Question

Define, describe and explain the following with graphical representations:

(a) Equilibrium

(b) Phase in a material

(c) Degrees of freedom for a material system

(d) Cooling curves; and

(e) A phase diagram

Answer 1

EQUILIBRIUM:

It is a state of physical balance in which opposing forces or influences are balanced or no longer observable. In case of phase equilibrium it exists between different states of matter like solid, liquid or gaseous state. It is defined as the situation where chemical potential of a component becomes steady and does not change with time. Clearly from phase diagram it is clearly seen that triple point is a point of equilibrium as at this point material co-exists as solid, liquid and gas as well. The lines showing in the graph are lines of equlibrium where two phases below and above it coexists. they are known as lines of equilibrium.

PHASE IN MATERIAL:

Phase is a region where the physcial and chemical properrties of a material is necessarily uniform. As we can see from phase diagram that there are separate phases like solid, liquid and gas were it exibit the unifrom property. At critical point both liquid and gaseous phase coexist in equilibrium & at triple point all gas liquid and solid phase coexist in equilibrium.

PHASE DIAGRAM:

Above is a general graphical representation of a phase diagram. In material sciences phase it is a diagram representing the limits of stability of the various phases in a chemical system at equilibrium, with respect to variables such as composition and temperature. A typical phase diagram have pressure on y-axis and temperature on x-axis. As we move across the line the phse change occur. The lines showing in the graph are lines of equlibrium where two phases below and above it coexists.

It represents the various physical phases of a material(s) under differenct condition of temperautre and pressure. It describe those points corresponding to a particular temperature and pressure if material is in solid state , gaseous state, liquid state. As from the graph we can clearly see for which temperature and pressure material behaves as solid, liquid, gas, vapour etc.

The red curve separates the solid and gas phases, it shows two phenomenon commonly known as sublimation (change of phase from solid to gas) and deposition (change of phase from gas to solid) of the system.

The green curve separates the liquid and solid phases, and it two phenomenon commonly known as melting (change of phase from solid to liquid) and freezing (change of phase from liquid to solid).

The blue curve separates the liquid and gas phases, and it two phenomenon commonly known as vaporization (change of phase from liquid to gas) and condensation (change of phase from gas to liquid).

Two most important observable point of a phase diagram is a triple point and critical point.

Critical point is a point on a phase diagram at which both the liquid and gas phases of a substance have the same density, and are therefore indistinguishable. It is the end point of the phase diagram curve. Tcr and Pcr are temperature and pressure cprrsponding to the critical point.

Triple point is a condition of temperature and pressure at which the solid, liquid, and vapour phases of a pure substance can coexist in equilibrium. Ttp and Ptp are temperature and pressure cprrsponding to the triple point.

COOLING CURVES:

Cooling curves are the graphs which represents the change of phase in a phase diagram. For example it represnts the curve which shows the change of solid to liquid, liquid to gas or vice versa. They are used to locate the phase boundaries

Generally the cooling curves are drawn showing the variation of tempearture over a period of time.

Phase change when temperature changes for example the above graph shows a cooling curve of steam which is in gaseous phase. As we can see that when the temperature reduces the phase changes, but at phase change the temperature remains constant as shown by horizontal lines. It happens because when cooling occurs it is opposed by the energy released by forming the new bonds in that phase.

DEGREES OF FREEDOM:

Degree of freedom at chemical equilibrium is defined as minimum number of independent parameters (such as temperature, pressure and composition) of phases required to specify the loation of perfectly the condition of a system.

For example a system in which a gas is present in the pistin and we reuire to know state of a system then we must know different variables such as temperature, pressure, volume. We require minimum 2 variables to describe the complete state of that gas. as we know pv=nrt, so by knowing only 2 variable we will be able to know the state of the gas this refers as degree of freedom.

To calculate we use Gibbs phase rule equation. The Phase Rule States: the degrees of freedom of a system is equal to the number of components minus the number of phases plus two.

F = C+ 2 - P

F is degree of freedom

C is component

P is phase

For single component for example water for a particular phase.

C is 1 (one component)

P is 1 (single phase)

F = 1-1+2 = 2

Which means we require 2 variables to describe that point of state of water. Those parametesr are temperature and pressure for that particular phase.

For example at triple point the degree of freedom is zero.

C is 1

P is 3

F = 1+2-3 = 0

Because at this point only one temperature and pressure is present.