by Trevor to the weight in a mechanical system. For instance, imagine a frictionless, reversible mechanical system, such as a weight suspended by a cord passing over a pulley, and let this weight by its fall to the ground do a certain amount of work, such as raising a body attached to the other end of the cord. The potential energy of the system is measured by the height of the weight above ground, and when the weight falls, the available energy of the system decreases at each point and moment of the descent, while the unavailable energy undergoes a corresponding increase point for point. On reversing the operation and raising the weight, the available energy of the system is seen to increase while the unavailable energy decreases (i. e., increases in a negative direction). So, in any reversible thermodynamic system, the entropy at any moment is an index, determinant, or coefficient of the relative amount of unavailable energy it possesses. When the temperature in an isolated reversible system is constant, as in jacketed steam, the system is "isothermal" and the entropy may vary at any instant; but if a reversible system be so isolated that no heat can enter or leave the body, the temperature might vary but the entropy would be constant, and such systems, of which we have an approximation in the insulated cylinder of an engine, were called "adiabatic" by Rankine and "isentropic" by Gibbs.
There are no mathematical or ideally reversible systems in existence, although we have natural approximations to them in the motions of the heavenly bodies and in certain chemical reactions, or human approximations in reversible heat engines or reversible electric apparatus; the spontaneous processes of nature are always irreversible, proceeding irrevocably in a definite direction with no negative or reversed dissipation of energy. In spontaneous, irreversible flow of heat from a warmer to a colder body, the entropy or unavailable thermal energy of the system increases inevitably to a maximum. In other words, the entropy of a system is a criterion of its loss of efficiency or available energy during irreversible change, and it follows, in the memorable and aphoristic statement of the first and second laws by Clausius, that, while the energy of the universe is constant, its entropy (or that part of its energy which is unavailable) tends to a maximum and can never decrease:
Die Energie der Welt ist constant,
Die Entropie der Welt strebt einem Maximum zu.
With this important generalization, which is the motto of Gibbs's principal memoir, the first stage of thermodynamics ends. By stating the second law as irreversible increase of entropy in natural processes and by adopting some definite standard of the latter, all exact or scalar relations in thermodynamics can be treated as shown by Rankine, Clausius, and Gibbs, in a precise and definite manner. But the
- Maxwell and Tait originally used the term "entropy" as a synonym of