Temperatue and Presssure after volume change

AI Thread Summary
To determine the new temperature T2 and pressure P2 after increasing the volume of a sealed syringe from V1 to V2, the ideal gas law can be applied: (P1*V1)/T1 = (P2*V2)/T2. Additionally, the relationship for a polytropic process is useful, given by P1 / P2 = (V2 / V1)^n, where n is the polytropic index, typically 1.4 for air under isentropic conditions. Since the volume change is rapid, it can be assumed that heat transfer is negligible. By combining these equations, one can estimate the values of P2 and T2. This approach provides a practical solution for real-life applications without requiring high precision.
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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).
 
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