Transformation of full thermodynamic values into pure gas components

Let us note the full thermodynamic values as symbols without indices, as P - pressure, E - internal energy, et al.

The radiative constant is accepted as

And radiative contribution to pressure and internal energy are

Then, pure gas thermodynamic values (denoted with index (nr) - no radiation) are calculated as

Finally, one can get pure gas adiabatic exponent in the form