I am trying to understand what will happen to the temperature under these conditions (starting temp T1 = 273K). I compress 1 atm air adiabatically to 200 atm. Using the formula T2/T1 = (P2/P1)^([g-1]/g) where g = 1.4 for air I get a temperature of about 1240 K. Is this correct? Now if I "heated" the air so the pressure went up to 200 atm, would the temperature be 273*200K? That is very hot. I'm now using the formula P1/T1 = P2/T2. This seems too hot, but is this right? Finally, for the question at the top, if I take the adiabatically compressed air and let the temperature fall to 273K, would I use the P1/T1 = P2/T2 formula? This seems to give a pressure of 44 atm. Is my reasoning correct?