Expansion of a Compressible Gas

[El Moriana]

Hi,

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
P₁V₁=P₂V₂ (assuming an isothermic expansion) cannot be used.

Instead, factoring in for compressibility, I get:
P₁V₁Z₁=P₂V₂Z₂ (again assuming isothermic expansion)

I know the cylinder used and expansion chamber and so I know P₁, V₁ and V₂ and can calculate Z₁.

This leaves me with two unknowns - P₂ and Z₂ - but only one equation. How do I get the second equation to solve this?

 

[Andrew Mason]

Hi,

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
P₁V₁=P₂V₂ (assuming an isothermic expansion) cannot be used.

Why not? An ideal gas is a gas and all gases can be compressed.

Instead, factoring in for compressibility, I get:
P₁V₁Z₁=P₂V₂Z₂ (again assuming isothermic expansion)

What is Z supposed to represent?

AM

 

[El Moriana]

Z is a compressibility factor. It is used to account for a gases behavior when it deviates from the ideal gas model (which uses a Z of unity). Essentially, no gas has a Z of exactly 1, but gases such as air come close enough to so as to be approximated as 1.

You were right, however. I was addle-brained at that time and for some reason I visualized the air acting as a liquid, where pressure changes the volume only slightly (why? I will never know.. *sigh*) and saw Z as the way to compensate for that. The solution was simply to assume air as an ideal gas and us the normal ideal gas equation.

Thanks for replying before and apologies for the late reply and the sub-par question. =)