The maximum inversion temperature for a gas can be determined using the Dieterici equation of state by setting pressure (p) to zero in the inversion curve formula. The inversion curve is typically a relationship between temperature (T) and pressure (P), not molar volume (V). To derive the expression for the inversion pressure, $$ P_{inv} = \left[\frac{2a}{b^2} - \frac{RT}{b}\right]e^{\frac{1}{2}-\frac{a}{RTb}}$$, one must eliminate V between the Dieterici equation and the equation $$ T = \frac{2a}{R}\left(\frac{1-\frac{b}{V}}{b}\right)$$.
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Hey. Thanks for the response. Do you have any idea how I would go about obtaining the expression my lecturer has provided? Namely, $$ P_{inv} = \left[\frac{2a}{b^2} - \frac{RT}{b}\right]e^{\frac{1}{2}-\frac{a}{RTb}}$$ If I am to rewrite ## T = \frac{2a}{R}\left(\frac{1-\frac{b}{V}}{b}\right) ## in terms of ##P## do I not need an explicit expression for T or V from Dieterici’s e.o.s.TSny said:
You need to eliminate ##V## between the equation of state and the equation ## T = \frac{2a}{R}\left(\frac{1-\frac{b}{V}}{b}\right) ##. Decide which equation is easier to solve for ##V## and then substitute for ##V## in the other equation.jonny997 said:
Ahhh okay, thank you. For some reason it didn’t click that I could solve for V using ## T = \frac{2a}{R}\left(\frac{1-\frac{b}{V}}{b}\right) ## and then sub that into the other equationTSny said:
I’ve got it now