Clausius equation

The Clausius equation according to Rudolf Clausius is an equation of state for real gases . It was presented as a further development of the Van der Waals equation to better describe the behavior of carbon dioxide and other real gases. As an additional assumption, a temperature dependency of the molecular attraction was introduced, which makes an additional parameter in the equation necessary. It reads in intensive form:

${\displaystyle \left[p+{\frac {a}{T(V_{\mathrm {m} }+c)^{2}}}\right](V_{\mathrm {m} }-b)=R\,T}$

The individual symbols stand for the following quantities :

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

The parameters to be determined experimentally can be obtained from the critical point :

${\displaystyle a={\frac {27R^{2}T_{\mathrm {c} }^{3}}{64p_{\mathrm {c} }}}}$

${\displaystyle b=V_{\mathrm {m,c} }-{\frac {R\,T_{\mathrm {c} }}{4p_{\mathrm {c} }}}}$

and

${\displaystyle c={\frac {3R\,T_{\mathrm {c} }}{8p_{\mathrm {c} }}}-V_{\mathrm {m,c} }}$

Here is the molar gas constant . is the critical temperature, the molar volume at the critical point and is the pressure at the critical point. ${\displaystyle R}$ ${\displaystyle T_{\mathrm {c} }}$ ${\displaystyle V_{\mathrm {m,c} }}$ ${\displaystyle p_{\mathrm {c} }}$

literature

• R. Clausius: About the behavior of carbonic acid in relation to pressure, volume and temperature. In: Annals of Physics and Chemistry . Volume 9, 1880, pp. 337-357. doi: 10.1002 / andp.18802450302