The discontinuous changes of volume Delta V-m entropy Delta S-m and heat capacity at constant pressure Delta C-P,C-m at the melting point have been predicted by the Landau theory of phase transition where the Gibbs free energy (P in order state is expressed by Phi = Phi(0) + A eta(2) - C eta(4) + E eta(6), where eta is an order parameter. In this work, A is given by a function that A = k(0) (T - T-0)(m) (P-0-P)(n), where k(0), m, n, T-0, and P-0 are constants. The order parameter eta(min) for the minimum of Phi(min) is related to the volume of solid V-s and is expressed by: (C/A*) (2) eta(4)min - (3/8) (C/A*) (3) eta(6)min = 1 - Delta V-m/Delta V where Delta V= V-s - V-m,V- (s,) Delta V-m = V-m,V-1 - V-m,V-s and A* is the value of A at the melting point. The volume of V-s changes from V-m,V-s to V-m,V-1, where Delta V-m,V- s and Delta V-m,V-1 are volumes of solid and liquid phases at the melting point, respectively. The discontinuous change of thermal pressure coefficient gamma(v) = (AP/AT)(V), thermal expansion (AV/AT)(P) and compressibility -(AV/AP)(T) at the melting point has been calculated. A typical function of Phi for a polymer has been demonstrated as a function of eta and C at the melting transition. (c) 2005 Elsevier B.V. All rights reserved.