would be 31·764, a number much more difficult to remember.

We see then that it is convenient to refer the density of argon to oxygen taken as 16. The density obtained by Professor Ramsay in February 1895, using a globe of small capacity (only 160 cubic centimetres), was 19·94; exactly the same result was given by Lord Rayleigh’s experiments in June 1895 on argon prepared by means of the electric discharge, with a balloon of much greater capacity, which held over two litres of gas. Now as a molecule of oxygen consists of two atoms, the weight of a molecule is twice the atomic weight, or 32; and as a given volume of argon must contain as many molecules as the same volume of oxygen, the weight of a molecule of argon must be twice 19·94, or 39·88.

But this gives no information regarding the relative weight of an atom of argon. To ascertain this important quantity two methods may be chosen. One is to make compounds of the element, and this will be first considered. Since an atom of an element is defined as the smallest amount which can exist in combination, then, if numerous compounds of an element be examined, that one which contains proportionally the least amount of the element may be regarded as containing an atom, unless there are reasons to the contrary. For example, reverting to the former instance of water, the relative proportions by weight of oxygen and hydrogen are, in round numbers, 16 to 2. Reasons have already been given showing why its formula should be H{2}O and not HO; its molecule must contain two atoms of hydrogen. But another compound of oxygen and hydrogen is known in which the proportions are 16 parts by weight of oxygen to 1 part by weight of hydrogen. Here also there are reasons for believing that this compound, hydrogen peroxide, contains two atoms of hydrogen; whence it follows that it must contain two atoms of oxygen, or 32 parts by weight to 2 parts by weight of hydrogen, and must therefore have the formula H{2}O_{2}. No other compound of oxygen and hydrogen is known; and it may be stated briefly that no compound of oxygen with any element whatever is known in which less than 16 parts by weight enters, compared, of course, with the atomic weight of the other element or elements in the compound. Hence 16 is accepted on this ground as the atomic weight of oxygen.

If now it were possible to prepare compounds of argon, similar reasoning might be applied to them, and that compound containing least argon would be regarded as indicating its atomic weight. Many attempts were therefore made to induce argon to enter into combination. And the consistent failure of these attempts led to the choice of the name “argon” or “idle” for the newly discovered element. The methods employed to prepare argon free from nitrogen, namely, by exposing the mixed gases to the action of oxygen in a discharge of electric sparks, and by passing them over red-hot magnesium, show that it cannot be induced to combine with one of the most electro-negative of elements, oxygen, and one of the most electro-positive, magnesium. It also refuses to combine with hydrogen or with chlorine when sparked with these gases; nor is it absorbed or altered in volume by passage through a red-hot tube along with the vapours of phosphorus, sulphur, tellurium, or sodium. Red-hot caustic soda, or a red-hot mixture of soda and lime, which attacks the exceedingly refractory metal platinum, was without action on argon. The combined influence of oxygen and an alkali in the shape of fused potassium nitrate or red-hot peroxide of sodium was also without effect. Gold would, however, have resisted such action, but it would have been attacked by the next agent tried, viz. persulphide of sodium and calcium. This mixture was exposed at a red-heat to a current of argon, again without result. Nascent chlorine, or chlorine at the moment of liberation, obtained from a mixture of nitric and hydrochloric acids, and from permanganate of potassium and hydrochloric acid, was without action. A mixture of argon with fluorine, the most active of all the elements, was exposed to a rain of electric sparks by M. Moissan, the distinguished chemist who first succeeded in preparing large quantities of fluorine in a pure state, without his observing any sign of chemical combination.

An attempt was also made to cause argon to combine with carbon by making an electric arc between two rods of carbon in an atmosphere of argon. It was at first believed that combination had taken place, for expansion occurred, the final volume of gas being larger than the volume taken; but subsequent experiments have shown that the expansion was due to the formation of some oxide of carbon from the oxygen adhering to the carbon rods. On absorption of this oxide by the usual absorbent, a mixture of cuprous chloride and ammonia, the argon was recovered unchanged.

M. Berthelot, the celebrated French chemist, has stated that, on exposing argon mixed with benzene vapour to a rain of electric sparks, he has succeeded in causing argon to combine. Its volume certainly decreases, but whether this decrease is to be attributed to true combination or not is very doubtful. The benzene is converted into a resinous mass, which coats the walls of the tube; and it is not improbable that the argon may be dissolved, or even mechanically retained, in the resinous deposit. Helium, a gas closely resembling argon in properties, may be made to enter into a similar combination with metallic platinum, if combination it can be called; but the amount absorbed in both cases is extremely minute, and the gas is evolved unchanged on heating the resin or the metal.

Professor Ramsay has also made experiments on the action of a silent electric discharge upon a mixture of argon with the vapour of carbon tetrachloride; the latter decomposes, giving, not a resin, but crystals of hexachlorobenzene and free chlorine; but the volume of the argon was unchanged. It was all recovered without loss. Lastly, the rare elements titanium and uranium have been heated to redness in a current of argon with no alteration or absorption of the gas. In short, all likely agents have been tried as absorbents for argon, but in no case has any true chemical combination been obtained.

These failures to produce compounds make it impossible to gain any knowledge regarding the atomic weight of argon by a study of its compounds, for it forms none. It is, indeed, in the highest degree improbable that, had compounds existed, none should have been found in Nature. There are, it is true, a few elements, such as platinum and those resembling it, which always occur native, i.e. in the elementary state; but even they yield to the attack of the agents tried with argon. It cannot, of course, be stated with absolute certainty that no element can combine with argon; but it appears at least improbable that any compounds will be formed.

It was therefore necessary to adopt some other method in attempting to determine the atomic weight of argon,--some method dependent on its physical rather than its chemical properties, for argon, unlike almost all other elements, appears to be devoid of chemical properties.

In order better to follow the train of reasoning based on experiment, it will be well to begin with an account of why the atomic weight of mercury is accepted as 200. The amount of mercury which combines with 16 parts by weight of oxygen is easily found by heating a weighed quantity of oxide of mercury, as Priestley and Scheele did, and weighing the residue of metal. The results of the most accurate experiments show that 200·36 grams of mercury combine with 16 grams of oxygen, and if the compound consists of one atom of each element, 200·36 must be the atomic weight of mercury. The first idea which naturally occurs is to find out the relative weight of mercury gas. This has been done, and it is found to have the ratio to that of oxygen of 100 to 16. Doubling these numbers will give the molecular weights, since a molecule of oxygen consists of two atoms, and must therefore possess twice the weight of one atom. We thus obtain the numbers 200 and 32 as the molecular weights of mercury and oxygen respectively. It might therefore be concluded that 200 is not the true atomic weight of mercury, but 100, and that the compound of mercury with oxygen contains not one but two atoms of mercury, and should therefore be represented by the formula Hg_{2}O, not HgO. But on surveying all known compounds of mercury, there is not one which contains less than 200 parts by weight of mercury in a molecule of the compound, or in which the mercury cannot be conceived to replace 2 parts by weight of hydrogen. And on weighing as gases the compounds of mercury with other elements, where such compounds do not decompose on heating like the oxide, the amount of mercury present must be always taken as 200, in order to add up to the molecular weight found. For example, a compound of mercury with carbon and hydrogen, named mercury methide, has a density of 120 compared with oxygen taken as 16, hence the comparative weight of its molecule must be 240. Now it is known to contain two atoms of carbon and six atoms of hydrogen, the atomic weights of which are 24 + 6 = 30. And deducting 30 from 240, 210 remains as an approximation to the atomic weight of mercury. It might, it is true, be the weight of two atoms of mercury, but if so it is singular that no compound contains a smaller proportion; and there is another reason, which follows immediately, that leads us to believe that 200 is correctly taken as the true weight of an atom.

It was discovered by Dulong and Petit, early in the century, that the higher the atomic weight of an element the less heat is required to raise its temperature through a given number of degrees. This heat can be measured by dropping a fragment of the element, carefully weighed and heated to a known temperature, into a known weight of cold water, and ascertaining what rise of temperature the water undergoes, owing to the heat communicated to it by the element. These comparative amounts of heat, if water is chosen as the standard, are termed specific heats. And as the specific heats of elements have been found by experiment to be inversely as their atomic weights, the product of the specific heat of any element and its atomic weight will give a constant number. If the quantity of element weighed is one gram, and its rise of temperature one degree, the numerical value of this product is about 6·4.

Now the specific heat of mercury has been found to equal 0·032; that is to say, it requires only a fraction of the value of 0·032 of heat to raise the temperature of say 1 gram of mercury through one degree, whereas the amount of heat necessary to raise 1 gram of water through one degree is represented by the number 1. Hence this number, 0·032, multiplied by the atomic weight of mercury, should yield the product 6·4; and it is seen at once that that number must be 200, for 200 × 0·032 = 6·4. This is an additional reason for believing that the atomic weight of mercury must be represented by the number 200.

We come next to a confirmatory piece of evidence which greatly strengthens the view that the atomic weight of mercury must be 200; but before entering into detail let us see what an atomic weight of 200 involves. The density of mercury gas is 100, and its molecular weight must be 200. But if its atomic weight is also 200, it follows of necessity that its molecule and its atom must be identical; that unlike oxygen and hydrogen, its molecule consists, not of two atoms, but of one single atom. There is nothing strange in this conclusion; there is no evident reason why single atoms should not act as molecules, or independent particles, able to exist in a free state, uncombined with each other or with any other molecules.

The specific heat of a gas is measured in much the same manner as that of a solid. A known volume of the gas is caused to pass through a spiral tube, heated to a certain definite high temperature; it then enters a vessel containing a known weight of water, traverses a spiral tube immersed in the water, and parts with its heat to the water. Knowing, therefore, the weight of the gas and its initial temperature, and also the rise of temperature of the water, the specific heat of the gas can be compared with that required to raise an equal weight of water through one degree. But gases are found to possess two specific heats. If the volume of the gas is kept constant, so that the gas does not contract during its loss of heat, one number for its specific heat is obtained; while if it is allowed to alter its volume a higher figure represents its specific heat. It will be necessary to consider the cause of this difference, in order to understand what conclusions can be drawn respecting the molecular nature of argon from a determination of the ratio between its two specific heats--that at constant pressure and that at constant volume.

If a gas is allowed to expand into a vertical cylinder so as to drive up a piston loaded with a weight, it is said to “do work.” The work is measured by the weight on the piston, and also by the height to which it is raised. Thus, if the weight is one pound, and the height one foot, one foot-pound of work is done; if the mass is one gram and the height one centimetre, one gram-centimetre of work is done. During this process the gas must expand; and if it were enclosed in some form of casing through which heat could not pass--we know of no such casing, but we can contrive casings through which heat passes very slowly--the temperature of the gas would fall during its expansion, and it would lose heat. For each loss of one heat-unit or calory--i.e. the amount of heat given off by 1 gram of water in cooling through 1° Centigrade--the gas would perform 42,380 gram-centimetres of work; it would raise a weight of nearly 4¼ kilograms, or about 9⅓ lbs., through 1 centimetre, or nearly half an inch.

When a gas expands into the atmosphere it may be regarded as “raising the atmosphere” through a certain height, for the atmosphere possesses weight, equal on the average to 1033 grams on each square centimetre of the earth’s surface, or between 15 and 16 lbs. on each square inch. Suppose a quantity of air, weighing 1 gram, to be enclosed in a long cylindrical tube of one square centimetre in section. At the usual pressure of the atmosphere on the earth’s surface, and at 0° Centigrade, the volume of the air would be 773·3 cubic centimetres; and, as the sectional area of the tube is 1 square centimetre, the air would occupy 773·3 centimetres’ length of the tube. If heat be given to this air, so that its temperature is raised from 0° to 1°, it will expand, as Gay-Lussac showed, by 1/273rd of its volume. Now the product of 773·3 and 1/273 is 2·83 centimetres; the level of the surface of the air will rise in the tube through that amount. In doing so it will perform the work of raising 1033 grams through 2·83 centimetres, or 2927 gram-centimetres. Careful measurements have shown that, in order to do this work, heat to the amount of 0·0692 calory must be given to the gas. But it has been found that to heat the air through one degree, without allowing it to expand, requires 0·1683 calory; that is, the same amount of heat which would raise a gram of air through one degree, its volume being kept constant, will raise a gram of water through 0·1683°; or, in other words, the specific heat of air is 0·1683. But if allowed to expand, more heat is required--an additional 0·0692 calory must be given it; consequently its specific heat at constant pressure is greater; it is actually the sum of these two numbers, 0·1683 + 0·0692 = 0·2375.

We have thus--

Specific heat at constant pressure 0·2375 " " " volume 0·1683

Ratio between these numbers: 0·2375/0·1683 = 1·41

This ratio is termed the ratio between the specific heats of air, and such a ratio is represented usually by the letter =γ=.

But it is not necessary to determine both kinds of specific heat in order to arrive at a knowledge of the value of this ratio. One plan, adopted by Gay-Lussac and Désormes at the suggestion of Laplace, is to actually measure the fall of temperature by allowing a known volume of gas, of which the weight can of course be deduced, to expand from a pressure somewhat higher than that of the atmosphere to atmospheric pressure. It is true that heat will rapidly flow in through the walls of the vessel; but by choosing a sufficiently large vessel, and surrounding its walls with badly-conducting material, the entry of heat will be so slow that it may, for practical purposes, be neglected. The number for this ratio, actually found by Gay-Lussac and Welters for air, was 1·376; but subsequent and more accurate experiments have given as a result 1·405, which is almost identical with that calculated above.

This method, however, can be employed only when an unlimited supply of gas is at disposal, for it entails the use of large vessels, and the compressed gas must be allowed to escape into the atmosphere, and is lost. There is, fortunately, another method by which the same results can be obtained, and which requires only a small amount of gas.

Sir Isaac Newton calculated that the velocity of sound in a gas was dependent on its pressure and on its density, in such a manner that

_________ c = √ (p/d_),

where c stands for velocity (celerity), p for pressure, and d for density. When waves of sound are transmitted through air, the air is compressed in parts and rarefied in parts, in such a manner that compression follows rarefaction very rapidly, that part which is compressed at one instant being rarefied at the next, compressed again at a third, and rarefied at a fourth, and so on. Laplace was the first to point out that during such rapid changes of pressure as occur while a sound-wave is passing, the pressure will not rise proportionally to the density, as would be the case if Boyle’s law were followed; for on sudden rise of pressure the temperature of the compressed portion of the gas will be increased; and, correspondingly, on sudden fall of pressure, the wave of compression having passed, the temperature will fall. He showed that instead of two pressures being inversely proportional to their two volumes, under such circumstances, as they are according to Boyle’s law, or

p/p{1} = v_{1}/v_,

they must be inversely proportional to the volumes raised to a power, the numerical expression of which is the ratio of the specific heats of the two gases, =γ=, thus:

p/p{1} = (v_{1}/v_)^γ;

or as

v{1} : v :: d : d__{1},

__________ c = √( γp/d), and γ = c^2d/p_.

The ratio of the two specific heats can therefore be determined by finding the velocity of sound in the gas, and by noting at the same time its density and its pressure.

To determine the velocity of sound in a gas, it is not necessary to adopt the plan which has been successfully carried out with air; that is, to make a sudden sound at one spot and to measure the interval of time which the sound takes to travel to another spot some miles distant. There is a simpler method, depending on the fact that the lengths of the waves of compression and rarefaction are proportional to the velocity of the sound. So that, knowing the velocity of sound in air, the velocity in any other gas may be found by determining the relative length of the sound-waves in air and in that gas.

The simple apparatus with which such determinations are made is due to the physicist Kundt. It consists of a glass tube, through one end of which a glass rod passes, so that half the rod is enclosed in the tube, while the other half projects outside it. In the experiments on argon, the rod was sealed into the tube; in other cases, it is better to attach it with indiarubber, or to cause the rod to pass through a cork. The open end of the tube is connected with a supply of the gas, so that, after the tube has been pumped empty of air, the gas, in a pure and dry condition, can be admitted. Some light powder (and for this purpose lycopodium dust--the dried spores of a species of fungus--is best) is placed in the tube, and distributed uniformly throughout it, so that when the latter is in a horizontal position, a streak of the powder lies along it from end to end. The portion of rod outside the tube is rubbed with a rag wetted with alcohol, when it emits a shrill tone or squeak, due to longitudinal vibrations; the pitch of the tone depends, naturally, on the length of the rod, a long rod giving a deeper tone than a short one. The vibrations of the rod set the gas in the tube in motion, and the sound-waves are conveyed from end to end of the tube through the gas. As the tube is closed at the end through which the gas was admitted, these waves echo back through it; and a great deal of care must be taken to make the echo strengthen the waves, so that the compressions produced by the back waves are coincident in position with the compressions produced by the forward waves travelling onwards from the rod. The gas, could we see it, would represent portions compressed and portions rarefied at regular intervals along the tube. Where the gas is compressed, it gathers the lycopodium dust together in small heaps, the position of each heap signifying a node of compression. Hence, comparing the distances between the nodes of compression for any gas and for air, we find the relative wave-lengths of sound in the two gases; and, as the velocity of sound in air has been accurately measured, we thus determine the velocity of sound-waves in the gas under experiment.

Such experiments were made by Kundt and by his co-worker Warburg on mercury gas, and they found that in this case the value of γ was 1·67; that is, in the equation

γ = c^{2}d/p the value 1·67 had to be ascribed to γ, in order to render it equal to the product of the square of the velocity into the density, divided by the pressure.

Similar experiments with argon led to the same result as Kundt and Warburg found for mercury gas; but the calculation becomes more simple if it is allowable to take for granted that the elasticity, or alteration of pressure produced by unit alteration of volume, is identical in the case of argon and air. The full equations are--

_________________________ nλ{air} = c{air} = √γ(p/d)(1 + at){air},

and

___________________________ nλ{argon} = c{argon} = √γ(p/d)(1 + at){argon},

where n is the number of vibrations per second, =λ= the wave-length of sound, and a the coefficient of the expansion of a gas for a rise of 1° in temperature, t, viz. 0·00367. Now if the expression p (1 + at) can be shown to be identical for argon and for air, the value of =γ= for argon can be calculated by the very simple proportion--

λ^{2}d{air} : λ^{2}d_{argon} :: 1·408 : γ{argon}.

This involved a measurement of the rate of rise of pressure of argon, p, per degree of rise of temperature, t; or, in other words, the verification of Boyle’s and Gay-Lussac’s laws for argon; and this research was successfully carried out by Dr. Randall of the Johns Hopkins University of Baltimore, U.S.A., and Dr. Kuenen, of Leyden, working in Professor Ramsay’s laboratory. They made use of a constant volume thermometer, and measured the rise of pressure corresponding to a definite rise of temperature, comparing the gases argon and helium in this respect with air. The values found between 0° and 100° for air, argon, and helium were--

One volume air, heated from 0° to 100°, raises pressure in the proportion of 1 to 1·3663 Argon 1·3668 Helium 1·3665

It may therefore be taken for certain that, within the limits of experimental error, the value of the expression p(1 + at) is identical for all three gases.

We see, then, that for argon, as for mercury gas, the value of =γ=, the ratio between the specific heats at constant volume and at constant pressure, is 1 to 1·66, whereas for air, hydrogen, oxygen, nitrogen, carbon monoxide, and nitric oxide, it is 1 to 1·4.

We have now to consider what conclusion can be drawn from this difference.

On the usually accepted theory of the constitution of matter, it is held that atoms may be regarded as spheres, hard, elastic, smooth, and practically incompressible. True, we really know little or nothing regarding the properties of such particles, if particles there be; but in considering their behaviour it is necessary to make certain suppositions, and to see whether observed facts can be pictured to our minds in accordance with such postulates. If, from the known behaviour of large masses, conclusions can be drawn regarding small masses, and if these conclusions harmonise with what is found to be the behaviour of large numbers of small masses acting at once, the justice of the supposition is, although not proved, at least rendered defensible as one mode of regarding natural phenomena.

Molecules, on this supposition, may consist of single atoms, or they may consist of pairs of such atoms, joined in some fashion like the bulged ends of a dumb-bell; or lastly, they may consist of greater numbers of atoms arranged in some different manner, the arrangement depending on their relative size and attraction for each other. It must be clearly understood, however, that such mental pictures are not to be taken as actually representing the true constitution of matter, but merely as attempts to picture such forms as will allow of our drawing conclusions regarding their behaviour from known configurations of large masses.

The molecules of gases are imagined to be in a state of continual motion, up and down, backwards and forwards, and from side to side. It is true that they must also move in directions which cannot be described by any of these expressions, but such other directions may be conceived as partaking more or less of motions in the three directions specified; i.e. in being resolvable into these. To these motions have been applied the term “degrees of freedom.” Such motions through space, in which the molecule is transported from one position in space to another, form three of the possible six degrees of freedom which a molecule may possess, and the molecules are said to possess “energy of translation” in virtue of this motion. The other three consist in rotations in three planes at right angles to each other.

Now, it can be shown that the product of pressure and volume of a gas, pv, is equal to ⅔rds of the energy of translation of all molecules of the gas, or

pv = ⅔(NR),

where N stands for the number of molecules in unit volume, and R for their energy of translation; inasmuch as a pressure diminishing a volume is of the nature of work, or energy. For one gram of air at O° C. and 76 cms. pressure (normal temperature and pressure), the pressure (p), measured in grams per square centimetre, is 1033, and the volume (v) is 773·3 cubic centimetres; and the raising of the temperature through 1°, as was shown before, requires 2927 gram-centimetres of work. Further, since the product of pressure into volume is equal to ⅔rds of the energy due to motion, or the translational energy of the gas,

NR = 3/2pv = 3/2 × 2927 = 4391 gram-centimetres.

Dividing this number by 42,380, the mechanical equivalent of heat, or the number of gram-centimetres corresponding to one calory, the quotient is 0·1040 calory. If the energy of the air were due to the translational motion of its molecules, we should expect this number, 0·1040, to stand for the specific heat of air at constant volume; but it has been found equal to 0·1683, as already shown.

We have seen that to convert specific heat at constant volume into specific heat at constant pressure 0·0692 must be added. Hence at constant pressure the specific heat of such an ideal gas should be 0·1732. And the relation between specific heat at constant volume and that at constant pressure should be 0·1040 to 0·1732, or 1 to 1⅔. The conclusion to be drawn from these numbers for air, 0·1683 and 0·2375, which bear to each other the ratio of 1: 1·41, is that air cannot be such an ideal gas; that in communicating heat to it some of that heat must be employed in performing some kind of work other than that of raising its temperature. What this work may possibly be we shall consider later.

But Kundt and Warburg found, from their experiments on the ratio between the specific heats of mercury gas, this ideal ratio, 1 to 1⅔; and Professor Ramsay obtained the same ideal ratio, or one very close to it indeed, 1 to 1·659, for argon. He subsequently found this ideal ratio also to hold for helium (1 to 1·652), and it must therefore be concluded that such gases possess only three degrees of freedom; or, in other words, their molecules, when heated, expend all the energy imparted to them in translational motion through space.

This is the consequence which we should infer from the supposition that such molecules are hard, smooth, elastic spheres. Were they each composed of two atoms, we should have to picture them as dumbbell-like structures; and here we enter on a theoretical conception put forward by Professor Boltzmann, but which has not been accepted universally by physicists.

Boltzmann imagines that to the three “degrees of freedom” of a single atom molecule there may be added, provided the molecule consists of two atoms, two other degrees of freedom, namely, freedom to rotate about two planes at right angles to each other. The knobs at the end of each imaginary dumb-bell may revolve round a central point in the handle joining them, and it is clear that they may revolve in one horizontal and in one vertical plane, as shown in Fig. 5. Such diatomic molecules are said to possess five “degrees of freedom.” They will not, it is supposed, rotate round the line joining the centres of the spheres, because, as before said, the atoms are pictured as perfectly smooth. But if the molecules are triatomic, as, for example, CO{2} or N{2}O, they will have six degrees of freedom, for with the addition of an additional atom they have an additional plane of rotation (see Fig. 6). Boltzmann has attempted to show that the ratio of the specific heats of diatomic molecules should be as 1 to 1·4. In actual fact it approximates to that number. For the commoner gases it is--

Oxygen 1·402 Nitrogen 1·411 Hydrogen 1·412 Carbon monoxide 1·418

In all cases the numbers are too large, and this is a serious difficulty, because any tendency to rotate round the central line would cause the values to be less, not greater than 1·4. For triatomic molecules the calculated value of γ is 1⅓, but in actual fact the ratio in the case of triatomic molecules, such as H{2}O, CO{2}, N_{2}O, etc., is always less than 1⅓. These speculations stand on a basis very different from the first conception, namely, that all heat must be employed in communicating translational motion to molecules of mercury gas, argon, and helium, and it appears that the atoms of these three elements must necessarily be regarded as having the properties of smooth elastic spheres. The atoms and the molecules must in their several cases be identical. And, inasmuch as the chemical evidence regarding mercury leads to the same conclusion, it appears legitimate to infer that argon and helium must also be monatomic elements.

Méchanique céleste, vol. v. p. 123.

Proc. Roy. Soc. vol. lix. p. 63.