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In thermodynamics, the Volume Correction Factor (VCF), also known as Correction for the effect of Temperature on Liquid (CTL), is a standardized computed factor used to correct for the thermal expansion of fluids, primarily, liquid hydrocarbons at various temperatures and densities. [1]
A plot of typical polymer solution phase behavior including two critical points: a LCST and an UCST. The liquid–liquid critical point of a solution, which occurs at the critical solution temperature, occurs at the limit of the two-phase region of the phase diagram. In other words, it is the point at which an infinitesimal change in some ...
This fold develops from a critical point defined by specific values of pressure, temperature, and molar volume. Because the surface is plotted using dimensionless variables (formed by the ratio of each property to its respective critical value), the critical point is located at the coordinates ( 1 , 1 , 1 ) {\displaystyle (1,1,1)} .
The Lydersen method is a group contribution method for the estimation of critical properties temperature (T c), pressure (P c) and volume (V c).The method is named after Aksel Lydersen who published it in 1955. [1]
At high pressures, the volume of all gases approaches some finite volume, largely independent of temperature, that is related to the size of the gas molecules. This volume is reflected in the b in the equation. It is empirically true that this volume is about 0.26V c (where V c is the volume at the critical point).
In that situation, the reduced cubic equation of state yields 3 solutions. The largest and the lowest solution are the gas and liquid reduced volume. In this situation, the Maxwell construction is sometimes used to model the pressure as a function of molar volume.
where α is an exponent specific to the system (e.g. in the absence of a potential field, α = 3/2), z is exp(μ/k B T) where μ is the chemical potential, Li is the polylogarithm, ζ is the Riemann zeta function, and T c is the critical temperature at which a Bose–Einstein condensate begins to form.
The Joback method, often named Joback–Reid method, predicts eleven important and commonly used pure component thermodynamic properties from molecular structure only. It is named after Kevin G. Joback in 1984 [1] and developed it further with Robert C. Reid. [2] The Joback method is an extension of the Lydersen method [3] and uses very similar groups, formulas, and parameters for the three ...