Thermodynamic origin and graphical methods of phase theory

Abstract

Thermodynamics is often considered difficult to understand due to extensive use of mathematics. In the present paper, a graphical approach will be used to explain the origin of phase diagrams starting from the fundamental equation of thermodynamics dU = Tds − Pdv defined by J.W. Gibbs. The characteristic variables of this equation are the specific entropy s and the specific volume v, which lead in a straightforward way to s-v phase diagrams. It will be demonstrated through monotonicity of the internal energy curves of the different phases of the system and graphical Legendre transformations how pressure-entropy (P-s) and temperature-volume (T-v) phase diagrams are linked to s-v phase diagrams and how the latter two phase diagrams are related to pressure-temperature (P-T) phase diagrams.