The following is a modified van der Waals equation with an improved temperature dependence 

The usual van der Waals one-fluid mixing rules are used with this equation of state. Develop an expression for the mixture constant volume heat capacity of a mixure at elevated pressures in terms of the mixture volume V_mix, the mole fractions, temperature, the equation of state parameters, and each of the pure component ideal gas heat capacities. 

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P = RT V mix a mix VT