4. (25 points) It can be shown that for a van der Waals gas, the Joule-Thompson

Question

4. (25 points) It can be shown that for a van der Waals gas, the Joule-Thompson coefficient is given by: Mujt = (2a/RT - b)/Cp For neon gas, the van der Waals constants are: a = 0.211 atm-1^2/mole^2 and b 0.0171 I/mole and Cp = 5/2 R. a) Find the Joule-Thompson inversion temperature for Ne. b) Sketch the graph Mujt(T) for a large range of T. c) In the limit of very large T., estimate the change in T for a pressure decrease of 100 atm. d) In the limit of very low T (let the initial temperature be T1 = 20K), estimate the change M T for a pressure decrease of 1 atm. (hint: in this limit you must integrate Mujt(T)).

Explanation / Answer

a) JT inversion temperature can be determined by setting 2a/RT -b = 0, This is where the reversal of sign happens.

Therefore, Tc = 2a/Rb = 2*0.211/0.0171*0.0821 = 300.6 K

b) please refer the image

c) at very large T, the term 2a/RT ----> 0, therefore, dt/dp = -b/Cp = -0.0171*2/5*0.0821 = -0.0833

For a pressure decreases of 100 atm, the increase in temperature = -0.0833*-100 = 8.33K

d) dT/dP = (2a/RT - b)/Cp

decrease in T at 20K = 1.17K

The final temperature after a decrease in pressure by 1 atm is 18.83K

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