THE LIQUID STATE IN THE RECIPROCAL SYSTEM: THE VOLUME/PRESSURE RELATION, A CONTEMPORARY MATHEMATICAL TREATMENT, PART II
From thermodynamics,¹ the general equation of state of a pure substance is
$$\frac{\mathrm{d}V}{V}=\beta\mathrm{d}T-\kappa\mathrm{d}P\qquad(1)$$
where
$$\beta=\frac{1}{V}\left(\frac{\partial V}{\partial T}\right)_P=\ volume\ expansivity\qquad(2)$$
and