A model for the temperature dependence of the isobaric heat capacity of associated pure liquids C-p,m(o)(T) is proposed. Taking the ideal gas as a reference state, the residual heat capacity is divided into nonspecific C-p(res,ns) and associational C-p(res,ass) contributions. Statistical mechanics is used to obtain C-p(res,ass) by means of a two-state model. All the experimentally observed C-p,m(o)(T) types of curves in the literature are qualitatively described from the combination of the ideal gas heat capacity C-p(id)(T) and C-p(res,ass)(T). The existence of C-p,m(o)(T) curves with a maximum is predicted and experimentally observed, for the first time, through the measurement of C-p,m(o)(T) for highly sterically hindered alcohols. A detailed quantitative analysis of C-p,m(o)(T) for several series of substances (n-alkanes, linear and branched alcohols, and thiols) is made. All the basic features of C-p,m(o)(T) at atmospheric and high pressures are successfully described, the model parameters being physically meaningful. In particular, the molecular association energies and the C-p(res,ns) values from the proposed model are found to be in agreement with those obtained through quantum mechanical ab initio calculations and the Flory model, respectively. It is concluded that C-p,m(o)(T) is governed by the association energy between molecules, their self-association capability and molecular size. (C) 2004 American Institute of Physics.