In the last two sentences we state, in one way, the second law of thermodynamics—in some respects the most fundamental result of our experience in the physical investigation of the universe. In its most technical form, as enunciated by Clausius, this law states that the value of a certain mathematical function, called entropy,[8] tends continually towards a maximum, when it is applied to the universe as a whole. When we say the “universe,” we mean all that comes within our power of physical investigation. Let us now see what this statement means.

The energy of the solar system is in part the kinetic energy of those parts of it which are in motion—planets, planetesimals,[9] and satellites. This quantity of energy is enormously great. In the case of our earth it is  1/2(mv2), m being the mass of the earth, and v its velocity. Translated into numerical symbols we find this quantity almost inconceivable. The greater part of this energy is unavailable, that is, it can undergo no transformations. But because the earth is in rotation at the same time as it revolves round the sun, and because the moon revolves round the earth, there are tides in the watery and atmospheric envelopes of the earth. The energy of the tides is the kinetic energy of water or air in motion, and we can employ this energy in the production of transformations, and it is therefore available. But well-known investigations have shown that the tides produce friction, and that the period of rotation of the earth is slowly becoming greater. Ultimately the earth will rotate on its own axis in the same time that it revolves round the sun—then a year and day will be of the same length. When that occurs, the sun, earth, and moon will be in equilibrium, and tidal phenomena due to the sun will cease. The kinetic energy of the earth, rotating once in 24 hours is obviously greater than its kinetic energy when rotating in the period which will then be its year. What has become of the balance? It has been transformed into the mechanical friction of the tides against the surface of the earth,[10] and this friction has been transformed into low-temperature heat, and this heat has been radiated off into space.

The solar system also contains energy in the form of the heated sun and planets, and in the form of chemical potential energy of the substances of which those bodies are composed. Let us think of the system, sun and earth. The sun contains enormous heat energy, its temperature being some 6000° C. absolute.[11] It contains enormous chemical energy in the shape of compounds existing beneath its outer envelopes, and it contains energy in the form of its own gravity—its contraction together produces heat. But this heat is being continually radiated away: chemical reactions must occur in which the potential chemical energy of its substances must become transformed into heat, and this heat is also radiated away; contraction of its mass must occur up to a point when the materials are as closely packed together as possible; heat is developed during the contraction, and this also passes away by radiation. Suppose that modern speculations are well founded and that radio-active substances are present in the sun: in the atomic disintegration of these substances heat is produced and again radiated. Therefore in whatever form energy exists in the sun, it transforms into heat and this radiates. The ultimate fate of the sun is to cool down and solidify. It will then move through space as a body having a cool, solid crust, and an intensely heated interior. Slowly, very slowly, this heated interior will cool down by the conduction of its heat from the core to the outer shell, and by the radiation of this heat from the shell into space. For incredibly long periods radio-active substances in the interior must generate heat, but even this process must reach an end.

The energy received by the earth is that of solar and stellar radiation. Stellar radiation is minute, the absolute temperature of cosmic space (or ether) being about −263° C. The absolute temperature of the earth is about +17° C., so that it radiates off more heat into space (other than that represented by the sun) than it receives. All energy-transformations on the earth (except tidal effects, and energy-conduction from the heated core, and possibly radio-active effects) are transformations of this solar energy received by radiation. We see these in oceanic and atmospheric circulations (currents, winds, rainfall, etc.). We see them also in the transformations of the chemical potential energy of coal and other products of life—products in which the contained potential energy has been absorbed from solar radiation.

Let us follow the transformations of this energy. Oceanic currents transport heat from the equatorial sea-areas to the colder temperate and polar areas, and compensatory polar currents flow towards the equator, absorbing heat from the waters of temperate and equatorial areas. Winds act in an analogous way. Water is evaporated where the solar radiation is intense, and heat is absorbed in the transformation of water into aqueous vapour. Then this water vapour is transported in the winds into regions where it becomes condensed and precipitated as rain or snow, heat being emitted in this condensation. In all these movements there is friction, and this friction transforms to heat. In all the effect is the general distribution over the earth of the heat which the equatorial regions receive in excess of that which the polar regions receive. Other mechanical effects are also produced by oceanic and atmospheric circulations—the denudation of the coasts by tides and storms, the erosion of the land by rivers, rains, snow, and ice, the transport of dust in winds, etc. In all these friction is produced, and this friction passes into heat.

The potential chemical energy which results from absorption of solar radiation by plants is principally accumulated as coal. Apart from the interference of man, this coal would slowly accumulate, perhaps it would more slowly disappear by bacterial action, or by physical transformations. In these transformations the energy of the coal would become heat energy and the potential energy of the gas produced by bacterial activity. By man’s agency the coal suffers other transformations, and in the present phase of civilisation it is his chief source of energy. It is available for doing work of many kinds, and in all these forms of work it becomes transformed by chemical action (burning) into high temperature heat.

We can cause this potential energy of coal to transform into mechanical energy of machines, vehicles, and ships in motion by causing it to pass into heat. In the steam-engine, or gas-engine, a highly heated gas (steam, or the mixture resulting from the explosion of coal gas and air in the cylinder of the engine) expands and propels a piston or rotates a turbine. (Obviously in the petrol engine the same essential process takes place.) We employ this kinetic energy directly in transport, or we cause it to undergo other transformations. In the dynamo, kinetic energy of machinery in motion transforms to electrical energy; and this may transform to radiant energy (light, heat in electric radiators, wireless telegraphy radiations), or it may transform to chemical energy (the manufacture of carborundum in the electric furnace, for instance), or it may transform again to the kinetic energy of bodies in motion (electric traction). In innumerable ways the human power of direction causes transformation of this accumulated potential energy, and the reader will notice the analogy of all this with the essential, unconsciously expressed activity of the animal organism in its own metabolism—a point to which we return later.

Notice now that all the energy-transformations we have noticed are irreversible. This is a matter of deep philosophical importance, and we must devote some time to it. Consider first of all the working of the steam-engine; what occurs is this—coal is burned in the boiler-furnace, that is to say, potential chemical energy passes into heat and this vaporises water in the boiler, producing a gas at high temperature (steam). This gas expands in the high-pressure cylinder of the engine, driving forward a piston; it expands further in the intermediate cylinder, propelling its piston also, and again in the low-pressure cylinder. It is then cooled by passing through the condenser, and in the contraction further mechanical energy is obtained. The train of events thus begins with a gas at a high temperature and ends with the same gas at the temperature of the water in the condenser. The heat lost is transformed into the mechanical energy of the engine. But not all of it. A certain quantity is lost by radiation from the boiler walls, the walls of the steam-pipes, the cylinders, and other parts of the engine; also some of the energy is transformed to friction, and this again to heat. In this way a very considerable part of the energy contained in the coal is frittered away in unavoidable heat-conduction and radiation, and a last residue of it goes down the drain, so to speak, with the condenser water. This loss is inherent in the nature of the mechanism of the engine.