The Equation of State relates thermodynamic properties of pressure, temperature, and density, and provides relations for the internal energy. For a gas-phase mixture, Ansys Forte supports two types of Equations of State, the ideal gas law and the real gas model.

The ideal gas law is the simplest and most widely used Equation of State. To apply the ideal gas law, the mixing of gas components is assumed to follow the Dalton model, that is, each component behaves as an ideal gas as if it were alone at the temperature and the volume of the mixture,

(2–7)

where is the universal gas constant, and is the molecular weight of species .

For an ideal gas, the internal energy is only a function of temperature. The specific internal energy of the gas mixture () is a mass-average of the specific internal energy of individual components (), which are tabulated with respect to temperature:

(2–8)

The real-gas model can more accurately predict thermodynamic property relations at a much wider range of pressures and temperatures. Forte implements the Peng-Robinson Equation of State, which writes the pressure-temperature-volume relation as:

(2–9)

in which  is the molar specific volume of the mixture (). The parameters  and  are computed based on the Van der Waals mixing rule:  

(2–10)

where the parameters for component ,  and are computed as:

(2–11)

in which  is the critical temperature,  is the critical pressure,  is the reduced temperature,  is a function of the accentric factor .

For a real gas, the specific internal energy is function of temperature and one more independent variable, the molar specific volume (). It is calculated as:

(2–12)

In which  is the mixture’s molecular weight, is the specific internal energy at the reference ideal state, calculated by in Equation 2–8 .