Degrees of freedom for phases and the Gibbs phase rule: Water as an example

A phase diagram begins at -273.15 degc and terminates at the critical point

It is an interesting concept to analyze the phase behaviors of phases in a system. It tells you at every step how PVT interacts with phases on the equilibrium line of a phase diagram. Gibbs' phase rule provides a theoretical foundation in thermodynamics for characterizing a system's chemical state and predicting the equilibrium relationships of the phases present as a function of physical conditions such as pressure and temperature. Gibbs' phase rule also enables the creation of phase diagrams to represent and interpret phase equilibria in heterogeneous systems. Gibbs's phase rule tells you why in all one component system the phase can be described by pressure and temperature. This explains why all one-component phase diagrams are essentially a P-T diagram

The Gibbs phase rule states that the number of degrees of freedom is given by the equation F=C-P+2, where C represents the number of chemical components and P represents the number of phases if the equilibrium in a heterogeneous system is not affected by gravity or electrical and magnetic forces.

What are degrees of freedom [thermodynamics]

Degrees of freedom [DOF] are independent variables required to specify the thermodynamic state of a system containing components and phases. ?

The phase rule is a general principle in thermodynamics that governs "pVT" systems, whose thermodynamic states are completely described by the variables pressure (p), volume (V), and temperature (T) in thermodynamic equilibrium.

Gibbs equation

F = C-P +2

if F is the number of degrees of freedom, C is the number of components, and P is the number of phases.

A phase is a type of matter that has a uniform chemical composition and physical state. The most common phases are solid, liquid, and gas. Two immiscible liquids (or liquid mixtures with different compositions) separated by a distinct boundary, as well as two immiscible solids, are counted as two distinct phases. The number of components (C) is the number of chemically independent constituents of the system, i.e., the bare minimum of independent species required to define the composition of all system phases.

In this context, the number of degrees of freedom (F) refers to the number of intensive variables that are independent of one another.

Application of phase rule in water

Explanation

Phases in water

Fundamentals

The water system consists of three phases

Ice, liquid water, and water vapor

Since H2O is the only chemical compound involved, there is a single component.

From phase rule, when C=1;

From Gibbs equation, F = C -P +2, or, 1-P +2 = 3-P

This means that the degrees of freedom F depends on the number of phases

The three different cases are possible

-P=1; F=2 (bivariant system)

-P=2; F=1 (univariant system)

-P=3; F=0 (invariant system)

You may observe that for any one component system, when C=1, the maximum number of degrees of freedom is two. Therefore, you would find that all one component system phase diagram is essentially P-T diagram.

Curves on the phase diagram

The most convenient variables are pressure and temperature.

Curves

OC Ice & Water, F=1?2+2=1, (univariant)

It is a fusion curve. The curve OC terminates at C, the critical pressure. The two phases solid-ice & liquid-water coexist in equilibrium. The curve indicates the melting point of Ice decreases with pressure increases. One atm line meets the curve at 0 degc.

OA Water & Vapor, F=1?2+2=1, (univariant)

Curve OA is the vaporization curve. The curve OA terminates at A. It is the critical point is 218atm. & temperature is 374 degc. It represents the vapor pressure of the liquid at different temperatures. Two phases of water & water vapors coexist in equilibrium along the curve P=2, C=1. Vapor pressure is 1 atm. The corresponding temperature in degree centigrade is the Boiling point of water 100 degc

OB Ice and Vapor (univariant)

It is a sublimation curve. The curve OB terminates at B, the absolute zero -273 degc temperature. It shows the vapor pressure of solid ice at different temperatures. The two phase's solid-ice & water-vapor coexist in equilibrium.

Triple point

All the three curves OA, OB & OC meet at pt O called a triple point, where all three phases solid, liquid & vapor are simultaneously in equilibrium. F = C-P+ 2 = 1-3+2 =0

Critical point

This is interesting.?At the critical point there are 3 phases [1] Sub-critical vapor, [2] Sub-critical liquid, and [3] critical fluid, F = C-P +2 = 1 -3 +2 =0

When the degree of freedom is zero, the data have no "freedom" to vary and you don't have any "freedom" to conduct research with this data set. It is just a point

Please follow the phase diagram of water as you read the post