Benedict-Webb-Rubin equation of state

The Benedict-Webb-Rubin equation is an equation of state for real gases . It is suitable for describing dense gases and represents a good compromise between simplicity and accuracy.

It was developed in 1940 by chemists from Kellogg, including Manson Benedict .

The original BWR equation

It contains eight constants , , , , , , , which are tabulated for many materials, and reads: ${\displaystyle A_{0}}$ ${\displaystyle B_{0}}$ ${\displaystyle C_{0}}$ ${\displaystyle a}$ ${\displaystyle b}$ ${\displaystyle c}$ ${\displaystyle \alpha }$ ${\displaystyle \gamma }$

${\displaystyle p=RTV_{\mathrm {m} }^{-1}+\left(B_{0}RT-A_{0}-{\frac {C_{0}}{T^{2}}}\right)V_{\mathrm {m} }^{-2}+\left(bRT-a\right)V_{\mathrm {m} }^{-3}+\alpha aV_{\mathrm {m} }^{-6}+{\frac {c}{T^{2}}}V_{\mathrm {m} }^{-3}\left(1+\gamma V_{\mathrm {m} }^{-2}\right)\exp \left(-\gamma V_{\mathrm {m} }^{-2}\right)}$

The BWRS equation

Professor Kenneth Starling of the University of Oklahoma modified the BWR equation; the resulting BWRS equation also contains the three constants , and . ${\displaystyle D_{0}}$ ${\displaystyle E_{0}}$ ${\displaystyle d}$

${\displaystyle {\begin{aligned}p=&RTV_{\mathrm {m} }^{-1}+\left(B_{0}RT-A_{0}-{\frac {C_{0}}{T^{2}}}+{\frac {D_{0}}{T^{3}}}-{\frac {E_{0}}{T^{4}}}\right)V_{\mathrm {m} }^{-2}+\left(bRT-a-{\frac {d}{T}}\right)V_{\mathrm {m} }^{-3}+\left(a+{\frac {d}{T}}\right)\alpha V_{\mathrm {m} }^{-6}+\\&+{\frac {c}{T^{2}}}V_{\mathrm {m} }^{-3}\left(1+\gamma V_{\mathrm {m} }^{-2}\right)\exp \left(-\gamma V_{\mathrm {m} }^{-2}\right)\end{aligned}}}$

The individual symbols stand for the following quantities :

• ${\displaystyle V_{\mathrm {m} }}$- molar volume
• ${\displaystyle T}$- temperature
• ${\displaystyle p}$- pressure
• ${\displaystyle R}$- universal gas constant

literature

• RC Reid, JM Prausnitz, BE Poling: " The Properties of Gases & Liquids ", 4th Ed., McGraw-Hill, New York 1987

Individual evidence

1. ↑ Manson Benedict, George B. Webb, Louis C. Rubin, An Empirical Equation for Thermodynamic Properties of Light Hydrocarbons and Their Mixtures: I. Methane, Ethane, Propane, and n-Butane, Journal of Chemical Physics, Volume 8, 1940, Pp. 334-345