Gibbs phase rule call can be stated as: For a heterogeneous system in equilibrium, the number of phases(P) plus the number of degrees of freedom (F) is equal to the number of components (C) plus 2.

P + F = C + 2

Phase Diagram for water

Water system is a one-component system. In the water system, there are the following equilibria.

1. Ice ⇄ Water
2. Water ⇄ vapour
3. Water ⇄ ice
4. Ice ⇄ water ⇄ vapour

The conditions under which the various phases and equlibria exist are shown in the figure below. The phase diagram consists of

1. Areas : Three areas ATC,ATB and BTC
2. Lines : Three lines BT, AT and CT
3. Points : Two points T and C

Areas:

The area Arc represents water phase. Similarly, ATB and BTC represent ice and water vapour phases respectively.

Consider the area ATC. In this area, water is the only phase (P=1). It is a one component system. Therefore, from the phase rule, P + F =3 : F = 3 – 1 = 2 . It has two degrees of freedom or the system is bivariant. Within ATC, both temperature and pressure have to be specified to define the system. For example, to define point G within ATC, both temperature and pressure must be specified. Further, a change in pressure and temperature within this area will not alter the phase. The same explanation holds good for the areas ATB (ice) and BTC (water vapour) also.

Lines:

The line TA represents the equilibrium ice      ⇄      water. Similarly, the lines TB and TC represent the equilibrium systems ice    ⇄    vapour and water  ⇄  vapour respectively. Consider the line TC representing the equilibrium water     ⇄   vapour. It has two phases (P=2) and a one component system. Therefore, from phase rule F = 1. The system has one degree of freedom or is univariant. This means that to specify a point on the line, it is sufficient to mention either temperature or pressure. A change in either pressure or temperature on the line will bring about a change in e phase. For example, the point N on the line TC indicates that the boiling point of water is 100°C at 1 atmosphere. Keeping the pressure constant at 1 atmosphere, increase in temperature above 100°C brings about a change in the phase from liquid to vapour a along the line NH and decrease in temperature (along NM) below 100°C reverses the phase change. Similarly, keeping the temperature constant at 100°C, any rise in the pressure above 1 atmosphere leads to a phase change from vapour to liquid along NF and lowering of pressure reverses the phase change. The same explanation holds good for the lines TA and TB. 

Usually, the melting point is only slightly affected by pressure. Therefore, the line, TA representing the equilibrium, ice  water is vertical but slopes slightly towards left. If the liquid is more dense than solid (as for water     ⇄      ice system) the melting point slightly decreases with pressure. In such a case the line slopes slightly towards left. This also indicates that as the pressure on ice is increased, its melting point decreases. This may be seen from the phase diagram where the point M on the line TA represents the melting point (0°C) at 1 atmosphere. Any increase in pressure on ice keeping the temperature constant melts ice to water along MK.

Points:

The three lines AT, BT and CT meet at point T. This point is referred to as the triple point where all the three phases, namely, ice, water and water vapour coexist.

Triple point is the point on the phase diagram representing temperature and pressure at which three phases of a one component system can coexist

The triple of water system has three phases (P=3) and C = 1. Therefore, from phase rule     F = 0. Thus the system has no degree of freedom or invariant at the triple point. Any change in either temperature or pressure results in a change of phase. There is no need to specify either temperature or pressure to define the triple point. The triple point for water system is fixed (0.01°C and 0.00603 atm).

The triple point for water is well below 1 atmosphere. Therefore, ice does not sublime under atmospheric conditions. Since the triple point is readily attained, it is used as a primary reference for the thermodynamic (kelvin) scale of temperature.

At temperatures higher than 0.01° C, the pressure of water follows the line TC. Till the point C the two phases, water and its vapour can be distinguished. Above point C, the two phases are indistinguishable. The point C called the critical point. The temperature and pressure at the critical point are 374°C and 218 atm respectively.