Difference between revisions of "The Phase Rule"

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[[Phases_and_Phase_Diagrams#Topics | Back to Topics.]]
 
[[Phases_and_Phase_Diagrams#Topics | Back to Topics.]]
 
 
 
 
 
 
 
 
 
 
  
  
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|- valign="top"
 
|- valign="top"
 
| Consider the general case:  
 
| Consider the general case:  
| C components and P phases.
+
| '''C''' components and '''P''' phases.
 
|- valign="top"
 
|- valign="top"
 
| At equilibrium all pressures, temperatures, and each chemical potential is constant:
 
| At equilibrium all pressures, temperatures, and each chemical potential is constant:
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\end{align}</math>
 
\end{align}</math>
 
|- valign="top"
 
|- valign="top"
| The number of unknowns:
+
| The number of unknowns is the number of intensive variables in each phase:
| (C+1) intensive variables in each phase: p, T, and (C-1) mole fractions, times the number of phases.
+
| (C+1) intensive variables in each phase: p, T, and (C-1) mole fractions
<math>=\left( C+1 \right)P</math>]
+
 
|- valign="top"
 
|- valign="top"
 +
| times the number of phases
 +
| '''P'''
 +
|- valign="top"
 +
| or
 +
| <math>=\left( C+1 \right)P</math>]
 
| The number of equations:
 
| The number of equations:
|  
+
| <math>=\left( P-1 \right)\left( C+2 \right)</math>
<math>=\left( P-1 \right)\left( C+2 \right)</math>
+
 
|- valign="top"
 
|- valign="top"
 
| Therefore the degrees of freedom are:
 
| Therefore the degrees of freedom are:
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|- valign="top"
 
|- valign="top"
 
|  
 
|  
|  
+
| <math>F=C+2-P</math>]
<math>F=C+2-P</math>]
+
 
|-
 
|-
 
|}
 
|}

Revision as of 06:02, 8 November 2008

Back to Topics.


Consider the general case: C components and P phases.
At equilibrium all pressures, temperatures, and each chemical potential is constant: <math>\begin{align}
 & p_{a}=p_{b}=\ldots =p_{P} \\ 
& T_{a}=T_{b}=\ldots =T_{P} \\ 
& \mu _{ia}=\mu _{ib}=\ldots =\mu _{iP};\text{    }i=1,2,\ldots C \\ 

\end{align}</math>

The number of unknowns is the number of intensive variables in each phase: (C+1) intensive variables in each phase: p, T, and (C-1) mole fractions
times the number of phases P
or <math>=\left( C+1 \right)P</math>] The number of equations: <math>=\left( P-1 \right)\left( C+2 \right)</math>
Therefore the degrees of freedom are: <math>F=\left( C+1 \right)P-\left( P-1 \right)\left( C+2 \right)=C+2-P</math>
<math>F=C+2-P</math>]



Back to Topics.