Temperature of Air escaping from tire

I have been trying to understand how to calculate the temperature of the air escaping from a blown up tire. I know its adiabatic cooling - but is it as simple as PV = nRT?
Thanks
 Recognitions: Gold Member Science Advisor Staff Emeritus An adiabatic expansion goes as: $$T_i V_i^{\gamma-1} = T_f V_f^{\gamma-1}$$ where $\gamma \equiv C_p/C_v$. - Warren
 In your equation 1. the i state (T, V) is the state of the air initally, in the tire. I have a tire that has a certain volume (Vi) and is at some temperature (Ti) 2. the f state is the final state, air coming out of the tire - I understand Tf - what is Vf since the air is escaping to the great outdoors. Is it the amount of air that is escaping - per unit time????? Why doesnt velocity of air come into equation size of nozzle Under expansion, such as though a JT valve, cant I expand air such that in some cases it gives me a decrease in temperature, and in some cases an increase in temperature - something called an inversion line. THANKS

Recognitions:
Gold Member