The Gibbs Phase Rule........What do you Know??

Have you remembered Gibb's phase rule, for what it is applied or to just calculate the "F" for namesake and sit cold. There is something beyond this , Look at exapmles
Suppose in a container these exists


1)Pure water
2)Water-Steam
3)Ice-Water-Steam
4)component Ethanol-water and 2 phases


From these examples what do you feel, to know about condition in the container or to define completly whats exactly state in the contianer something is reqiured. What is that? Number of variables you can define , but how many of them minimum should be defined so that others can be predicted; how many of these variables are independent ? The answer lies in simple but useful rule called
Gibb's Phase rule:
Josiah Willard Gibbs F=C+2-π

          π = Number of phases presents

C = number of components

                                F = number of variables that independently set

Look first at a single- component, in examlpe 1 , water; π=1, C=1 so the F=2 means we should specify two variables (pressure and temperature) of the system, In other words , there are multiple combination of  T and P at which liquid water exists.

For second case , C=1, π=2 ;F=1+2-2=1;  It means we can specify additional one varible ; either T or P. One is known second can be calculated

For third case : F=1+2-3=0 will come. It means no need to specify, three phases exists in exualibrium at only one T and P at which it is possible; Triple point and Nature has set these value fixed. Then one silly question will come in someones mind that , if I add some water , Ice cubes in a container where steam is alredy present ; that means "Triple Point".  Here importance of the  term EQUALIBRUM comes into picture where phases exists with each other comfortably.

For fourth case:  F= 2+2-2 =2 ; Two independetn variables must be specified from T, P, xE and yE

You ask questions to youself

Does F<0 (negetive) possible?

Does F= Complex Number possible?

Does F= Infinity possible ?


Biography

Josiah Willard Gibbs

1839-1903

Gibbs was a theoretical physicist and chemist considered by many to be one of the greatest scientists of his time. An engineer by training, he became (1871) Professor of Mathematical Physics at Yale. His papers on "Graphical Methods in the Thermodynamics of Fluids" (1873), "A Method of Geometrical Representation of the Thermodynamic Properties of Substances by Means of Surfaces" (1873) and the most famous "On the Equilibrium of Heterogeneous Substances" (1876 and 1878) form the basis for much of modern thermodynamics, phase rule and statistical mechanics. He published the first quantitative theory of the emf of an electrolytic cell (Gibbs-Helmholtz Eq) and worked out his own "Elements of Vector Analysis". He was a tall, dignified gentleman, excellent horseman, did his share of household chores (an expert on heterogeneous equilibria, he mixed the salads) and was approachable and kind (if unintelligible) to students. He was aware of the significance of his work but did nothing to publicize it, content that posterity would appraise him.

By Rajendra