The second law of thermodynamics deals with changes in the free energy of a system. A system only possesses "free energy" when it is capable of doing work. It is only capable of doing work if it will change spontaneously into another system of greater stability. Only an unstable system has free energy. A stable system can be changed into an unstable system by the performance of work, or by the transference of free energy from another system. The whole of life, and of civilization as we know it, depends on thermodynamic instability ; as Boltzmann (1886) put it, the struggle for existence is a struggle for free energy available for work. Nearly all manufacturing processes depend essentially on using the free energy stored in coal to convert a useless stable system into a useful unstable system. For instance, the synthetic manufacture of fertilizers depends essentially on the use of a small part of the free energy available when coal is burnt, to convert the stable system nitrogen+ water, into the unstable system ammonia+oxygen. The ammonia in various forms can be made use of to fertilize plants, i.e., to in crease the free energy in the plant world which the animal world can convert again into useful work. The enormous amount of energy which the earth continuously receives from the sun is theoretically almost completely available for useful work, for the energy jeaves the sun at a temperature over 8,000° and is finally dissipated into space at a temperature of about 300° Ab solute. Calculation shows that the energy so received is at least a million times greater than the energy given by the world's power plants. But unfortunately we know of no means for making use of anything more than a minute fraction of the sun's energy. A very small part of it is converted into mechanical energy by water power plants ; another very small part is used by the plant world to build up "unstable" organic compounds, and thus to supply the free energy available in food. One of the chief tasks of the scientist of the future will be to devise means for con verting into useful work, or storing, a greater part of the energy received from the sun. The second law shows that this should be possible. If he does not succeed the advance, and even the maintenance, of civilization may be impossible when the energy stored in coal through the agency of the plant world in past ages is exhausted.
It has already been pointed out that although the Gibbs—Helmholtz equation enables us to calculate from purely thermal data the change in any equilibrium with the temperature, it does not give any informa tion on the actual value of the equilibrium constant unless this is already known from experimental observations under one set of conditions. To obtain the actual value from purely thermal
data, it is necessary to integrate the fundamental equation d
and integration introduces an unknown integration constant.
In 1901 Nernst advanced a method of evaluating this constant, and his theorem is often referred to as the "third law" of thermo dynamics, although its universal applicability is still open to some doubt.
In Condensed Systems.—Nernst postulates that in the case of chemical reactions in condensed systems, i.e., reactions in solids or between solids and liquids, not only does A become =U at absolute zero (T= o), as is required by the Gibbs-Helmholtz equation, but that they both reach their final (equal) value at temperatures not far removed from the absolute zero. In mathe matical language, dA/dT=dU /dT =o when T=o. Now dU /dT is equal to the difference between the sum of the molecular heat capacities
of the reacting substances and of the products. Since it is found by experiment that the specific heats of sub stances can be expressed with sufficient accuracy by equations of the form
etc. it follows that U can also be expressed in the form of heptane formed at atmospheric pressure will be quite negligible. All the higher liquid hydrocarbons, such as occur in natural petroleum oil, are thermodynamically unstable at ordinary tem peratures. They tend to pass into carbon and methane, but the velocity of this reaction at ordinary temperatures is very slow. If they are heated, however, they are "cracked"; hydrocarbons of lower boiling point, such as occur in petrol, are formed, and coke and gas are formed at the same time. If the cracking is continued for a long time at atmospheric pressure, the whole liquid forms into coke and gas (mainly methane). But high pres sure tends to prevent the formation of gas and coke, and to give therefore a higher yield of "petrol." This is in complete general agreement with the Nernst equation, which enables us to predict approximately the conditions for the best technical success.
The further development of the third law, and its quantitative application to chemical problems depends on the provision of accurate data on the specific heats of substances over a wide range of temperature. The increase in the specific heat of gases as the temperature is raised lacks at present any sound theoretical explanation. The classical kinetic theory of gases does not account for it, and the more recent developments of the quan tum theory have hitherto failed to be of assistance. But there can be little doubt that the third law provides in principle a complete explanation of the connection between chemical equili bria and the thermal changes associated with chemical reactions.
(H. T. T.)