| The equation of state is a basic problem of studying in physics. The rapid development of the contemporary natural science and engineering requires knowing the properties and states of the material system .which are produced under hot and dense environment. The simulation of experiment under this kind of environment is unrealistic,so what people did is through various kinds of theoretical calculation, obtaining the macroscopical data of this sort of process.When we study the state equation of hot and dense gas mixture system,firstly we must have known the internal structure of all kinds of atoms that should compose the material. The main difficulty when calculating the electronic structure of hot and dense gas mixture system lies in how to determine the common thermodynamical and chemical environments of each kind of element, also is the temperature, the pressure, the chemical potential ,etc. Here we present an average-atom model to calculate the pressure of mixture. A self-consistent scheme is used to reach the requirements of the same temperature and chemical potential for all kinds of atoms in the mixture,the same electron density at the boundaries between the atoms,and the electrical neutrality within each atomic sphere. The electronic wavefunctions and orbital energies for the bound eletrons are given by the Dirac equation. The average occupation numbers at each orbital of each kind of atom are determined by the Dirac-Fermi distribution. As examples, the pressure of Al, the mixture of Al and Mg, Fe, and the explosive HMX(C4 H8 N8 08) is calculated at some temperatures and densities. We drew the curve graph, which shows how the pressure changes with the temperature and density, and made detailed analysis. The result of calculation indicates, the average-atom model is simple and effective for calculating the pressure of hot and dense mixture, it can give a rational description for some physical effects ,such as shell structure, ionization balance of the electron, etc.
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