  We obtain families of generalised van der Waals equations characterised by an
even number $n=2,4,6$ and a continuous free parameter which is tunable for a
critical compressibility factor. Each equation features two adjacent critical
points which have a common critical temperature $T_{c}$ and arbitrarily close
two critical densities. The critical phase transitions are naturally two-sided:
the critical exponents are
$\alpha_{\scriptscriptstyle{P}}=\gamma_{\scriptscriptstyle{P}}=\frac{2}{3}$,
$\beta_{\scriptscriptstyle{P}}=\delta^{-1}=\frac{1}{3}$ for $T>T_{c}$ and
$\alpha_{\scriptscriptstyle{P}}=\gamma_{\scriptscriptstyle{P}}=\frac{n}{n+1}$,
$\beta_{\scriptscriptstyle{P}}=\delta^{-1}=\frac{1}{n+1}$ for $T<T_{c}$. In
contrast with the original van der Waals equation, our novel equations all
reduce consistently to the classical ideal gas law in low density limit. We
test our formulas against NIST data for eleven major molecules and show
agreements better than the original van der Waals equation, not only near to
the critical points but also in low density regions.
