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I'm trying to figure out the pressure exerted by a compressible gas (air) after it has expanded out of a cylinder for a simple conceptual design. I'm pretty sure that it's a simple problem, but I'm a little thickheaded atm. Here is my thinking so far:

Due to the compressibility of air, I assume that I cannot use the ideal gas model, hence

P

_{1}V

_{1}=P

_{2}V

_{2}(assuming an isothermic expansion) cannot be used.

Instead, factoring in for compressibility, I get:

P

_{1}V

_{1}Z

_{1}=P

_{2}V

_{2}Z

_{2}(again assuming isothermic expansion)

I know the cylinder used and expansion chamber and so I know P

_{1}, V

_{1}and V

_{2}and can calculate Z

_{1}.

This leaves me with two unknowns - P

_{2}and Z

_{2}- but only one equation. How do I get the second equation to solve this?