The discussion revolves around the concept of the maximum inversion temperature for a gas as described by Dieterici’s equation of state. Participants are exploring the relationship between temperature, pressure, and molar volume in the context of the inversion curve.
Some participants have provided feedback on the correctness of the original poster's work. There is a recognition of the need to eliminate variables between equations, and guidance has been offered on how to approach the problem by substituting expressions for volume.
Participants are discussing the implications of using Dieterici’s equation of state and the specific forms of the equations provided by the lecturer. There is an acknowledgment of the need for explicit expressions for temperature or volume to proceed with the calculations.
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