"Air expanding to ambient pressure turns expansion turbine, is greatly cooled, and drives compressor."
I understand all of that except for the "air expanding to ambient pressure" part.
Ambient means relating to immediate surroundings of something so the pressure can change. I understand that if it decreases in size like at #1 it would get hotter or if it increases in size it would become colder, but how can it be ambient if all the air is expanding to the same size when at #3 the column that the air passes through doesn't change shape to change the pressure?
Basically, how can it be ambient pressure if the column doesn't change size?