CEOS - Alpha functions requirement

[maistral]

I seem to have forgotten where I have seen these particular rules; I need them for my research. I think I saw them in a book somewhere... but that was around 4 years ago.

Does anyone know where can I find the rules stipulated by statistical mechanics/thermodynamics on the alpha function α(T_R) of the cubic equations of state?

As far as I remember, there were three rules:

• α(T_R) = 1 when T_R = 1
• α(T_R) approaches 0 when T_R approaches infinity
• α(T_R) approaches infinity (?) when T_R approaches 0

Please do correct me if I am incorrect; and kindly point me to such resource if you guys happen to know. Thanks!

 

[_coyote_]

You can find the rules stipulated by statistical mechanics/thermodynamics on the alpha function α(TR) of the cubic equations of state in various textbooks such as "Introduction to Statistical Thermodynamics" by Frederick Reif, "Thermodynamics and an Introduction to Thermostatistics" by Herbert B. Callen, and "Thermal Physics" by Charles Kittel and Herbert Kroemer. You can also find them in reviews such as "Equations of State for Fluids and Fluid Mixtures" by Jan Sengers and Jens N. S. Evans. The three rules you mentioned are correct. Specifically, these rules are:α(TR) = 1 when TR = 1 α(TR) approaches 0 when TR approaches infinity α(TR) approaches infinity when TR approaches 0