trying to iterate within a piecewise function

I am trying to iterate within a piecewise function. Specifically, I have a model for the heat release of an engine, and the second range of pressures is found through iteration. I know the initial condition. On the attached worksheet, the variable 'P_q' is the one that is found via iteration, i.e. P_q,new = f(P_q,old, etc.).

Thank you in advance for any assistance with correcting the logic in my attempt.