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.
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.
[2]. A foot-pound is the amount of energy required to raise a pound weight through a height of one foot.