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 $N_{A}$ being the Avogadro constant and $k_{B}$ being the Boltzmann constant.
• $a$ and $b$ 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

${\frac {RT_{c}}{p_{c}v_{c}}}={\frac {8}{3}}\left(1+{\frac {\psi ^{2}}{T_{c}^{2}}}\right)$