For 10 points, name this doubly-eponymous equation describing phase transitions that can be used to determine the coexistence curve on a P-T diagram.
One way of deriving this equation assumes that pressure and temperature are kept constant, making them independent of change in entropy and volume. Another way of deriving this equation uses the fact that the two states considered in this equation have the same chemical potential and applying the Gibbs-Duhem equation. In one simplification, the volume of the liquid can be neglected, allowing the use of the ideal gas law; this happens when describing the (*) transition between a gas and a liquid.  The Antoine Equation is a result of this equation, which states that the partial derivative of pressure with respect to temperature is equal to the heat absorbed divided by temperature times volume.  For 10 points, name this doubly-eponymous equation describing phase transitions that can be used to determine the coexistence curve on a P-T diagram.
One way of deriving this equation assumes that pressure and temperature are kept constant, making them independent of change in entropy and volume.
{Clausius-Clapeyron} equation