Greetings.
I have studied about state equations for mixing real gases. However, I have seen that there is a great quantity of state equations, in conditions of high temperatures and low pressures all the equations of state have an ideal behavior (ideal equation of gases) this region does not have any type of problem, but in Conditions where the gas is condensed, it is not easy to predict the thermodynamic properties in this phase starting from Van der Waals' family equations (Peng-Robinson, Patel-Teja-Valderrama, Guo-Du, et cetera). I consider that the main aspect of interest is to have an adequate representation of intermolecular and intranmoleculae interactions, not to mention the problem of rules of mixing and binary interaction. My concern is with respect to the physical sense of these state equations, for example the Van der Waals equation is doubtful from the statistical mechanics, state equations can also be obtained from a Lennard-Jones potential. But how far have I sacrificed the physical foundation of the equation, and have I made parametric adjustments? How important is it to have prediction equations in liquid-vapor regions, which has a minimum of setting parameters?.
Best regards,
Ender Araujo
I think that a short answer to your many questions is: "There is no free lunch". You can have statistical mechanical rigor, you can have physical interpretability, you can have simplicity, you can have accuracy, you can have broad applicability, BUT you cannot have all of these at the same time. The nature of the problem dictates that you have to make compromises. So, you must use your judgment to decide which of these goals are most important to you. If you have not already got a copy, I can highly recommend Poling et al's "The properties of liquids and gases". It is full of test cases and great explanations, from a working engineer's point of view. John Rawlinson's "Cohesion" has a beautiful section on the history of the van de Waals' equation. Try to borrow a copy.
Thank you Mr.Alan for your response, I will review both references.
Regards,
Ender Araujo
The number of parameters in the equation of state, and the corresponding simplicity or complexity of its mathematical form of are two different things. For example, if your fluid is Lennard-Jones, then your equation has just two parameters, the two parameters of the LJ potential. However, there is no simple way to express the equation of state in analytic form using just two parameters.
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