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In order to determine the pressure rise due to fault arcs in electrical installations, the portion of energy heating the surrounding gas of the fault arc has to be known. The ratio of the portion of energy to the electrical energy, the thermal transfer coefficient, well known in literature as kp-factor, is adopted here. This paper presents a theoretical approach to calculate the thermal transfer coefficient kp and to determine the pressure rise in an electrical installation. It is based on the solution of the fundamental hydro- and thermodynamic conservation equations taking into account melting and evaporation of metals as well as chemical reactions with the surrounding gas of the fault arc. The results for closed arc chambers show that factors such as the kinds of insulating gas and of electrode material, the size of the test vessel, and the gas density considerably influence the thermal transfer coefficient and thus the pressure rise. Furthermore it is demonstrated, with an example of a short-circuit in a compact medium-voltage station with heavy metal evaporation, that the mathematical approach is a reliable tool to assess the development of pressure.