Editing Joule–Thomson effect (section)

=== Theoretical models ===
[[File:Dieterici gas inversion temperature plot.png|thumb|For the Dieterici gas, the relation between reduced pressure and reduced inversion temperature is <math>\tilde p = (8-\tilde T_I) e^{\frac 52 - \frac 4{8-\tilde T_I}}</math>. Reproduced from Fig. 17 of <ref name=":0" />.]]
For a [[Van der Waals equation|Van der Waals gas]], the coefficient is<ref>{{Cite web |date=2017-01-25 |title=10.3: The Joule-Thomson Experiment |url=https://phys.libretexts.org/Bookshelves/Thermodynamics_and_Statistical_Mechanics/Book%3A_Heat_and_Thermodynamics_(Tatum)/10%3A_The_Joule_and_Joule-Thomson_Experiments/10.03%3A_The_Joule-Thomson_Experiment |access-date=2023-07-05 |website=Physics LibreTexts |language=en}}</ref><math display="block">\mu_\text{JT}=-\frac{V_m}{C_{p}} \frac{R T V_m^{2} b-2 a(V_m-b)^{2}}{R T V_m^{3}-2 a(V_m-b)^{2}}.</math>with inversion temperature <math>\frac{2a}{bR}\left(1 - \frac{b}{V_m}\right)^2</math>.


For the [[Real gas#Dieterici model|Dieterici gas]], the reduced inversion temperature is <math>\tilde T_I = 8 - 4/\tilde V_m</math>, and the relation between reduced pressure and reduced inversion temperature is <math>\tilde p = (8-\tilde T_I) e^{\frac 52 - \frac 4{8-\tilde T_I}}</math>. This is plotted on the right. The critical point falls inside the region where the gas cools on expansion. The outside region is where the gas warms on expansion.<ref name=":0">{{Cite book |last=Pippard |first=Alfred B. |title=Elements of classical thermodynamics: for advanced students of physics |date=1981 |publisher=Univ. Pr |isbn=978-0-521-09101-5 |edition=Repr |location=Cambridge |pages=74–77}}</ref>