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Can one cool air using the Joule-Thomson effect?  I have 250 cfm of 6 bar air at 35 ⁰C.  Can I release this pressure in a throttle and cool this air by using the Joule-Thomson effect?

To say that you're going to "cool air using the Joule-Thomson effect" sounds a bit funny.  The Joule-Thomson effect is more of an observation of cooling by adiabatic expansion.  You sure can cool air at 35 ⁰C and 6 bar by releasing the pressure, that much is certain.  I'm sure that you're interested in finding out what the new temperature will be for a given pressure.  You could start by estimating the solution by using Boyle's Law (I think?) which states that P1/T1 = P2/T2.  This relation will give you an estimate only because it assumes that the gas is "ideal" which means that the molecular collisions are perfectly elastic.  This of course is seldom the case, especially at higher pressures like you have here.  You should really use what is called an "Equation of State" or an EOS.  There are many of them.  Try looking up the Peng-Robinson equation or the Redlich-Wong equation.  Another option that can be used is a compressibility factor with the ideal gas law.  The compressibility factor helps bring a sense of reality to the equation PV=znRT which I'm sure you're familiar with.  So, you can use an EOS or the Ideal Gas Law with the compressibility factor to find out what the temperature of air will be at a given pressure.