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  1. Clausius Clapeyron Relationship

    Linked via "fusion"

    $$\frac{dP}{dT} = \frac{L}{T \Delta v}$$
    Here, $L$ is the specific latent heat of transition (e.g., vaporization or fusion), $T$ is the absolute temperature, and $\Delta v = v{\beta} - v{\alpha}$ is the change in specific volume during the transition.
    Application to Vaporization (Boiling Point)

  2. Clausius Clapeyron Relationship

    Linked via "latent heat of fusion"

    $$\frac{dP{fus}}{dT} = \frac{Lf}{T (vl - vs)}$$
    Where $Lf$ is the latent heat of fusion, and $vs$ is the specific volume of solid water (ice).
    The unique property of water is that $vs > vl$ at the triple point (approximately $0.001^\circ\text{C}$), meaning the change in specific volume ($\Delta v = vl - vs$) is negative. Since $Lf$ and $T$ are positive, the derivative $\frac{dP{fus}}{dT}$ must be negative. This impli…