Ok, I wasn't thinking of why it heats up as it leaves the turbo, I was thinking more along the lines of why would an air with a certain volume and temperature increase in temp as the pressure went up with volume and amount remaining the same. The turbo explanation is another mess.
I'm glad no one called me on my previous examples because they are just plain wrong.
Back to my assumption. The IGL is basically saying that you can change pressure of an ideal gas in three ways, changing volume, temperature or amount . Now as far as I'm concerned there is no such thing as an ideal gas, it was made up to allow for analysis, kinda like the normal force. The IGL is also assuming these changes take place in a controlled box where you have complete control of the inputs and outputs, another analysis "trick". Note, what they teach you as an engineer only exists in school.
Now I'm thinking that in a fixed volume, with a certain amount of air, the only way to increase pressure would be through heat, so that is why temp would increase. Now if you don't use this "ideal gas" then the equations is meaningless and you get something that doesn't explain so simple.
Does "air" react similarly, based upon the observation with my paintball tank, I'm inclined to believe so. Back to the paintball tank example. If my tank has 1000 psi, and it gets filled to 4500 psi, additional air is being added creating the pressure increase. I'm thinking as that 4500 psi air is added, it is increasing the pressure of the existing air in the tank creating that warm tank effect. The heat is prob also due to the velocity of the incoming air. Now once the tank has cooled down, the pressure is no longer what it was when it was filled, only a hundred or so psi, but it has dropped. Now my tank doesn't leak, and it is off usually when I get the first fill of the day, so I'm thinking that the ideal gas law applies to this particular situation, although I introduced velocity for a heat source.
Ok, I think I just had to explain what I was thinking to myself more than anything. Sorry for the long post.