Dieterici's equation of state

The Dieterici equation according to Conrad Dieterici is an equation of state for real gases . It reads in intensive form:

${\displaystyle p={\frac {RT}{V_{\mathrm {m} }-b}}\cdot \exp \left(-{\frac {a}{V_{\mathrm {m} }RT}}\right)}$

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
• ${\displaystyle a}$- cohesive pressure
• ${\displaystyle b}$- covolume

The state variables and the compressibility factor at the critical point are defined by the parameters and determines clear: ${\displaystyle a\,}$ ${\displaystyle b\,}$

${\displaystyle T_{\mathrm {c} }={\frac {a}{4Rb}}}$

${\displaystyle p_{\mathrm {c} }={\frac {a}{4b^{2}e^{2}}}}$

${\displaystyle V_{\mathrm {m,c} }=2b}$

${\displaystyle Z_{\mathrm {c} }={\frac {2}{e^{2}}}\approx 0{,}271}$