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,[28] 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_ = √( γ_p_/_d_), and γ = _c_^2_d_/_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.
[Illustration: FIG. 4.]
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--
__________________________
_n_λ_{air} = _c__{air} = √γ(_p_/_d_)(1 + _at_)_{air},
and
____________________________
_n_λ_{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.[29] 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 = 3/2_pv_ = 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.
[Illustration: FIG. 5.]
[Illustration: FIG. 6.]
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.
[28] _Méchanique céleste_, vol. v. p. 123.
[29] _Proc. Roy. Soc._ vol. lix. p. 63.