CHAPTER VIII. The Thermal Energy of the Sun

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.