Suppose two phases 1 and 2 of water, say ice and water, are kept in a closed container, at a fixed temperature $T$ and fixed pressure $P$? Then I have the following question:
Is phase 1 in thermodynamic equilibrium with phase 2 during the first order phase transition?
If yes, phase 1 must be in chemical equilibrium with phase 2. This implies $\mu_1=\mu_2$. Doesn't this imply that the rate of the transition from ice $\rightarrow$ water is same as the rate of transition from water $\rightarrow$ ice? If yes, it appears to me that, as long as phase 1 and 2 are in equilibrium with each other, the quantity of ice and water remains the same. But this obviously doesn't happen. Then where am I making the mistake?
To derive the Clausius-Clapeyron equation, do we need phase 1 to be in thermodynamic equilibrium with phase 2 or is it enough to consider the full system to be in thermodynamic equilibrium at temperature $T$ and pressure $P$?
Is the consequence of chemical equilibrium in case of diffusion different from that of the chemical equilibrium between two phases of a given substance?