A thermodynamic model for solids under pressure is developed by assuming the universal equation of state and that under zero pressure the free energy is equal to the harmonic crystal (Debye) free energy. The model is applied to gold. In the case of nanocrystals this model reproduces the observed enhancement of the isobaric heat capacity and of the thermal expansion. Our model calculations are free of the ambiguities and inconsistencies connected with the Gruneisen equation, which was used in previous theoretical work.