Treatise on Thermodynamics by Max Planck

Author:Max Planck
Language: eng
Format: epub, pdf
Publisher: Dover Publications
Published: 1969-06-20T16:00:00+00:00

CHAPTER II.

SYSTEM IN DIFFERENT STATES OF AGGREGATION.

§ 165. WE shall discuss in this chapter the equilibrium of a system which may consist of solid, liquid, and gaseous portions. We assume that the state of each of these portions is fully determined by mass, temperature, and volume; or, in other words, that the system is formed of but one independent constituent (§ 198). For this it is not necessary that any portion of the system should be chemically homogeneous. Indeed, the question with’regard to the chemical homogeneity cannot, in general, be completely answered (§ 92). It is still very uncertain whether the molecules of liquid water are the same as those of ice. In fact, the anomalous properties of water in the neighbourhood of its freezing-point make it probable that even in the liquid state its molecules are of different kinds. The decision of such questions has no bearing on the investigations of this chapter. The system may even consist of a mixture of substances in any proportion; that is, it may be a solution or an alloy. What we assume is only this : that the state of each of its homogeneous portions is quite definite when the temperature T and the specific volume υ are definitely given, and that, if the system consists of different substances, their proportion is the same in all portions of the system. We may now enunciate our problem in the following manner :—

Let us imagine a substance of given total mass, M, enclosed in a receptacle of volume, V, and the energy, U, added to it by heat-conduction. If the system be now isolated and left to itself, M, V, and U will remain constant, while the entropy, Φ, will increase. We shall now investigate the state or states of equilibrium which the system may assume, finding at the same time the conditions of its stability or instability. This investigation may be completely carried through by means of the proposition expressed in equation (77), that of all the states that may adiabatically arise from one another, the most stable state of equilibrium is characterized by an absolute maximum of the entropy. The entropy may in general, however, as we shall see, assume several relative maxima, under the given external conditions. Each maximum, which is not the absolute one, will correspond to a more or less unstable equilibrium. The system in a state of this kind (e.g. as supersaturated vapour) may occasionally, upon appropriate, very slight disturbances, undergo a finite change, and pass into another state of equilibrium, which necessarily corresponds to a greater value of the entropy.

§ 166. We have now to find, first of all, the states in which the entropy Φ becomes a maximum. The most general assumption regarding the state of the system is that it consists of a solid, a liquid, and a gaseous portion. Denoting the masses of these portions by M1, M2, M3, but leaving open, for the present, the question as to which particular portion each suffix refers, we have for the entire mass of the system

M1 + M2 + M3 = M.

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