A calclation method is that of the "method of characteristics". Boundary conditions have to be known.
1. How fast does the valve open and what are its flow characteristics.
2. What is at the upstream or inlet to the valve? ie. dead ended? a reservoir as a source?
3. Initial temperature of the air?
See a text such as The Dynamics and Thermodynamics of Compressible Fluid Flow--Ascher Shapiro.
Regards