italia:
I'm not sure any of us really have a good idea of what is happening or else we would have this solved by now!
Engineers and meteorologists
have solved this. There is a variation in density (even for a given MAP), back pressure and throttle losses all going on. The principles are well described. You had the density bit right to begin with, it's just that you hadn't considered the other two things at that stage.
The standard lapse rate is based on that ideal gas law and that's what ft showed.
No. What ft showed was that if you take pressure and density from sea level and apply the ISA derived correction for a given altitude (which accounts for gravity, radiation, convection, humidity etc), when you put them back into the gas law, lo and behold you can get the ISA correction for temperature at that altitude!
As I said before: the environmental lapse rate and the inlet tract are different processes that exchange energy with their surroundings at a different rate. It doesn't matter whether you use standard conditions or real time conditions.