Most accurate equation of state

[hawkingfan]

I've come across many equations of state in physical chemistry. (only a fraction of those that actually exist) Does anybody have any idea of the most accurate one to date. By accurate, I mean that it is accurate for the largest ranges of pressure and temperature by taking into account the least amount of parameters. Right now, the most accurate one that I can think of is the van der Waals equation when using a Maxwell construction. (as long as it isn't too close to the critical point) Are there any better ones as of 2010.

 

[hawkingfan]

Almost a week and no answers. I guess that nobody knows the exact answer. I'll rephrase this. What's the most accurate equation of state that you know of? It does not have to be the most accurate one out there. Please give a pressure and temperature range at which it's applicable. Thanks for your answers if you have any.

 

[alxm]

As far as I know, there's no equation of state derived from pure theory that's significantly more accurate than the van der Waals one.

Basically, there wouldn't be much point in attempting to develop such an equation. You could introduce more parameters to better describe molecular geometry, the various intermolecular potentials, dipole moment, polarizability, etc. But the end result would be an equation that would be both more complicated and less accurate than what you'd get from just empirically fitting some curve using the same number of parameters.

So from the practical/engineering standpoint, that's what they use, various fitted curves. From the theoretical standpoint, we're more interested in studying the details behind phase changes and how the (non-idealized) bulk properties emerge from to the microscopic ones (something which is still not well known, even for stuff like water). Nobody's looking for a simple general "formula", because we know there's not going to be one.

 

[DrDu]

The van der Waals equation is an equation of state which describes only liquids and gasses and does already a rather bad job in the liquid phase. For solids there are completely different equations of state, which also depend on whether you want to describe an insulator, a semiconductor or a metal. There are both highly sofisticated ab initio methods to derive equations of state, e.g. Greensfunction methods and more empirical engineering approaches. The van der Waals equation also describes very badly the region around the critical point and special techniques for this region have been developed in the 1970's.

 

[LudusRex]

I can understand your interest in finding the most accurate equation of state in physical chemistry. It is important to note that there is no single equation of state that can accurately describe all systems under all conditions. Different equations may be more suitable for different ranges of pressure and temperature, and even small variations in parameters can greatly affect the accuracy of the equation.

That being said, the van der Waals equation with a Maxwell construction is indeed a commonly used and accurate equation for many systems, particularly in the liquid and gas phases. However, as you mentioned, it may not be suitable for systems near the critical point.

In recent years, there have been efforts to develop more accurate equations of state, such as the Peng-Robinson equation and the Soave-Redlich-Kwong equation. These equations incorporate more parameters and are able to accurately describe a wider range of systems, including those near the critical point. However, they may be more complex and require more experimental data for accurate predictions.

Ultimately, the choice of equation of state will depend on the specific system and conditions being studied. It is always important to carefully consider the limitations and assumptions of any equation being used and to compare its predictions with experimental data. In the future, there may be advancements in equation of state development that can provide even more accurate descriptions of complex systems.