Scientific Papers of J. Willard Gibbs Volume 1; Thermodynamics

This historic book may have numerous typos and missing text. Purchasers can download a free scanned copy of the original book (without typos) from the publisher. Not indexed. Not illustrated. 1906 Excerpt: ...this is sufficient for determining the equilibrium of any given state of the non-homogeneous solid. An equation, therefore, which expresses for any kind of solid, and with reference to any determined state of reference, the relation between the quantities denoted by e, tjT,, „... p, involving also the quantities which express the composition of the body, when that is capable of continuous variation, or any other equation from which the same relations may be deduced, may be called a fundamental equation for that kind of solid. It will be observed that the sense in which this term is here used, is entirely analogous to that in which we have already applied the term to fluids and solids which are subject only to hydrostatic pressure. When the fundamental equation between eT, J?v'. j-y is known, we may obtain by differentiation the values of t, X,... Zv in terms of the former quantities, which will give eleven independent relations between the twenty-one quantities Cv ' 'v' die" ' ' ' Ez" ' "x ' " z' (415) which are all that exist, since ten of these quantities are independent. All these equations may also involve variables which express the composition of the body, when that is capable of continuous variation. If we use the symbol //T to denote the value of i/r (as defined on page 89) for any element of a solid divided by the volume of the element in the state of reference, we shall have T=er--ttiT. (416) The equation (356) may be reduced to the form 8Y=-t,v'St+(xx.S). (417) Therefore, if we know the value of yfrv in terms of the variables ( doc ( i'-rp,...-rp, together with those which express the composition of the body, we may obtain by differentiation the values of Ijt, Xx,,... Zv in terms of the same variables. This will make ele...