THE THERMAL ENERGY OF THE SUN
The sun’s heat and the conservation of energy—Mayer’s
meteoric hypothesis—Helmholtz and contraction under
gravity—The earth’s dependency upon solar radiation—The
work of Kelvin and Ritter—The insufficient contributions of
atomic disintegration—Arrhenius’ view of the importance of
molecular energy—Cyclic development of the universe.
Before the doctrine of the conservation of energy was established, the
steady radiation of solar light and heat was not, in its quantitative
aspect, a phenomenon to be wondered at. Regarding the sun merely as a
gigantic fire, philosophers such as Leibnitz and Kant were satisfied
that the intense emission of energy was sustained simply by combustion.
As soon as the chemistry of combustibles came to be studied, it was
at once evident that the energy derived from burning alone would be
hopelessly insufficient. If the sun had been originally a colossal
mass of the most powerful explosives known to us, then, under the
most favourable conditions for maintaining the present output of
heat, all would have been at an end within a few thousand years. The
total amount of available energy would not have sufficed even for the
historical period—a period which is merely a ripple in the vast ocean
of geological time.
What, then, can be the source of the energy which for millions of years
has enabled the sun to bathe the earth in a welcome glow of light and
heat? How is the loss to be accounted for? For how long can the sun
continue to radiate its energy without becoming perceptibly colder?
These critical questions must have appealed to Mayer with some force
when he recognised the truth that energy could neither be created nor
destroyed. For the first time a sound explanation became an imperative
demand. Mayer realised that in the collision and friction of bodies,
heat energy is acquired in strict equivalence to the energy of motion
which has apparently disappeared. He saw that the mechanical generation
of heat would be of vastly greater importance in cosmic evolution than
the limited possibilities of combustion. A piece of coal falling into
the sun from infinite space would yield, by the stoppage of its motion,
six thousand times as much heat as it could provide by burning.
Applying these principles, Mayer thought that the sun’s heat might be
traced to the kinetic energy of swarms of meteorites. These bodies
falling into the sun with enormous velocities, would be competent, if
only the supply were ample, to generate the heat annually required.
Kelvin at first also advocated this view, but he was soon compelled to
relinquish it in favour of another explanation less at variance with
known facts. The observations of astronomers were all against there
being a circulation and influx of meteorites to the extent required by
the sun if income and expenditure of heat were to balance. Comets would
suffer resistance in their passage round the sun. The rotational
velocity of the sun would be constantly impeded, and probably, far back
in the past, it would have been brought to a standstill. The sun’s mass
would be appreciably increased every year, and an immediate effect
of this would be to hurry up the earth in its orbit, so that each
year would be notably shorter than the preceding one. Happily for the
stability of the solar system, there is no evidence for an infalling of
meteorites on the scale first contemplated.
In 1856, Helmholtz, another early worker in the domain of energy, found
a more satisfactory escape from the dilemma. Instead of looking outside
the sun for the origin of the heat supply, he sought for an internal
source, and found one—certainly a more efficient substitute—in the
contraction of the sun’s diameter under its own strong gravitation.
Knowing the amount of heat annually radiated, it is easy to calculate
that a shrinkage of 1000 feet would make up the loss for five years.
The decrease in the apparent diameter would, at this rate, never become
detectable in human experience. Helmholtz imagined a time when the
sun existed as a nebula spreading far out into space. As it slowly
cooled and contracted, the mechanical work of shrinkage would reappear
as heat. Assuming the present sun to be a globe of uniform density,
Helmholtz calculated that its past history must have been restricted to
about 20 million years.
The annual output of heat had been determined by Pouillet, and his
result, which was too low, was used by Helmholtz in this estimate. The
solar constant of radiation is measured by the heat in calories, which
would be absorbed in one minute by a surface of one square centimetre
placed outside the earth’s atmosphere at right angles to the sun’s
rays. Allowance is made in this way for the absorptive effects of gases
and of the load of dust held by the lower strata of the atmosphere.
Pouillet’s value in these units was 1·76 and the results of subsequent
experiments, made up to 1905, varied between his figure and 4·1.
This was unsatisfactory, and, under the auspices of the Smithsonian
Institution, work has recently been done to clear up the discrepancy.
The constant is now known with some certainty to be 1·95. Using this
figure the duration of the sun’s heat would, according to Helmholtz, be
limited to 18 million years.
The surface temperature of the earth can owe but little to its internal
energy. Taking the temperature gradient at 1° C. in 32 metres, and the
average conductivity of rock as 0·004, the temperature maintained by
this flow of heat alone would reach only 34° Absolute (239° C. below
zero). It is evident then that the genial warmth of the greater part
of the earth’s surface is maintained almost wholly by the absorption
of solar radiation. For this reason the active life of our planet is
intimately bound up with that of the sun, and any age limit assigned
to the latter becomes a still more embarrassing restriction in its
application to the earth.
We may now return to our discussion of the sun’s vast expenditure of
energy, armed with data worthy of confident acceptance, and with the
knowledge that, for at least as long as the earth has been a habitable
globe, so long has the sun emitted its life-giving rays at a rate
not very different from that of the present. The evidence of geology
is clear on this point. The geographical distribution of plants and
coral reefs in past ages betrays no sign of a steadily cooling sun. In
some of the oldest sedimentary rocks which are known, the imprints of
raindrops have been found, and the size and force of the latter were
evidently not very different from those which fall to-day by the shores
of seas and lakes. The intensity of climatic forces has remained, on
the average, unchanged.
Kelvin somewhat mitigated the consequences of Helmholtz’s extreme view
in his later treatment of the problem. Helmholtz had assumed a sun of
uniform density; but Kelvin pointed out that, as the density probably
increases enormously towards the centre, the amount of heat which
has been already available may have been very much greater than that
previously calculated. Kelvin’s cautious spirit was not shared by his
contemporaries, who readily accepted the smaller estimates. The more
daring investigations of Ritter, and of other physicists who followed
his lead, did not support any period which exceeded 12 million years.
Ritter showed that as the sun contracted from the nebulous state its
temperature would at first begin to rise. Not only would contraction
supply the energy necessary to sustain radiation, but an even greater
quantity of energy would be available for heating purposes. An
interesting summary of Ritter’s work will be found in the second of
the fascinating little volumes by Arrhenius on _The Life of the
Universe_.
Geologists found no consolation in these speculative studies, and
even from Kelvin’s more liberal allowance of time, an element of
embarrassment was not absent. While an annual shrinkage of the sun’s
diameter by 200 feet would suffice for the present, yet, unless at
some time the sun’s temperature begins to fall, it is not clear why
shrinkage should continue. Cooling is none the less certain because it
is temporarily delayed, nor because its rate is for a time diminished.
Increasing density would gradually put an end to effective contraction,
and the sun would then cool as a white-hot ball would do—its capacity
for replenishing its losses having been exhausted for ever. If this
were all, then, in the course of a few more million years, an icy
death would overtake the earth. In the last gleams of the fading solar
twilight our planet would disappear—a barren and frozen world.
More recent views lead to a less pessimistic outlook, and the
twilight of the sun, though ultimately inevitable, is removed to
an indeterminately remote future. Gravitation is manifestly an
insufficient cause to maintain the sun’s heat for the periods required.
We need a supply not for less than a dozen million years, nor even for
the 100 million years which would have satisfied geologists a decade
ago. Some source a hundred times as fruitful as contraction under
gravity is required. Happily there is no longer any need to regard the
sun as a serious difficulty, for there are locked within its atoms and
molecules stores of potential energy capable of fulfilling every
terrestrial requirement.
The importance of radio-thermal action in the sun was pointed out by
Rutherford and Soddy in 1903. A month or two later, W. E. Wilson made
a calculation of the amount of radium which, if distributed throughout
the sun, would entirely explain the evolution of its radiant energy.
He found that 2·5 parts of radium in every million of the sun’s mass
would be necessary. In uranium the equilibrium amount of radium is only
0·34 part in a million, so that, even if the sun consisted entirely
of uranium and its disintegration products, the heat generated would
account for only one-seventh of the total expenditure. Wilson used in
his calculation a solar constant of three calories per minute, which
is certainly too high. His result must also be modified to allow for
the heating effects of the other radioactive bodies. According to the
most recent determinations, a million grams of uranium would give out
77 calories per hour, and in the same time a million grams of thorium
would give out one-third as much, each element being in radioactive
equilibrium. The energy from the sun when divided throughout its mass
averages 300 calories per hour per cubic metre. To sustain this steady
evolution of heat four million grams of uranium would be required. The
average weight of a cubic metre of solar matter is only 1·44 million
grams, so that by no possibility could more than one-third of the sun’s
heat be accounted for by radioactivity.
That radioactive bodies do exist in the sun can admit of little doubt.
Helium was first known as a solar element and its abundance suggested
the presence of those radioactive elements from which it could have
been generated. Direct spectroscopic evidence has not yet revealed any
traces of radium, and, indeed, so minute are the quantities involved
that until recently there was little hope of detecting it in this way.
Uranium lines have now been found in the sun’s spectrum, and unless the
laws of radioactivity are totally different at the temperature of the
sun, we may safely assume that uranium exists in equilibrium with its
associated elements. The sun’s radiation is destitute of the Becquerel
rays, but this in no way denies their emission from solar matter.
Before reaching the earth, the rays would be obliged to pass through
both solar and terrestrial atmospheres, and the latter alone would be
more than sufficient to absorb them completely.
In the materials of the earth’s crust, uranium only averages about one
part in 150,000, and thorium one part in 50,000. If the proportions of
these elements which enter into the constitution of the sun are of the
same order, their contributions to the sun’s energy can only be very
small. The importance of radio-thermal phenomena is not felt until
cooling has progressed to a more advanced stage, as exemplified by the
earth, when the heat lost is balanced against that set free by atomic
disintegration. We must therefore find some other means of escape from
the embarrassment of a rapidly cooling sun.
Arrhenius has made a bold attempt in this direction. He calls to his
aid a universal law, first enunciated by Le Chatelier, which may be
stated as follows: _If a system in equilibrium is subjected to
external influences which disturb its equilibrium, then the internal
reaction within the system will be such as to oppose the external
influences_, i.e. the normal effects of the latter will be partially
overcome. This general statement may be illustrated by the particular
example to which the chief appeal is made. In the chemical changes
which constitute combustion, heat is evolved, and the reaction is said
to be exothermic. But the heat so liberated tends all the while to
prevent the reaction from proceeding, and were an external source of
heat of sufficient intensity applied so as to raise the temperature,
the compounds previously formed would be again separated into their
constituent elements. The liberated elements possess a greater quantity
of intrinsic energy than when they are united to form a compound. That
is to say, not all the heat supplied is able to exercise its normal
effect of raising temperature; the internal reaction is responsible
for the withdrawal and absorption of _part_ of the energy. If
now still more heat is applied the same opposing tendency continues,
and the elements will again combine, this time forming endothermic
compounds characterised by further absorption of heat, and consequently
by higher intrinsic energy than that which the free elements possessed.
The system shows a conservative disinclination to be made hotter, and
as more and more heat is supplied, enormous quantities of energy are
accumulated in the recesses of the molecule itself. In the case of
water, the general tendency is well illustrated. Ice at the freezing
point absorbs 80 calories and becomes water at the same temperature.
Water at boiling-point absorbs 540 calories and becomes steam. This
in turn, when raised to about 3000° C., dissociates into hydrogen
and oxygen, the absorption of energy being 3800 calories. Although
laboratory conditions do not allow us to experiment further, there are
no grounds on which to suggest that this is the end of the process.
While matter thus opposes an increasing temperature by its internal
reactions, it nevertheless resists the reverse change quite as
actively, and for the same reason. If an intensely energetic exothermic
compound be allowed to cool, it will strenuously refuse to do so at
numerous stages. The energy previously gained is emitted steadily or
explosively according to the thermal environment.
In discussing the constitution of the sun and the source of its
powerful radiation, this _Law of Reaction_, as it is called,
finds a pertinent application. With its help Arrhenius has pointed
out the path which appears to lead us safely out of the difficulty in
which we were left by Helmholtz. The chromosphere which, disregarding
the mysterious corona, constitutes the outermost strata of the solar
atmosphere, is largely composed of free elements at a temperature of
6000°-7000° C. Lower down in the photosphere, 9000° C. is probably
attained. Temperature and pressure both increase enormously with
depth, and indeed, the average solar temperature has been estimated at
a thousand times that of the chromosphere. Under these conditions it
seems reasonable to suppose that the sun’s interior is characterised
by compounds charged with a high concentration of energy. Brought by
convection currents towards the surface such highly explosive compounds
would dissociate with expansion and an immense evolution of heat. It
may be to explosions of this sort that the prominences are due. These
violently projected gaseous tongues are shot out with velocities which
sometimes reach a thousand times that of the swiftest rifle bullet.
Since energy is proportional to the square of the velocity, it would
appear from this that solar energies are at least a million times
greater than those of our most powerful explosives. It has already been
stated that if the life of the sun depended solely on the latter it
would endure for only a few thousand years. As it is, the energy seems
amply sufficient to last a million times as long. Here then, furnishing
a regular and sufficient income from within, we have found an almost
inexhaustible source of heat, which is competent to maintain the sun’s
present expenditure for inconceivably long ages, as most probably it
already has done in the past.
True, we are in the face of a new difficulty. Whence arose this
absorption and concentration of energy in the first place? It is
evident that once extinct, our sun could not be re-awakened to the
warmth of its former activity merely by collision. Gravitational energy
alone affords no escape from the ultimate _Wärmetod_, the thermal
extinction towards which the universe would appear to be tending. If
the development of the universe be everywhere toward the equalisation of
temperature implied by the laws of thermo-dynamics, the question
arises—Why, in the abundance of past time, has this melancholy
state not already overtaken us? Either we must believe in a definite
beginning, in the creation of a universe furiously ablaze with energy,
or else we must assume that the phenomena which we have studied simply
reflect our limited experience. Toward the latter alternative we
readily incline, the more so because of the hint it affords of cyclic
processes in the scheme of Nature. Not only is energy being diffused;
somewhere, our hazy conception tells us, energy is being elevated and
stored up. With profound insight, Spencer pointed out in 1864 that it
is to the attenuated nebulæ that we should look for the absorption and
concentration of energy. In the universe nothing is lost, and perhaps
its perfect mechanism is the solitary and only possible example of
perpetual motion. In its cyclic development we may find the secret of
its eternity and discover that the dismal theory of thermal extinction
is, after all, but a limited truth.