A new and sensitive differential drop solution calorimetric technique was developed for very small samples. A single experiment using one 5.18-milligram sample of perovskite, synthesized at 25 gigapascals and 1873 Kelvin, gave 110.1 +/- 4.1 kilojoules per mole for the enthalpy of the ilmenite-pervoskite transition in MgSiO(3). The thermodynamics of the reaction of MgSiO(3) (ilmenite) to MgSiO(3) (perovskite) and of Mg(2)SiO(4) (spinel) to MgSiO(3) (pervoskite) and MgO (periclase) were assessed. Despite uncertainties in heat capacity and molar volume at high pressure and temperature, both reactions clearly have negative pressure-temperature slopes, -0.005 +/- 0.002 and -0.004 +/- 0.002 gigapascals per Kelvin, respectively. The latter may be insufficiently negative to preclude whole-mantle convection.