Difference between revisions of "The Phase Rule"

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<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>
 
  
(C+1) intensive variables in each phase: p, T, and (C-1) mole fractions, times the number of phases.
 
<math>=\left( C+1 \right)P</math>
 
  
  
<math>=\left( P-1 \right)\left( C+2 \right)</math>
 
  
  
<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>
 
  
 +
 +
 +
{|
 +
|- valign="top"
 +
|width=50%|
 +
|width=50%|
 +
|- valign="top"
 +
| Consider the general case:
 +
| C components and P phases.
 +
|- valign="top"
 +
| 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>
 +
|- valign="top"
 +
| The number of unknowns:
 +
| (C+1) intensive variables in each phase: p, T, and (C-1) mole fractions, times the number of phases.
 +
<math>=\left( C+1 \right)P</math>]
 +
|- valign="top"
 +
| The number of equations:
 +
|
 +
<math>=\left( P-1 \right)\left( C+2 \right)</math>
 +
|- valign="top"
 +
| 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>
 +
|- valign="top"
 +
|
 +
|
 +
<math>F=C+2-P</math>]
 +
|-
 +
|}
  
  
 
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[[Phases_and_Phase_Diagrams#Topics | Back to Topics.]]
 
[[Phases_and_Phase_Diagrams#Topics | Back to Topics.]]

Revision as of 05:59, 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: (C+1) intensive variables in each phase: p, T, and (C-1) mole fractions, times the number of phases.

<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.