A phenomenological thermodynamic theory of PbTiO3 was developed using a modified Devonshire form of the elastic Gibbs free energy. The spontaneous strain as a function of temperature was determined from pure sol-gel derived PbTiO3 powder and used with selected data from the literature to determine the coefficients of the energy function. The theoretical prediction of the phase stability, spontaneous polarization and strains, and dielectric and piezoelectric properties agree well with experimental data. This theory provides a way of predicting the intrinsic single domain dielectric and piezoelectric properties of PbTiO3, which have not been completely determined from experimental measurements.