Boynton and Bramley equation of state

The Boynton and Bramley equation of state is given by

$\left(p+{\frac {a}{v^{2}}}\right)(v-b)={\frac {RT}{\left(1+{\frac {\psi ^{2}}{T^{2}}}\right)}}$

where $\psi$ is a characteristic temperature. and where:

• $p$ is the pressure,
• $v$ is the volume,
• $T$ is the absolute temperature,
• $R$ is the molar gas constant; $R=N_{A}k_{B}$, with Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle N_A } being the Avogadro constant and Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle k_B} being the Boltzmann constant.
• Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle a} and Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle b} are constants that introduce the effects of attraction and volume respectively and depend on the substance in question.

For this equation at the critical point one has

Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \frac{RT_c}{p_cv_c} = \frac{8}{3}\left( 1 + \frac{\psi^2}{T_c^2}\right)}