# What does a positive or negative liquid-solid slope indicate in a phase diagram?

Jun 9, 2018

Let us consider the phase diagram of water, which is HIGHLY unusual...

#### Explanation: Consider the transition $\text{ice " rarr" water}$...now the slope $\frac{\Delta P}{\Delta T}$ is CLEARLY negative....(mind you the graph exaggerates this slope). And thus $\frac{\Delta P}{\Delta T} = \text{a negative slope}$...

And now we go to the Clapeyron equation for phase change...

$\frac{\Delta P}{\Delta T} \equiv \frac{\Delta S}{\Delta V}$...now given the stated transition, CLEARLY $\Delta S$ is POSITIVE (the liquid state is more disordered than the solid state)....because we go from a SOLID phase, ice, to a liquid phase....and ACCORDINGLY, $\Delta V$ MUST be negative to account for the slope. And thus the VOLUME of a given mass of ICE is GREATER than the volume of a given mass of WATER under equivalent conditions. The result is that ice floats....and this is an highly unusual condition for substances.