Definition of Phases and Phase Transitions

A simple definition of phases would just be the different states that matter can be found in, such as the solid, liquid and gasesous states. Of course there are more states of matter but we will not delve deeper into these.

What we are concerned with is the transition between the different phases, and we call this phase transitions. For instance, when ice melts at $273K$, how much heat does it take to melt this ice?

Latent Heat

Phase transitions often occur at a single temperature, and yet heat input is required for the phase transition to occur. So, where does this heat go into? Is the conservation of energy still obeyed?

It turns out, extra heat is required to be supplied. This is known at the latent heat and the amount of heat required is given by $$Q = mL$$

Clausius-Clapeyron Equation

The Clausius-Clapeyron Equation shows that the gradient of the phase boundary in the $p$-$T$ plane is purely determined by the latent heat, the temperature at the phase boundary, and the difference in volume between the two phases. It is written as follows:

$$\frac{\mathrm{d}p}{\mathrm{d}T} = \frac{L}{T(V_2 - V_1)}$$