THE LE CHATELIER-BRAUN PRINCIPLE.
[Transactions of the Chemical Society, Vol. cxi. pp. 250—252, 1917.]
IN a paper with the above title, Ehrenfest (Zeitsch. pliysikal. Chem. 1911, 77, 2) has shown that, as usually formulated, the principle is entirely ambiguous, and that nothing definite can be stated without a discrimination among the parameters by which the condition of a system may be defined. The typical example is that of a gas, the expansions and contractions of which may be either (a) isothermal or (/3) adiabatic, and the question is a comparison of the contractions in the two cases due to an increment of pressure Bp. It is known, of course, that if Bp be given, the contraction | Bv \ is less in case (/9) than in case (a). The response of the system is said to be less in case (/3), where the temperature changes spontaneously. But we need not go far to encounter an ambiguity. For if we regard 8v as given instead of Bp, the effect Bp is now greater in (/3) than in (a). Why are we to choose the one rather than the other as the independent variable?
When we attempt to answer this question, we are led to recognise that the treatment should commence with purely mechanical systems. The equilibrium of such a system depends on the potential energy function, and the investigation of its character presents no difficulty. Afterwards we may endeavour to extend our results to systems dependent on other, for example, therrnodynamic, potentials.
As regards mechanical systems, the question may be defined as relating to the operation of constraints. A general treatment (Phil. May. 1875, [iv], Vol. XLIX. p. 218; Scientific Papers, Vol. I. p. 235 : also Theory of Sound, § 75) shows that "the introduction of a consbraint has the effect of diminishing the potential energy of deformation of a system acted, on by given forces; and the amount of the diminution is the potential energy of the difference of the deformations.
" For an example take the case of a horizontal rod clamped at one end and free at the other, from which a weight may be suspended at the point Q. If a constraint is applied holding a point P of the rod in its place (for example, by a support situated under it), the potential energy of the bending. The only mention of it that I know is a casual one in Threlfall's Laboratory Arts. In an experiment tried some years ago, a glass plate was coated thickly with a warm solution of gelatine and allowed to dry on a levelling stand. Nothing particular happened afterwards for days or weeks; but eventually parts of the gelatine film lifted, carrying up with them material torn away from the glass. The plate is still in my possession, and there is now but little of the original glass surface left. If the process is in regular use, I should much like to know the precise procedure. It seems rather mysterious that a film of gelatine, scarcely thicker than thick paper, should be able to tear out fragments of-solid glass, but there is no doubt of the fact.