Temperatue and Presssure after volume change

[GT1]

I have a sealed syringe with air at known pressure P1, temperature T1 and volume V1. at some time I increase the volume of the syringe to V2, what will be the temperature T2 and pressure P2 at volume V2, right after the system reach to volume V2? The volume change process is relatively fast.

I know I can use the ideal gas law:

(P1*V1)/T1 = (P2*V2)/T2

But I'm still missing one more equation to find P2 and T2.

Any suggestions how it can be done? (It's a real life problem, I don't need a super accurate solution, estimated values are also good).

 

[jack action]

It is also a polytropic process, so:

P1 / P2 = (V2 / V1)ⁿ

Where n is the polytropic index, which is 1.4 for air if the process is isentropic (or one assume there is no heat transfer). You have all the relations derived for you on the isentropic process page of Wikipedia.