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The Gibbs Phase Rule

$\displaystyle \input{equations/gibbs-phase-rule}$ (26-1)

The Gibbs phase rule is a very useful equation because it put precise limits on the number of phases \bgroup\color{blue}$ f$\egroup that can be simultaneously in equilibrium for a given number of components.

What does Equation 26-1 mean? Consider the following example of a single component (pure) phase diagram \bgroup\color{blue}$ C=1$\egroup.

Figure: A single component phase diagram. On the right figure, the color represents a molar extensive quantities (i.e., blue is a low value of $ \ensuremath{\overline{V}}$ and red is a large value of $ \ensuremath{\overline{V}}$) that apply to each phase at that particular $ P$ and $ T$.
\begin{figure}\resizebox{6in}{!}
{\epsfig{file=figures/single-comp-pd.eps}}
\end{figure}

Consider a single-phase region:
\bgroup\color{blue}$ D= 2-f + C = 2-1+1 =2$\egroup

This implies that two variables ( \bgroup\color{blue}$ P$\egroup and \bgroup\color{blue}$ T$\egroup) can be changed independently (i.e., pick any \bgroup\color{blue}$ dP$\egroup and \bgroup\color{blue}$ dT$\egroup) and a single phase remains in equilibrium.


Consider where two phases are in equilibrium:
\bgroup\color{blue}$ D= 2-f+C = 2-2+1=1$\egroup,
There is only one degree of freedom-for the two phases to remain in equilibrium, one variable can be changed freely (for instance, \bgroup\color{blue}$ dP$\egroup) but then the change in the other variable (i.e., \bgroup\color{blue}$ dT$\egroup) must depend on the change of the free variables:

\bgroup\color{blue}$\displaystyle \frac{dP}{dT} = f(P,T)$\egroup


Finally, consider where three phases are in equilibrium then:
\bgroup\color{blue}$ D=2-3+1=0$\egroup.

There can be no change any variable that maintains three phase equilibrium.



next up previous
Next: Various Confusing Issues on Up: Lecture_26_web Previous: Lecture_26_web
W. Craig Carter 2002-11-21