The processes and variation of the physical parameters, inside a constant area equilibrium MHD generator, are examined and modelled. A one dimensional model is derived, which assumes uniform properties over the generator cross sectional area and allows for variations of velocity, pressure, temperature, density, electric field, current density and electrical conductivity in the direction of the flow. The plasma composition is determined by particle balance equations which include collisional, radiative, diffusion and flow processes. This comprehensive model should result in an accurate description of the processes inside a MHD generator and allow for a better interpretation of experimental results. An example of a linear constant area segmented electrode generator operating in the Faraday mode with a gaseous mixture of Helium seeded with a few percent Cesium, is presented in this study. The calculations for typical MHD generator values of velocity U=1000 m/s, pressure p=2 atm, temperature T=2000 K, seed fraction ε=0.005, magnetic field strength B=3.5 T, load factor KF=0.75 and generator length L=2 m with a cross sectional area A=1x1 m2 show large deviations of predicted performance between the Particle Balance and Saha-Boltzmann models.