Phase equilibria in the system Tm-Rh-O at 1200 K is established by isothermal equilibration of selected compositions and phase identification after quenching to room temperature. Six intermetallic phases (Tm3Rh, Tm7Rh3, Tm5Rh3, Tm3Rh2, TmRh, TmRh2 +/-delta) and a ternary oxide TmRhO3 are identified. Based on experimentally determined phase relations, a solid-state electrochemical cell is devised to measure the standard free energy of formation of orthorhombic perovskite TmRhO3 from cubic Tm2O3 and beta-Rh2O3 in the temperature range from (900 to 1300) K. The results can be summarized as: Delta G(f,ox)(o) +/- 104/J.mol(-1) = -46474 + 3.925(T/K). Invoking the Neumann-Kopp rule, the standard enthalpy of formation of TmRhO3 from its constituent elements at 298.15 K is estimated as -1193.89 (+/- 2.86) kJ.mol(-1). The standard entropy of TmRhO3 at 298.15 K is evaluated as 103.8 (+/- 1.6) J.mol(-1).K-1. The oxygen potential-composition diagram and three-dimensional chemical potential diagram at 1200 K and temperature-composition diagrams at constant partial pressures of oxygen are computed from thermodynamic data. The compound TmRhO3 decomposes at 1688 (+/- 2) K in pure oxygen and at 1583 (+/- 2) K in air at standard pressure.