Expanding gases and temperatures

[xRIEx]

I remember small amounts my GCSE and A-Level physics education, and know roughly that gases cool as they expand. So if compressed air from, say, a 200 bar cylinder vents to atmosphere it's going to get colder. How can I work out how much colder it will get? How about when filling a tyre?

Do I need to use P1.V1/T1 = P2.V2/T2? (Which is about all I can remember from my school days.)

[xRIEx]

It's sounding a bit complicated for me now! I think I'll categorise this as "rocket science without the combustion"

[xRIEx]

Cheers all, I'll get my learning cap on