Hakan YORULMUŞ 030070111 WEEK 9 2nd part

4)Primitive surface  (Group: Surface)


no previous answer


(new)-better

The fundamental equation —relating energy, entropy, and volume for a homogeneous phase-corresponds to what he called the primitive surface. It includes all equilibrium states, regardless of their stability. When the system consists of several homogeneous parts, its states form the derived surface. This is constructed by recognizing that "the volume, entropy, and energy of the whole body are equal to the sums of the volumes, entropies, and energies re­spectively of the parts, while the pressure and temperature of the whole are the same as those of each of the parts." In a two-phase system the point representing the compound stale must then lie on the straight line joining the two pure (that is, single-phase) state points which are themselves on the primitive surface. The pressure and temperature are the same at all points on this line. But the direction of the tangent plane at any point of the primitive surface is determined by the pressure and temperature, since we have from equation (4),

Since the line joining the two points on the primitive surface that represent the two phases in equilibrium must lie in the tangent planes at both points, and since those planes are parallel, they must be the same plane. This condition, that there be a common tangent plane for the points representing two phases in equilibrium, is easily expressed analytically in the form where the subscripts 1 and 2 refer to the two phases and where p, t are the common values of pressure and temperature.

(Peter L. Duren,Richard Askey,Uta C. Merzbach, A Century of Mathematics in America,1989,page114)