Calculating temperature change due to Joule-Thomson effect I have a 10 L compressed argon cylinder with filling pressure of 10 MPa. According to Perry's Chemical Engineer's Handbook, argon's J-T coefficient (unit: K/MPa) is 3.7 at 0.1 MPa, 2.6 at 10 MPa. (Temperature is 300 K.) 

When I open up the cylinder valve, 10 MPa argon in the cylinder will expand into 0.1 MPa atmosphere. So the $\Delta P$ is 9.9 MPa. 


  How much will the temperature change?
  The initial temperature is 300 K.



$9.9 \times 3.7 = 36.63$ 


(Which means the temperature of argon outside the cylinder will be 263.37 K)


$9.9 \times 2.6 = 25.74$
Something in between (like when the J-T coefficient in effect changes continuously as the gas expands).
It is going to be something in between.  The definition of the JT coefficient is $$\mu=\left(\frac{\partial T}{\partial P}\right)_H$$If the temperature-dependence can be neglected, then this gives $$\Delta T=-\int_{0.1}^{10}{\mu(P)dP}$$