Temperature of Air escaping from tire

[agurule]

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

 

[chroot]

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

 

[agurule]

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 doesn't velocity of air come into equation
size of nozzle

Under expansion, such as though a JT valve, can't 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

 

[chroot]

You can easily calculate how much volume the air will occupy once outside the tire (and thus at 1 atm pressure).

- Warren