Since is a function of the temperatures of the two tanks alone, it is possible to give such numbers to the temperatures of these tanks as will be independent of the working substance (i.e. thermometric substance). Kelvin—then William Thomson—suggested that the numbers T, and T, he so chosen for the temperatures of Qt = the tanks that — = In this case '1' — 0 2 Qq-Q, w t2 , - - - and is therefore independent of every thing thing except the temperatures; T,— T. may he T, chosen to have any arbitrary value; is fixed by tile above definition as depending upon mak ing the thermometric substance pass around a Carnot's cycle; and then T, and arc obtained.
It is found by direct experiment that if T, — T, is chosen as 100 for two tanks of melting ice and boiling water, the numbers on 'Thomson's absolute scale' are almost exactly the same as obtained in a gas thermometer using the 'abso lute centigrade scale.' See THERMOMETRY.
Since the efficiency increases as T, becomes smaller, and since the efficiency cannot be greater than unity, there must he a minimum temperature in the universe. This is known as the 'absolute zero ;' its value is about 273' C., as shown by the agreement between the two 'absolute scales' just described.
Carnot stated further that the efficiency of an irreversible process could not be greater than that of a. reversible one with the two limiting
temperatures of the tanks; and Clausius proved that this is true if the second principle of thermodynamics is true.
It is generally accepted that the efficiency of an irreversible process is less than that of a re versible one between the same two temperatures, but it cannot he regarded as a deduction from the two principles of thermodynamics. All pro cesses in nature—chemical, electrical, etc.—are irreversible; and a natural system will therefore be in equilibrium if all imaginable processes compatible with the existing conditions necessa rily involve an efficiency equal to or greater than that which corresponds to a reversible process.
This general idea forms the basis of the modern development, of thermodynamics by Gibbs, Planck, and others.
BIBLIOGRAPHY. Buckingham, Theory of Tht rBibliography. Buckingham, Theory of Tht r- modynamies (New York, 1900) ; Gibbs, "Equilib rium of Heterogeneous Substances," in Trans actions of the Connecticut Academy of Sci ences, vols. ii. and iii.: Mach, Die Prineipicn der Weirmelehre (Leipzig, 1896) ; Planck, Ther modynamik (ib., ; Magie, The Second Prin-riplc of Thermodynamics, Scientific Memoir Series, vol. vi. (New York, 1899) : Ames, The Free Expansion of Gases, Scientific Memoir Series, vol. i. (ib., 1898).