If you take a look in "Thermodynamics: An Engineering Approach", 5th edition by Yunus A. Çengel and Michael A. Boles a very interesting hanbook in thermodynamic you will find your need and more.
In short the specifics heats Cp & Cv of a gas mixture are not that given by the sum of specifics heats of the individual gases. They are equal to the sum of (mass fraction x heat specific) related to individual gas.
The specific heat of mixture contains also the part, connected with interaction of molecules. At high densities and low temperatures this part may be large enough to influence the resulting heat capacity.
Thank you, Wilfried, for reasonable words! Now there are many dogmatic followers of simplified concepts in Thermal Physics. The Nature is more complex than the models used by many of scientists in their simulations.
The following somewhat related discussion ― on Cp/Cv ratio for reacting gases ― may possibly be found interesting by followers of this discussion: https://www.researchgate.net/post/how_can_we_calculate_gamma_specific_heat_ratio_for_real_gas_chemical_non-equili
INTEGRAL OF CP MIXTURE BETWEEN T1 T0 T2 DIVIDED BY T2 MINUS T1 WILL GIVE THE MEAN OF THE SPECIFIC HEAT CAPACITIES OF THE COMPONENTS OF THE MIXTURE , WHERE T1 IS INITIAL TEMPERATURE AND T2 THE FINAL TEMPERATURE. CP MIXTURE = A+BT+CT SQUARE + DT CUBE
WHERE T IS THE TEMPERATURE AND A,B,C,D,E..... THE SPECIFIC HEAT CAPACITY OF EACH COMPONENT OF THE MIXTURE. THE INTEGRATION OF THIS WILL GIVE YOU THE MEAN OR AVERAGE SPECIFIC HEAT CAPACITY OF THE MIXTURE. THANK YOU.