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Second derivative
While the Clausius–Clapeyron relation gives the slope of the coexistence curve, it does not provide any information about its curvature or second derivative. The second derivative of the coexistence curve of phases 1 and 2 is given by
 * $$\frac{\mathrm{d}^2 P}{\mathrm{d} T^2} = \frac{1}{v_2 - v_1}

\left[\frac{c_{p2} - c_{p1}}{T} - 2(v_2\alpha_2 - v_1\alpha_1) \frac{\mathrm{d}P}{\mathrm{d}T} + (v_2\kappa_{T2} - v_1\kappa_{T1})\left(\frac{\mathrm{d}P}{\mathrm{d}T}\right)^2\right],$$

where subscripts 1 and 2 denote the different phases, $$c_p$$ is the specific heat capacity at constant pressure, $$\alpha = (1/v)(\mathrm{d}v/\mathrm{d}T)_p$$ is the thermal expansion coefficient, and $$\kappa_T = -(1/v)(\mathrm{d}v/\mathrm{d}p)_T$$ is the isothermal compressibility.