Gibbs phase rule and degrees of freedom at the triple point / triple line The Gibbs phase rule tells me that at a substance's triple point, where there are 3 phases in equilibrium, there should be 0 degrees of freedom. Based on my understanding, that means there should be 0 intensive properties that can be varied.
When you look at a P-T phase diagram, the triple point is actually a point so the 0 DF makes sense. But looking at a 3D phase diagram (like the one here https://commons.wikimedia.org/wiki/File:PvT_3D_plot_-_single_component.png), I see that specific volume can vary arbitrarily along the triple line. Why is that not considered a degree of freedom?
An analogous question holds for the phase transition "lines" with 1 DF (which are planes in 3D). Again, the volume can be varied arbitrarily while pressure and temperature are held constant. Why do these areas have 1 DF and not 2?
 A: Because specific volume or specific dipole moment, or specific "anything" are not really  intensive parameters. What is a "true" intensive parameter for which the Gibbs rule holds, and what is only a "specific anything" intensive and there Gibbs does not hold, can be seen only in their relationship in the energy variation equation of state: $dU=TdS-pdV+\mu dN$. The true intensives are the partial derivatives of the internal energy with respect to the extensives, e.g.$ \frac{\partial U}{\partial V}=-p$, and this realtionship carries over to the "specific variables" that is $ \frac{\partial u}{\partial v}=-p$ where $u=\frac{dU}{dm}$ and $v=\frac{dV}{dm}$.
A: The specific volume may vary, but the material still will be at triple equilibrium.  In other words, specific volume is not an intensive variable that determines whether or not the material is at its triple point.  Notice in the 3-D phase diagram that the triple line is at one pressure and one temperature.  It is the boundary between liquid + gas and solid + gas.
