This paper is divided into three major sections with the first one introducing the concept of generalized entropy in extended irreversible thermodynamics briefly, that is, the entropy of a non-equilibrium system depend not only on the classical variables but also on the dissipative fluxes, which makes the hyperbolic equation of heat conduction based on the Cattaneo-Vernotte model compatible with the second law of thermodynamics. The second section deals with the hyperbolic heat conduction based on the thermomass model. According to the Einstein's mass-energy relation, the phonon gas in dielectrics can be viewed as a kind of weighty compressible fluid, and the momentum equation of the phonon (thermomass) gas in the dielectrics, which consists of the driving force, inertia and resistance of phonon (thermomass) gas, is just the damped thermal wave equation. In the third section our analyses show that the contribution of the kinetic energy of the phonon gas in the expression of extended entropy based on the thermomass model is identical with that of the heat flux in the expression of generalized entropy in extended irreversible thermodynamics. It implies that the hyperbolic heat conduction based on the thermomass model is compatible with the second law of thermodynamics. (C) 2011 Elsevier Ltd. All rights reserved.