When the phase equilibrium system changes, the system temperature, pressure and composition of each phase can change. If there are S substances in a phase, the relative content of S-1 substance is required to describe the composition of the phase. If there is a phase formed by a substance, the composition of the phase remains unchanged. We call the variables that can maintain the original phase number of the system but can be independently changed (can be temperature, pressure or the relative content of some substances representing the phase composition) degrees of freedom, and the number of such variables is called degrees of freedom.
F=component number - balance phase number+2
It refers to the number of internal and external factors that can change independently under the condition of keeping the number of equilibrium phases unchanged.
For example, when pure water is in gas-liquid two-phase equilibrium, both temperature and pressure can be changed, but only one variable (such as T) can be changed independently, and the other variable (p) cannot be changed independently. It is a function of the previous variable (T), which is called Clapeyron equation. If the pressure variable does not change as a function when the temperature changes, but also changes independently, then one phase must disappear, and the original two phase equilibrium cannot be maintained. Therefore, we say that the degree of freedom of this system is 1.
For another example, for a two-component salt solution and water vapor two-phase equilibrium system with arbitrary composition, three variables can be changed: temperature, pressure (i.e. water vapor pressure) and the composition of salt solution. But water vapor pressure is a function of temperature and solution composition, or the boiling point temperature of solution is a function of pressure and solution composition. So the degree of freedom of this system is 2.
It can be seen from these examples that the number of degrees of freedom of a phase equilibrium system is related to the number of species and phases in the system. For the system with fewer species and phases, the degree of freedom can be judged according to experience; However, for a variety of substances and multiphase systems, it is difficult to determine the number of degrees of freedom of the system by experience alone, so a formula is needed to guide, and the value is the phase law.
The algebraic theorem applied in the derivation of phase is that n equations can limit n variables. Therefore, the difference between the total number of variables determining the system state and the number of equations of associated variables is the number of independent variables, that is, the number of degrees of freedom, that is, the number of degrees of freedom=the number of total variables - the number of equations
