In this work, a non-equilibrium mathematical model for an air inductively coupled plasma torch with a supersonic nozzle is developed without making thermal and chemical equilibrium assumptions. Reaction rate equations are written, and two coupled energy equations are used, one for the calculation of the translational–rotational temperature Thr and one for the calculation of the electro-vibrational temperature Tev. The viscous dissipation is taken into account in the translational–rotational energy equation.The electro-vibrational energy equation also includes the pressure work of the electrons, the Ohmic heating power and the exchange due to elastic collision.Higher order approximations of the Chapman–Enskog method are used to obtain better accuracy for transport properties, taking advantage of the most recent sets of collisions integrals available in the literature. The results obtained are compared with those obtained using a chemical equilibrium model and a one-temperature chemical non-equilibrium model. The influence of the power and the pressure chamber on the chemical and thermal non-equilibrium is investigated.