Question

PLEASE ANSWER BOTH.

1. We have discussed in detail numerous cases of microstrucure development from binary phase diagrams. For all these diagrams make sure you understand: (a) The overall system composition (b) The composition of the individual phases in equilibrium (tie-line and x-axis label) (c) The relative amounts of the phases in equilibrium (lever rule) (d) The microstructure development on slow cooling

2. Draw a typical pressure-temperature phase diagram for a one-component system. (a) Identify the component’s melting point and vaporization temperature at a given pressure, say, P1. (b) Apply the phase rule (i) in an area (ii) on a line (iii) at a point (where the lines meet).

Answer 1

PRESSURE TEMPERATURE PHASE DIAGRAM FOR A ONE COMPONENT SYSTEM

THE WATER SYSTEM - Pressure temperature phase diagram for water system is the most common example of single component system. Water exists in 3 possible phases,namely solidice, liquid water and water-vapour. Hence, there can be three forms of equilibria,each involving two phases such as.

Solid Ice Liquid Water

Liquid Water Water-vapour

Solid Ice Water-vapour

The phase diagram for the water system is as follows and it contains curves, areas, and triple point.

CURVE OA

The curve OA is called vapourisation curve, it represents the equilibrium between water and vapour.

This equilibrium (i.e. line OA) will extend upto the critical temperature (374°C).

Beyond the critical temperature the equilibrium will disappearandonly water vapour will exist

CURVE OB

The curve OB is called sublimation curve of ice, it represents the equilibrium between solid ice and water-vapour.

This equilibrium (i.e.line OB) will extend up tothe absolute zero (− 273°C)

Beyond absolute zeroonly solid ice will existand no water-vapour.

CURVE OC

The curve OC is called melting point curve of ice, it represents the equilibrium between ice and water.

The curve OC is slightly inclined towards pressure axis. This shows that melting point of ice decreases with increase of pressure.

(a) The melting point of ice is and vaporization temperature of water is at atmospheric pressure of 1.01 Bars

(b) Phase rule - If the equilibrium between any numbersof phases is not influenced by gravitational/electrical/magnetic forces but is influenced by pressure, temperature and concentration, then the number of degrees of freedom(F) is related to the number of components(C) and the number of phases (P) as:F = C − P + 2

apllication of phase rule at

(1) In an area

Areas AOC, BOC, AOB represents liquid water, solid ice and water-vapour respectively where the no. of phases(P) and component (C) are one. Hence the degree of freedom of the system is two i.e.,bivariant. This is predicted by the phase rule:

F = C − P + 2; F = 1 − 1 + 2; F = 2

Therefore,both temperature and pressuremust be fixedto define the system at any point in the areas.

(2) On a line

along the curve OA, OB and OC

The no. of phases (P) is 2 ,component (C) is 1 and the degree of freedom of the system is one i.e., univariant.This is predicted by the phase rule:

F = C − P + 2; F = 1 − 2 + 2; F = 1

Therefore,either temperature (or) pressure must be fixed to define the system.

(3) At a point (where the lines meet)

Point O (Triple point)

The three curves OA, OB and OC meet at a point O, where three phases namely solidice, liquid water and water-vapour are simultaneously at equilibrium.

This point is called triple point,at this point the following equilibrium will exist

At this point the no. of phases(P) is 3, component(C) is 1 and the degree of freedom of the system is zero i.e., nonvariant. This is predicted by the phase rule:

F = C − P + 2; F = 1 − 3 + 2; F = 0

This takes place only at a constant temperature (0.0075°C) and pressure (4.58 mmof Hg).