THE HEAT OF THE SUN.
The Sun to be first considered: its Evolution is in vigorous
Progress—Considerations on Solar Heat—Size of the Sun—Waste of
Sun-heat—Langley’s Illustration—Sun in Ancient Days—Problem
Stated—The Solar Constant explained—Its Value determined—Estimate of
Radiation from a Square Foot of the Sun—Illustrations of Solar
Energy—Decline of Solar Energy—The Warehouse of Grain—White-hot
Globe of Iron would Cool in Forty-eight Years—Sun’s Heat is
not sustained by Combustion—Inadequacy of Combustion
Demonstrated—Joule’s Unit—Energy of a Moving Body—Energy of a Body
moving Five Miles a Second—Energy of the Earth due to its Motion.
IT will be convenient to consider different bodies in the solar system,
and to study them with the special object of ascertaining what
information they afford as to the great celestial evolution. We cannot
hesitate as to which of the bodies should first claim our attention. Not
on account of the predominant importance of our sun to the inhabitants
of the earth, but rather because the sun is nearly a thousand times
greater than the greatest of the planets, do we assign to the great
luminary the first position in this discussion.
The sun is, indeed, especially instructive on the subject with which we
are occupied. By reason of its great mass, the process of evolution
takes place more slowly in the sun than in the earth or in any other
planet. Evolution has, no doubt, largely transformed the sun from its
primæval condition, but it has not yet produced a transformation so
radical as that which the earth and the other planets have undergone. On
this account the sun can give us information about the process of
evolution which is not to be so easily obtained from any of the other
heavenly bodies. The sun can still exhibit to us some vestiges, if we
may so speak, of that great primæval nebula from which the whole system
has sprung.
The heat of the sun is indeed one of the most astonishing conceptions
which the study of Nature offers to us. Let me try to illustrate it.
Think first of a perfect modern furnace in which even steel itself,
having first attained a dazzling brilliance, can be further melted into
a liquid that will run like water. Let us imagine the temperature of
that liquid to be multiplied seven-fold, and then we shall obtain some
conception of the fearful intensity of the heat which would be found in
that wonderful celestial furnace the great sun in the heavens.
Ponder also upon the stupendous size of that orb, which glows at every
point of its surface with the astonishing fervour that this illustration
suggests. The earth on which we stand is a mighty globe; yet what are
the dimensions of our earth in comparison with those of the sun? If we
represent the earth by a grain of mustard seed, then on the same scale
the sun should be represented by a cocoanut. We may perhaps obtain a
more impressive conception of the proportions of the orb of day in the
following manner. Look up at the moon which revolves round the heaven,
describing as it does so majestic a track that it is generally at a
distance of two hundred and forty thousand miles from the earth. Yet the
sun is so large that if there were a hollow globe equally great, and the
earth were placed at its centre, the entire orbit of the moon would lie
completely within it.
Every portion of that stupendous desert of flame is pouring forth
torrents of heat. It has, indeed, been estimated that the heat which
issues from an area of two square feet on the sun would more than
suffice, if it could be all utilised, to drive the engines of the
largest Atlantic liner between Liverpool and New York.
This solar heat is scattered through space with boundless prodigality.
No doubt the dwellers on the earth do receive a fair supply of sunbeams;
but what is available for the use of mankind can be hardly more than an
infinitesimal fraction of what the sun emits. We shall scarcely be so
presumptuous as to suppose that the sun has been designed solely for the
benefit of the poor humanity which needs light and warmth. The heat and
light daily lavished by the sun would suffice to warm and to illuminate
two thousand million globes, each as great as the earth. If, indeed, it
were true that the only object of the sun’s existence was to cherish
this immediate world of ours, then all we can say is that the sun
carries on its business in a most outrageously wasteful manner. What
would be thought of the prudence of one who, having been endowed with a
fortune of ten million pounds, spent one single penny of that vast sum
in a profitable manner and dissipated every other penny and every other
pound of his fortune in aimless extravagance? But this is apparently the
way in which the sun manages its affairs, so far as our earth is
concerned. Out of every ten million pounds worth of heat issuing from
the glorious orb of day, we on this earth secure one pennyworth, and all
but that solitary pennyworth seems to be utterly squandered. We may say
it certainly is squandered so far as humanity is concerned. What,
indeed, its actual destination may be science is unable to tell.
And now for the great question as to how the sun’s heat is sustained.
How is it that this career of tremendous prodigality has not ages ago
been checked by absolute exhaustion? Every child knows that the fire on
the hearth will go out unless coal be provided. The workman knows that
his devouring furnace in the ironworks requires to be incessantly stoked
with fresh supplies of fuel. How, then, comes it that the wonderful
furnace on high can still continue, as it has continued for ages, to
pour forth its amazing stores of heat without being exhausted?
Professor Langley has supplied us with an admirable illustration showing
the amount of fuel which would be necessary, if indeed it were by
successive additions of fuel that the sun’s heat was sustained. Suppose
that all the coal-seams which underlie England and Scotland were made to
yield up their stores; that the vast coalfields in America, Australia,
China, and elsewhere were compelled to contribute every combustible
particle they contained; suppose, in fact, that we extracted from this
earth every ton of coal which it possesses in every isle and every
continent; suppose that this mighty store of fuel, sufficient to supply
all the wants of the earth for centuries, were to be accumulated, and
that by some mighty effort that mass were to be hurled into the sun and
were forthwith to be burnt to ashes; there can be no doubt that a
stupendous quantity of heat would be produced. But what is that heat in
comparison, we do not say with the heat of the sun, but with the daily
expenditure of the sun’s heat? How long, think you, would the combustion
of so vast a mass of fuel provide for the sun’s expenditure? We are
giving deliberate expression to a scientific fact when we say that a
conflagration which destroyed every particle of coal contained in this
earth would not generate as much heat as the sun lavishes in the tenth
part of every single second. During the few minutes that you have been
reading these words a quantity of heat has gone for ever from the sun
which is five thousand times as great as all the heat that ever has been
or ever will be produced by the combustion of the coal that this earth
has furnished.
But we have still another conception to introduce before we can
appreciate the full significance of the sun’s extraordinary expenditure
of heat and light. We have been thinking of the sun as it shines now;
but as the sun shines to-day, so it has shone yesterday, and so it shone
a hundred years ago, a thousand years ago; so it shone in the earliest
dawn of history, so it shone during those still remoter periods when
great animals flourished which have now vanished for ever; so the sun
shone during those remote ages when life began to dawn on an earth which
still was young. We do not, indeed, say that the intensity of the
sunbeams has remained actually uniform throughout a period so vast; but
there is every reason to believe that throughout these illimitable
periods the sun has expended its radiance with the most lavish
generosity.
A most important question is suggested by these considerations. The
consequences of frightful extravagance are known to us all; we know that
such conduct tends to bankruptcy and ruin; and certainly the expenditure
of heat by the sun is the most magnificent extravagance of which our
knowledge gives us any conception. Accordingly, the important question
arises: As to how the consequences of such awful prodigality have been
hitherto averted. How is it that the sun is still able to draw on its
heat reserve, from year to year, from century to century, from æon to
æon, ever squandering two thousand million times as much heat as that
which genially warms our temperate regions, as that which draws forth
the exuberant vegetation of the tropics or which rages in the desert of
Sahara? That is the great problem to which our attention has to be
given.
We must first ascertain, with such precision as the circumstances
permit, the actual amount of heat which the sun pours forth in its daily
radiation. The determination of this quantity has engaged the attention
of many investigators, and the interpretation of their results is by no
means free from difficulty. It is to be observed that what we are now
seeking to ascertain is not exactly a question of temperature, but of
something quite different. What we have to measure is a quantity of
heat, which is to be expressed in the proper units for quantities of
heat. The unit of heat which we shall employ is the quantity of heat
necessary to raise one pound of water through one degree Fahrenheit.
The _solar constant_ is the number of units of heat which fall, in one
minute, on one square foot of a surface placed at right angles to the
sun’s rays, and situated at the mean distance of the earth from the sun.
We shall suppose that losses due to atmospheric absorption have been
allowed for, so that the result will express the number of units of heat
that would be received in one minute on a square foot turned directly to
the sun, and at a distance of 93,000,000 miles.
[Illustration: Fig. 14.—THE SUN (July 8th, 1892).
(Royal Observatory, Greenwich.)
(_From the Royal Astronomical Society Series._)]
This is a matter for determination by actual observation and
measurement. Theory can do little more than suggest the precautions to
be observed and discuss the actual figures which are obtained. There
have been many different methods of making the observations, and the
results are somewhat various, but the discrepancies are not greater than
might be expected in an investigation of such difficulty. The mean value
which has been arrived at is _fourteen_, and the fundamental fact with
regard to the solar radiation which we are thus enabled to state is that
an area of a square foot exposed at right angles to the solar rays, at a
distance of 93 millions of miles, will in each minute receive from the
sun as much heat as would raise one pound of water fourteen degrees
Fahrenheit.
It follows that the total radiation from the sun must suffice to convey,
in each minute, to the surface of a sphere whose radius is 93,000,000
miles, fourteen units of heat per square foot of that surface. This
radiation comes from the surface of the sun. It is easily shown that the
heat from each square foot on the sun will have to supply an area of
46,000 square feet at the distance of the earth. Hence the number of
units of heat emerging each minute from a square foot on the sun’s
surface must be about 640,000.
We can best realise what this statement implies by finding the amount of
coal which would produce the same quantity of heat. It can be shown that
the heat given out by each square foot of the solar surface in one
minute will be equivalent to that produced in the combustion of
forty-six pounds of coal. If the sun’s heat were sustained by
combustion, every part of the sun’s surface as large as the grate of an
ordinary furnace would have to be doing at least one hundred times as
much heating as the most vigorous stoking could extract from any actual
furnace.
The radiation of heat from a single square foot of the solar surface in
the course of a year must, therefore, be equivalent to the heat
generated in the combustion of 11,000 tons of the best coal. If we
estimate the annual coal production of Great Britain at 250,000,000
tons, we find that the total heat which this coal can produce is not
greater than the annual emission from a square of the sun’s surface of
which each side is fifty yards. All the coal exported from England in a
year does not give as much heat as the sun radiates in the same time
from every patch on its surface which is as big as a croquet ground.
There is perhaps no greater question in the study of Nature than that
which enquires how the sun’s heat is sustained so that the radiation is
still dispensed with unstinted liberality. If we are asked how the sun
can be fed so as to sustain this expenditure, we have to explain that
the sun is not really fed. If, then, it receives no adequate supplies of
energy from without, we have to admit that the sun must be getting
exhausted.
I ought, indeed, to anticipate objection by at once making the admission
that the sun does receive some small supply of energy from the meteors
which are perennially drawn into it. The quantity of energy they yield
is, however, insignificant in comparison with the solar expenditure of
heat. We may return to this subject at a later period, and it need not
now receive further attention.
We must deliberately face the fact that the energy of the sun is
becoming exhausted. But the rate of exhaustion is so slow that it
affords no prospect of inconvenience to humanity; it does not excite
alarm. We grant that we are not able to observe by instrumental means
any perceptible diminution of solar energy. Still, as we know that
energy is being steadily dissipated from the sun, and that energy cannot
be created from nothing, it is certain the decline is in progress. But
the reserve of energy which the sun possesses, and which can be
ultimately rendered available to sustain the radiation, is so enormous
in comparison with the annual expenditure of energy, that myriads of
centuries will have to elapse before there is any appreciable alteration
in the effectiveness of the sun.
Let me illustrate the point by likening the sun to a grain warehouse, in
which 2,500 tons of wheat can be accommodated. Let us suppose that the
warehouse was quite full at the beginning, and that the wheat was to be
gradually abstracted, but only at the rate of one grain each day. Let us
further suppose that no more wheat is to be added to that already in the
warehouse, and let us assume that the wheat thus stored away experiences
no deterioration and no loss whatever except by the removal of one grain
per diem. It is easy to see that very many centuries would have to
elapse before the grain in that warehouse had decreased to any
appreciable extent.
With a consumption at the rate of a single grain a day a ton of corn
would last about four thousand years, and 2,500 tons of corn would
accordingly last about ten million years. It follows, therefore, that if
the grain in that store were consumed at the rate of only one grain per
day the warehouse would not be emptied for ten million years.
[Illustration: Fig. 15.—I. SPECTRUM OF THE SUN.
II. SPECTRUM OF ARCTURUS.
(_Professor H. C. Lord._)]
The quantity of heat, or rather the reserve of energy equivalent to
heat, which still remains stored up in the sun bears to the quantity of
heat which the sun radiates away in a single day a ratio something like
that which a single grain of corn bears to 2,500 tons of corn.
The sun’s potential store of heat is no doubt very great, though not
indefinitely great. That heat is beyond all doubt to be ultimately
exhausted; but the reserve is so prodigious that for the myriads of
years during which the sun has been subjected to human observation there
has been no appreciable alteration in the efficiency of radiation.
It might be supposed that the sun was merely a white-hot globe cooling
down, and that the solar radiation was to be explained in this way. But
a little calculation will prove it to be utterly impossible that the
heat of the great luminary could be so accounted for. A knowledge of the
current expenditure of solar heat shows that if the sun had been a globe
of iron at its fusing point, then at the present rate of radiation it
would have sunk to the temperature of freezing water in forty-eight
years.
Perhaps I ought here to explain a point which might otherwise cause
misapprehension. For our ordinary sources of artificial heat we, of
course, employ some form of combustion. Whenever combustion takes place
there is chemical union between the carbon or other fuel, whatever it
may be, and the oxygen of the atmosphere. A certain quantity of carbon
enters into chemical union with a definite quantity of oxygen, and, as
an incident in the process, a definite quantity of heat is liberated. So
much coal, for instance, requires for complete combustion so much air,
and, granted a sufficiency of air, the union of the carbon and hydrogen
in the coal will give out a certain quantity of heat which may be
conveniently expressed by the number of pounds of water which that heat
would suffice to transform into steam. It is necessary to observe that
there are definite numerical relations among these quantities. The
quantity of heat that can be produced by the combustion of a pound of
any particular substance will depend upon the nature of that substance.
As chemical combination is the main source of the artificial heat which
we employ for innumerable purposes on the earth, it seems proper to
consider whether it can be any form of chemical combination which
constitutes the source of the heat which the sun radiates in such
abundance. It is easy to show that the solar radiation cannot be thus
sustained. The point to which I am now referring was very clearly
illustrated by Helmholtz in a lecture he delivered many years ago on the
origin of the planetary system.
To investigate whether the solar heat can be attributed to chemical
combination, we shall assume for the moment that the sun is composed of
those particular materials which would produce the utmost quantity of
heat for a given weight; in other words, that the sun is formed of
hydrogen and oxygen in quantities having the same ratio as that in which
they should be united to form water. The quantity of heat generated by
the union of known weights of oxygen and hydrogen has been ascertained,
by experiments in the laboratory, to exceed that which can be generated
by corresponding weights of any other materials. We can calculate how
much of the sun’s mass, if thus constituted, would have to enter into
combination every hour in order to generate as much heat as the hourly
radiation of the sun. We need not here perform the actual calculation,
but merely state the result, which is a very remarkable one. It shows
that the heat arising from the supposed chemical action would not
suffice to sustain the radiation of the sun at its present rate for more
than 3,000 years. Thirty centuries is a long time, no doubt, yet still
we must remember that it is no more than a part even of the period known
to human history. If, indeed, it had been by combustion that the sun’s
heat was produced, then from the beginning of the sun’s career as a
luminous object to its final extinction and death could not be longer
than 3,000 years, if we assumed that its radiation was to be uniformly
that which it now dispenses.
But it may be said that we are dealing only with elements known to us
and with which terrestrial chemists are familiar, and it may be urged
that the sun possibly contains materials whose chemical union produces
heat in much greater abundance than do the elements with which alone we
are acquainted. But this argument cannot be sustained. One of the most
important discoveries of the last century, the discovery which perhaps
more than any other has tended to place the nebular theory in an
impregnable position, is that which tells us that the elements of which
the sun is composed are the same as the elements of which our earth is
made. We shall have to refer to this in detail in a later chapter. We
now only make this passing reference to it in order to dismiss the
notion that there can be unknown substances in the sun whose heat of
combustion would be sufficiently great to offer an explanation of the
extraordinary abundance of solar radiation.
There is nothing more characteristic of the physical science of the
century just closed than the famous discovery of the numerical relation
which exists between heat and energy. We are indebted to the life-long
labours of Joule, followed by those of many other investigators, for the
accurate determination of the fundamental constant which is known as the
mechanical equivalent of heat. Joule showed that the quantity of heat
which would suffice to raise one pound of water through a single degree
Fahrenheit was the precise equivalent of the quantity of energy which
would suffice to raise 772 pounds through a height of one foot. It would
be hard to say whether this remarkable principle has had a more profound
effect on practical engineering or on the course of physical science. In
practical engineering, the knowledge of the mechanical equivalent of
heat will show the engineer the utmost amount of work that could by any
conceivable apparatus be extracted from the heat potentially contained
in a ton of coal. In the study of astronomy the application of the same
principle will suffice to explain how the sun’s heat has been sustained
for illimitable ages.
[Illustration: Fig. 16.—BROOKS’ COMET AND METEOR TRAIL.
(November 13th, 1893. Exposure 2 hours.)
(_Photographed by Professor E. E. Barnard._)]
It will be convenient to commence with a little calculation, which will
provide us with a result very instructive when considering celestial
phenomena in connection with energy. We have seen that the unit of
heat—for so we term the quantity of heat necessary to raise a pound of
water one degree—will suffice, when transformed into mechanical energy,
to raise 772 pounds through a single foot. This would, of course, be
precisely the same thing as to raise one pound through 772 feet. Suppose
a pound weight were carried up 772 feet high and were then allowed to
drop. The pound weight would gradually gather speed in its descent, and,
at the moment when it was just reaching the earth, would be moving with
a speed of about 224 feet a second. We may observe that the work which
was done in raising the body to this height has been entirely expended
in giving the body this particular velocity. A weight of one pound,
moving with a speed of 224 feet a second, will therefore contain, in
virtue of that motion, a quantity of energy precisely equivalent to the
unit of heat.
It is a well-known principle in mechanics that if a body be dropped from
any height, the velocity with which it would reach the ground is just
the velocity with which the body should be projected upwards from the
ground in order to re-ascend to the height from which it fell (the
resistance of the air is here overlooked as not having any bearing upon
the present argument). Thus we see that a weight, moving with a velocity
of 224 feet per second, contains within itself, in virtue of its motion,
energy adequate to make it ascend against gravity to the height of 772
feet. That is to say, this velocity in a body of a pound weight can do
for the body precisely what the unit of heat can do for it; hence we say
that in virtue of its movement the body contains a quantity of energy
equal to the energy in the unit of heat.
Let us now carry our calculation a little further. If a pound of good
coal be burned with a sufficient supply of oxygen, and if every
precaution be taken so that no portion of the heat be wasted, it can be
shown that the combustion of the coal is sufficient to produce 14,000
units of heat. In other words, the burning of one pound of coal ought to
be able to raise 14,000 pounds of water one degree, or 140 pounds of
water a hundred degrees, or 70 pounds of water two hundred degrees. I do
not mean to say that efficiency like this will be attained in the actual
circumstances of the combustion of coal in the fireplace. A pound of
coal does, no doubt, contain sufficient heat to boil seven gallons of
water; but it cannot be made to effect this, because the fireplace
wastes in the most extravagant manner the heat which the coal produces,
so that no more than a small fraction of that heat is generally rendered
available. But in the cosmical operations with which we shall be
concerned we consider the full efficiency of the heat; and so we take
for the pound of coal its full theoretical equivalent, namely, 14,000
thermal units. Let us now find the quantity of energy expressed in
foot-pounds[2] to which this will correspond. It is obtained by
multiplying 14,000 units of heat by 772, and we get as the result
10,808,000. That is to say, a pound of good coal, in virtue of the fact
that it is combustible and will give out heat, contains a quantity of
energy which is represented by ten or eleven million foot-pounds.
Footnote 2:
A foot-pound is the amount of energy required to raise a pound weight
through a height of one foot.
We now approach the question in another way. Let us think of a piece of
coal in rapid motion; if the coal weighed a pound, and if it were moving
at 224 feet a second, then the energy it contains in consequence of that
velocity would, as we have seen, correspond to one thermal unit. We
have, however, to suppose that the piece of coal is moving with a speed
much higher than that just stated; and here we should note that the
energy which a moving body possesses, in virtue of its velocity,
increases very rapidly when the speed of that body increases. If the
velocity of a moving body be doubled, the energy that it possesses
increases fourfold. If the velocity of the body be increased tenfold,
then the energy that it possesses will be increased a hundredfold. More
generally, we may say that the energy of a moving body is proportional
to the square of the velocity with which the body is animated. Let us,
then, suppose that the piece of coal, weighing one pound, is moving with
a speed as swift as a shot from the finest piece of artillery, that is
to say, with a speed of 2,240 feet a second; and as this figure is ten
times 224, it shows us that the moving body will then possess, in virtue
of its velocity, the equivalent of one hundred units of heat.
But we have to suppose a motion a good deal more rapid than that
obtained by any artillery; we shall consider a speed rather more than
ten times as fast. It is easy to calculate that if the piece of coal
which weighs a pound is moving at the speed of five miles a second, the
energy that it would possess in consequence of that motion would
approximate to 14,000 thermal units. In other words, we come to the
conclusion that any body moving with a velocity of five miles a second
will possess, in virtue of that velocity, a quantity of energy just
equal to the energy which an equally heavy piece of good coal could
produce if burnt in oxygen, and if every portion of the heat were
utilised.
It is quite true that the speed of five miles a second here supposed
represents a velocity much in excess of any velocity with which we are
acquainted in the course of ordinary experience. It is more than ten
times as fast as the speed of a rifle bullet. But a velocity of five
miles a second is not at all large when we consider the velocities of
celestial bodies. We want this fact relating to the energy in a piece of
coal to be remembered. We shall find it very instructive as our subject
develops, and therefore we give some illustrations with reference to it.
The speed of the earth as it moves round the sun is more than eighteen
miles a second—that is to say, it is three and a half times the critical
speed of five miles. In virtue of this speed the earth has a
corresponding quantity of energy. To find the equivalent of that energy
it must, as already explained, be remembered that the energy of a moving
body is proportional to the square of its velocity; it follows that the
energy of the earth, due to its motion round the sun, must be almost
twelve times as great as the energy of the earth would be if it moved at
the rate of only five miles a second. But, we have already seen that a
body with the velocity of five miles a second would, in virtue of that
motion, be endowed with a quantity of energy equal to that which would
be given out by the perfect combustion of an equal weight of coal. It
follows, therefore, that this earth of ours, solely in consequence of
the fact that it is moving in its orbit round the sun, is endowed with a
quantity of energy twelve times as great as all the energy that would be
given out in the combustion of a mass of coal equal to the earth in
weight. This may seem an astonishing statement; but its truth is
undoubted. If it should happen that the earth came into collision with
another body by which its velocity was stopped, the principle of the
conservation of energy tells us that this energy, which the earth has in
consequence of its motion, must forthwith be transformed, and the form
which it will assume is that of heat. Such a collision would generate as
much heat as could be produced by the combustion of twelve globes of
solid coal, each as heavy as the earth. We may indeed remark that the
coal-seams in our earth’s crust contain, in virtue of the fact that they
partake of the earth’s orbital motion, twelve times as much energy as
will ever be produced by their combustion.
It can hardly be doubted that such collisions as we have here imagined
do occasionally happen in some parts of space. Those remarkable new
stars which from time to time break out derive, in all probability,
their temporary lustre from collisions between bodies which were
previously non-luminous. But we need not go so far as inter-stellar
space for a striking illustration of the transformation of energy into
heat. In the pleasing phenomena of shooting stars our own atmosphere
provides us with beautiful illustrations of the same principle. The
shooting star so happily caught on Professor Barnard’s plate (Fig. 16)
may be cited as an example.
------------------------------------------------------------------------