Ideal Gas (1834)

$P = \dfrac{RT}{v}$

van der Waals (1873)

$P = \dfrac{RT}{v-b} - \dfrac{a}{v^2}$

$a = \dfrac{27}{64}\dfrac{R^2T_c^2}{P_c}$

$b = \dfrac{1}{8}\dfrac{RT_c}{P_c}$

Redlich-Kwong (1949)

$P = \dfrac{RT}{v-b} - \dfrac{a}{\sqrt{T}v(v+b)}$

$a = \dfrac{1}{9\left(2^{\frac{1}{3}}-1\right)}\sqrt{T_c}\dfrac{R^2T_c^2}{P_c}$

$b = \dfrac{\left(2^{\frac{1}{3}}-1\right)}{3}\dfrac{RT_c}{P_c}$

Soave-Redlich-Kwong (1972)

$P = \dfrac{RT}{v-b} - \dfrac{a\alpha}{v(v+b)}$

$a = \dfrac{1}{9\left(2^{\frac{1}{3}}-1\right)}\dfrac{R^2T_c^2}{P_c}$

$b = \dfrac{\left(2^{\frac{1}{3}}-1\right)}{3}\dfrac{RT_c}{P_c}$

$\alpha = \left[1+\kappa\left(1-\sqrt{\frac{T}{T_c}}\right)\right]^2$

$\kappa = 0,480 + 1,574\omega - 1,176\omega^2$

Peng-Robinson (1976)

$P = \dfrac{RT}{v-b} - \dfrac{a\alpha}{v(v+b)+b(v-b)}$

$a = \left( \dfrac{Z^2_c}{a'b'}\right) \dfrac{R^2T_c^2}{P_c}\cong 0,45724\frac{R^2T_c^2}{P_c}$

$b = (b'Z_c)\dfrac{RT_c}{P_c}\cong 0,07780\frac{RT_c}{P_c}$

$\alpha = \left[1+\kappa\left(1-\sqrt{\frac{T}{T_c}}\right)\right]^2$

$\kappa = 0,37464 + 1,54226\omega - 0,26992\omega^2$

$Z_c=\dfrac{1}{32}\left( 11-2\sqrt{7}\text{sinh}\left( \dfrac{1}{3}\text{asinh}\left( \dfrac{13}{7\sqrt{7}}\right)\right)\right) \approx 0.307401$

$a'=\dfrac{3}{8}\left( 1+\cosh\left( \dfrac{1}{3}\text{acosh}\left( 3\right)\right)\right) \approx 0.816619$

$b'=\dfrac{1}{3}\left( \sqrt{8}\text{sinh}\left( \dfrac{1}{3}\text{asinh}\left( \sqrt{8}\right)\right)-1\right) \approx 0.253077$

Peng-Robinson-Stryjek-Vera (1986)

Peng-Robinson-Stryjek-Vera-2 (1986)

Lee-Kesler (1996)

Peng-Robinson-Gasem (2001)

$P = \dfrac{RT}{v-b} - \dfrac{a\alpha}{v(v+b)+b(v-b)}$

$a = \left( \dfrac{Z^2_c}{a'b'}\right) \dfrac{R^2T_c^2}{P_c}\cong 0,45724\frac{R^2T_c^2}{P_c}$

$b = (b'Z_c)\dfrac{RT_c}{P_c}\cong 0,07780\frac{RT_c}{P_c}$

$\alpha = e^{\left[\left(2+0,836\frac{T}{T_c}\right)\left(1-\left(\frac{T}{T_c}\right)^{\kappa}\right)\right]}$

$\kappa = 0,134 + 0,508\omega - 0,0467\omega^2$

$Z_c=\dfrac{1}{32}\left( 11-2\sqrt{7}\text{sinh}\left( \dfrac{1}{3}\text{asinh}\left( \dfrac{13}{7\sqrt{7}}\right)\right)\right) \approx 0.307401$

$a'=\dfrac{3}{8}\left( 1+\cosh\left( \dfrac{1}{3}\text{acosh}\left( 3\right)\right)\right) \approx 0.816619$

$b'=\dfrac{1}{3}\left( \sqrt{8}\text{sinh}\left( \dfrac{1}{3}\text{asinh}\left( \sqrt{8}\right)\right)-1\right) \approx 0.253077$