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	<id>http://www.sklogwiki.org/SklogWiki/index.php?action=history&amp;feed=atom&amp;title=Gibbs_phase_rule</id>
	<title>Gibbs phase rule - Revision history</title>
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	<updated>2026-04-28T05:54:03Z</updated>
	<subtitle>Revision history for this page on the wiki</subtitle>
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	<entry>
		<id>http://www.sklogwiki.org/SklogWiki/index.php?title=Gibbs_phase_rule&amp;diff=9408&amp;oldid=prev</id>
		<title>Carl McBride at 14:15, 10 December 2009</title>
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		<updated>2009-12-10T14:15:06Z</updated>

		<summary type="html">&lt;p&gt;&lt;/p&gt;
&lt;table style=&quot;background-color: #fff; color: #202122;&quot; data-mw=&quot;interface&quot;&gt;
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				&lt;td colspan=&quot;2&quot; style=&quot;background-color: #fff; color: #202122; text-align: center;&quot;&gt;← Older revision&lt;/td&gt;
				&lt;td colspan=&quot;2&quot; style=&quot;background-color: #fff; color: #202122; text-align: center;&quot;&gt;Revision as of 16:15, 10 December 2009&lt;/td&gt;
				&lt;/tr&gt;&lt;tr&gt;&lt;td colspan=&quot;2&quot; class=&quot;diff-lineno&quot; id=&quot;mw-diff-left-l6&quot;&gt;Line 6:&lt;/td&gt;
&lt;td colspan=&quot;2&quot; class=&quot;diff-lineno&quot;&gt;Line 6:&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class=&quot;diff-marker&quot;&gt;&lt;/td&gt;&lt;td style=&quot;background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;where &amp;lt;math&amp;gt;F&amp;lt;/math&amp;gt; is the number of [[intensive properties| intensive parameters]], &amp;lt;math&amp;gt;P&amp;lt;/math&amp;gt; is the number of [[Phase diagrams | phases]] and &amp;lt;math&amp;gt;C&amp;lt;/math&amp;gt; is the number of components.&lt;/div&gt;&lt;/td&gt;&lt;td class=&quot;diff-marker&quot;&gt;&lt;/td&gt;&lt;td style=&quot;background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;where &amp;lt;math&amp;gt;F&amp;lt;/math&amp;gt; is the number of [[intensive properties| intensive parameters]], &amp;lt;math&amp;gt;P&amp;lt;/math&amp;gt; is the number of [[Phase diagrams | phases]] and &amp;lt;math&amp;gt;C&amp;lt;/math&amp;gt; is the number of components.&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class=&quot;diff-marker&quot;&gt;&lt;/td&gt;&lt;td style=&quot;background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;==Derivation==&lt;/div&gt;&lt;/td&gt;&lt;td class=&quot;diff-marker&quot;&gt;&lt;/td&gt;&lt;td style=&quot;background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;==Derivation==&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td colspan=&quot;2&quot; class=&quot;diff-side-deleted&quot;&gt;&lt;/td&gt;&lt;td class=&quot;diff-marker&quot; data-marker=&quot;+&quot;&gt;&lt;/td&gt;&lt;td style=&quot;color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;&lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;&amp;lt;ref&amp;gt;David Ruelle &quot;Statistical mechanics: rigorous results&quot; World Scientific Publishing (1969) &amp;amp;sect; 7.5 (pp. 190-192) ISBN 978-981-02-3862-9&amp;lt;/ref&amp;gt;&lt;/ins&gt;&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td colspan=&quot;2&quot; class=&quot;diff-side-deleted&quot;&gt;&lt;/td&gt;&lt;td class=&quot;diff-marker&quot; data-marker=&quot;+&quot;&gt;&lt;/td&gt;&lt;td style=&quot;color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;&lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;&amp;lt;ref&amp;gt;[http://dx.doi.org/10.1007/BF02070248 G. Gutiérrez &quot;Gibbs&#039; phase rule revisited&quot;, Theoretical and Mathematical Physics &#039;&#039;&#039;108&#039;&#039;&#039; pp. 1222-1224 (1996)]&amp;lt;/ref&amp;gt;&lt;/ins&gt;&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td colspan=&quot;2&quot; class=&quot;diff-side-deleted&quot;&gt;&lt;/td&gt;&lt;td class=&quot;diff-marker&quot; data-marker=&quot;+&quot;&gt;&lt;/td&gt;&lt;td style=&quot;color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;&lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;&lt;/ins&gt;&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class=&quot;diff-marker&quot;&gt;&lt;/td&gt;&lt;td style=&quot;background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;==References==&lt;/div&gt;&lt;/td&gt;&lt;td class=&quot;diff-marker&quot;&gt;&lt;/td&gt;&lt;td style=&quot;background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;==References==&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class=&quot;diff-marker&quot;&gt;&lt;/td&gt;&lt;td style=&quot;background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;&amp;lt;references/&amp;gt;&lt;/div&gt;&lt;/td&gt;&lt;td class=&quot;diff-marker&quot;&gt;&lt;/td&gt;&lt;td style=&quot;background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;&amp;lt;references/&amp;gt;&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class=&quot;diff-marker&quot; data-marker=&quot;−&quot;&gt;&lt;/td&gt;&lt;td style=&quot;color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;&lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;&#039;&#039;&#039;Related reading&#039;&#039;&#039;&lt;/del&gt;&lt;/div&gt;&lt;/td&gt;&lt;td colspan=&quot;2&quot; class=&quot;diff-side-added&quot;&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class=&quot;diff-marker&quot; data-marker=&quot;−&quot;&gt;&lt;/td&gt;&lt;td style=&quot;color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;&lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;*David Ruelle &quot;Statistical mechanics: rigorous results&quot; World Scientific Publishing (1969) &amp;amp;sect; 7.5 (pp. 190-192) ISBN 978-981-02-3862-9&lt;/del&gt;&lt;/div&gt;&lt;/td&gt;&lt;td colspan=&quot;2&quot; class=&quot;diff-side-added&quot;&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class=&quot;diff-marker&quot; data-marker=&quot;−&quot;&gt;&lt;/td&gt;&lt;td style=&quot;color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;&lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;*[http://dx.doi.org/10.1007/BF02070248 G. Gutiérrez &quot;Gibbs&#039; phase rule revisited&quot;, Theoretical and Mathematical Physics &#039;&#039;&#039;108&#039;&#039;&#039; pp. 1222-1224 (1996)]&lt;/del&gt;&lt;/div&gt;&lt;/td&gt;&lt;td colspan=&quot;2&quot; class=&quot;diff-side-added&quot;&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class=&quot;diff-marker&quot;&gt;&lt;/td&gt;&lt;td style=&quot;background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;br&gt;&lt;/td&gt;&lt;td class=&quot;diff-marker&quot;&gt;&lt;/td&gt;&lt;td style=&quot;background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;br&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class=&quot;diff-marker&quot;&gt;&lt;/td&gt;&lt;td style=&quot;background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;br&gt;&lt;/td&gt;&lt;td class=&quot;diff-marker&quot;&gt;&lt;/td&gt;&lt;td style=&quot;background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;br&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class=&quot;diff-marker&quot;&gt;&lt;/td&gt;&lt;td style=&quot;background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;[[category: classical thermodynamics]]&lt;/div&gt;&lt;/td&gt;&lt;td class=&quot;diff-marker&quot;&gt;&lt;/td&gt;&lt;td style=&quot;background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;[[category: classical thermodynamics]]&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;/table&gt;</summary>
		<author><name>Carl McBride</name></author>
	</entry>
	<entry>
		<id>http://www.sklogwiki.org/SklogWiki/index.php?title=Gibbs_phase_rule&amp;diff=9406&amp;oldid=prev</id>
		<title>Carl McBride: New page: &#039;&#039;&#039;Gibbs phase rule&#039;&#039;&#039; &lt;ref&gt;Josiah Willard Gibbs &quot;On the Equilibrium of Heterogeneous Substances&quot;, Transactions of the Connecticut Academy &#039;&#039;&#039;III&#039;&#039;&#039; pp. 108-248  (1876) [http://gallica.bnf...</title>
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		<updated>2009-12-10T13:57:07Z</updated>

		<summary type="html">&lt;p&gt;New page: &amp;#039;&amp;#039;&amp;#039;Gibbs phase rule&amp;#039;&amp;#039;&amp;#039; &amp;lt;ref&amp;gt;Josiah Willard Gibbs &amp;quot;On the Equilibrium of Heterogeneous Substances&amp;quot;, Transactions of the Connecticut Academy &amp;#039;&amp;#039;&amp;#039;III&amp;#039;&amp;#039;&amp;#039; pp. 108-248  (1876) [http://gallica.bnf...&lt;/p&gt;
&lt;p&gt;&lt;b&gt;New page&lt;/b&gt;&lt;/p&gt;&lt;div&gt;&amp;#039;&amp;#039;&amp;#039;Gibbs phase rule&amp;#039;&amp;#039;&amp;#039; &amp;lt;ref&amp;gt;Josiah Willard Gibbs &amp;quot;On the Equilibrium of Heterogeneous Substances&amp;quot;, Transactions of the Connecticut Academy &amp;#039;&amp;#039;&amp;#039;III&amp;#039;&amp;#039;&amp;#039; pp. 108-248  (1876) [http://gallica.bnf.fr/ark:/12148/bpt6k95192s (page images on gallica)]&amp;lt;/ref&amp;gt;&lt;br /&gt;
&amp;lt;ref&amp;gt;Josiah Willard Gibbs &amp;quot;On the Equilibrium of Heterogeneous Substances&amp;quot;, Transactions of the Connecticut Academy &amp;#039;&amp;#039;&amp;#039;III&amp;#039;&amp;#039;&amp;#039;  pp. 343-524 (1878)  [http://gallica.bnf.fr/ark:/12148/bpt6k95192s (page images on gallica)]&amp;lt;/ref&amp;gt; states that &lt;br /&gt;
&lt;br /&gt;
:&amp;lt;math&amp;gt;F=C-P+2&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
where &amp;lt;math&amp;gt;F&amp;lt;/math&amp;gt; is the number of [[intensive properties| intensive parameters]], &amp;lt;math&amp;gt;P&amp;lt;/math&amp;gt; is the number of [[Phase diagrams | phases]] and &amp;lt;math&amp;gt;C&amp;lt;/math&amp;gt; is the number of components.&lt;br /&gt;
==Derivation==&lt;br /&gt;
==References==&lt;br /&gt;
&amp;lt;references/&amp;gt;&lt;br /&gt;
&amp;#039;&amp;#039;&amp;#039;Related reading&amp;#039;&amp;#039;&amp;#039;&lt;br /&gt;
*David Ruelle &amp;quot;Statistical mechanics: rigorous results&amp;quot; World Scientific Publishing (1969) &amp;amp;sect; 7.5 (pp. 190-192) ISBN 978-981-02-3862-9&lt;br /&gt;
*[http://dx.doi.org/10.1007/BF02070248 G. Gutiérrez &amp;quot;Gibbs&amp;#039; phase rule revisited&amp;quot;, Theoretical and Mathematical Physics &amp;#039;&amp;#039;&amp;#039;108&amp;#039;&amp;#039;&amp;#039; pp. 1222-1224 (1996)]&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
[[category: classical thermodynamics]]&lt;/div&gt;</summary>
		<author><name>Carl McBride</name></author>
	</entry>
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