This paper gives all the necessary physical equations to determine the composition and the thermodynamic properties in a multitemperature plasma utilizing two different method : the first method is based an Gibbs free energy minimization and the second is based on the resolution of the mass action law. The lowering terms of the ionization potential and thermodynamic properties are given for a multitemperature plasma using the Debye-Huckel approximation. Numerical application is mane to a nitrogen plasma.