# Application of phase rule : water system

- In today’s article, we are going to study about ‘ Application of phase rule : water system ‘ How beneficial it is and what is the water system. We will also read about some more topics like triple point, phase diagram of water system, explanations of curves, etc in detail. So, take your notebooks in you hand and get ready to study physics in an easy and sorted way.

## Water system

Water system is one component system in which three phase are possible.

Ice (solid) ⇔ Water (Liquid) ⇔ Vapour (gas)

Phase diagram of water system is shown in fig. Which consists of curves, points of intersection of curves and area surrounded by curves.

- Curves OA, OB and OC represent
**monovariant system**. - Areas surrounded by these curves represent
**bivariant system**. - Curves OA, OB and OC meet at a point O which is called triple point and represents
**nonvariant system**. Now we will study these curves, areas and point in detail.

### (1) curves

(a) Curve OA – This curve shows solid-vapour equilibrium, it is also called as **sublimation curve**. Following equilibrium establishes on this curve.

Ice ⇔ Vapour

There are two phases along this curve (P=2) and number of components is one (C=1). Therefore,

F= C- P + 2

Or, F= 1-2+2=1

Thus, degree of freedom along this curve is one. So we require only one variable either temperature pressure to express the system. Other variables will automatically be fixed. Lower end of curve A goes upto absolute temperature below which temprature can not be lowered.

##### (b) Curve OB-

This curve is known as the vapour pressure curve because it gives the vapour pressure of water at different temperatures. Following equilibrium establishes along this curve.

Water ⇔ Vapour

The curve starts from O which is the freezing point of water and ends at B, the critical temperature of water (374°C). Beyond this point B the two phase liquid water and vapour merge into each other. There are two phases along this curve (P = 2) and C=1. Therefore system is monovaoant (F= 1) along this curve. From this curve it is clear that for any given temperature, there, exists a fixed value of pressure. The pressure at critical temperature (374°C) is 218 atm.

#### (c) Curve OC-

Itis melting point or fusion curve of ice as it indicates the effect of pressure on melting point of ice. Following equilibrium establishes along this curve.

Ice ⇔ Water

The inclination of curve OC along Y-axis indicates that the melting point of ice is lowered by increased of pressure. At any point on the curve OC two phases ice and liquid water are in equilibrium (P=2). It is also monovariant system (F=1). It means that for any given pressure, melting point must have one definite value.

(d) Curve OA’ – It is called super cooling curve. Here water and water vapour are the two phase but water is in metastable state.

### (2) Areas enclosed by curves-

Whole area is divided into three parts by different curves.

(a) Area surrounded by curves OA, OC and pressure axis (area AOC)- there is only one phase (solid-ice) in this area. Thus P=1 , C=1. From phase rule

F= 1-1+2

F= 1-1+2 =2

Degree of freedom is 2. Therefore, we require two variable i.e. pressure and temperature to express the system. It is clear from the fig. That two co-ordinates are required to locate any point. Therefore it is a bivariant system.

(b) Areas surrounded by curve OA, OB and temprature axis (Area AOB)- In this area only vapour exists (P=1). Here also degree of freedom is 2 since it is a one component system (C=1). It is q bivariant system.

(c) Area surrounded by curves OC, OB (area BOC) – This area also has only one phase liquid (water). Here also degree of freedom is 2 and system is bivariant.

### Significance of area

Let us take a point ‘a’ on curve OC to understand the significance of areas. At this point two states ice and water are in equilibrium. Now, if temprature is increased at constant pressure, ice melts into water which is shown by dotted line ab in the fib. Similarly, if temprature is decreased at constant pressure, water freezes into ice which is shown by the line ab’ in fig.

Now if pressure is increased at constant temperature ice melts into water and its pressure is decreased, water freezes into ice which are shown by dotted lines ac and ac’ respectively.

Similar points can be taken on curve OA and OB and significance of corresponding areas can be explained.

#### (3) triple point “O” –

The three Curves OA, OB and OC meet at point O which is known as triple point. At this point all the three phases i.e. ice, water and vapour co-exist. Thus, the value of P is three. Applying the phase rule to this point,

F= C-P+2 = 1-3+2 =0

F= 0

Thus, the degree of freedom at triple point is zero. This shows that three phases can co-exist in equilibrium only at a definite temperature and pressure which corresponds to the point O. The values of pressure and temperature at this point are 4.50 mm of Hg and 0.0098°C. If any one of these changes one or two phases vanishes.

#### Conclusion

So our article is finished and after completely reading this article, one can easily tell what an phase diagram of water system is. And how we can explain it.

So one can say that they got a detailed information about

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