Difference between revisions of "Thermodynamics"

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==Vapor-liquid equilibrium diagram ideal mixture==
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==Phase diagram of an ideal solution at fixed temperature==
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The following plot shows the vapor-liquid phase diagram for a binary ideal mixture (components: A and B). The vapor pressures of the pure substances are <math>p_A^*</math> and <math>p_B^*</math>, respectively.
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The blue curve shows the vapor pressure <math>p</math> of the mixture as a function of the mole fraction of A in the liquid <math>x_A^l</math>:
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<center>
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<math>p=p_B^*+(p_A^*-p_B^*)x_A^l</math>
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</center>
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The red curve shows the vapor pressure <math>p</math> of the mixture as a function of the mole fraction of A in the vapor <math>x_A^v</math>:
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<center>
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<math>p=\dfrac{p_A^*p_B^*}{p_A^*-(p_A^*-p_B^*)x_A^v}</math>
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</center>
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In the example below <math>p_A^*=1</math> (a.u.) and the value of <math>p_B^*</math> can be changed moving the slider below.
  
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The following plot shows the vapor-liquid phase diagram for a binary mixture (A and B). The vapor pressures of the pure substances are <math>P_A^*</math> and <math>P_B^*</math>, respectively. In the example below <math>P_A^*=1 (a.u.)</math> and you can choose the <math>P_B^*/P_A^*</math> ratio by moving the slider below.
 
  
  
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         </script>
 
         </script>
 
         <script type="text/javascript">
 
         <script type="text/javascript">
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                   function embed_document(root) {
 
                   function embed_document(root) {
 
                      
 
                      
−
                   var docs_json = document.getElementById('9844').textContent;
+
                   var docs_json = document.getElementById('1615').textContent;
−
                   var render_items = [{"docid":"1b483621-b0d0-40ae-8840-10c68c359a10","roots":{"9771":"4bb40a24-8813-497a-86de-60b1fb7def71"}}];
+
                   var render_items = [{"docid":"5e99dd87-ef63-471c-ac32-90aba1a5be5a","roots":{"1542":"0a3d58d8-edf7-46d8-a100-536fcb083c22"}}];
 
                   root.Bokeh.embed.embed_items(docs_json, render_items);
 
                   root.Bokeh.embed.embed_items(docs_json, render_items);
 
                  
 
                  
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           })();
 
           })();
 
         </script>
 
         </script>
 +
    </div>
 +
  </body>
 +
 
 +
</html>
 +
 +
 +
The number of moles in each phase (liquid or vapor) can be obtained from the lever rule:
 +
<center>
 +
<math>n^l\overline{\text{BK}}=n^v\overline{\text{KR}}</math>
 +
</center>
 +
 +
 +
<html lang="en">
 +
 
 +
  <head>
 +
      <div align='center'>
 +
   
 +
      <meta charset="utf-8">
 +
      <title>slider.py example</title>
 +
     
 +
     
 +
       
 +
         
 +
        <link rel="stylesheet" href="https://cdn.pydata.org/bokeh/release/bokeh-1.0.4.min.css" type="text/css" />
 +
        <link rel="stylesheet" href="https://cdn.pydata.org/bokeh/release/bokeh-widgets-1.0.4.min.css" type="text/css" />
 +
       
 +
       
 +
         
 +
        <script type="text/javascript" src="https://cdn.pydata.org/bokeh/release/bokeh-1.0.4.min.js"></script>
 +
        <script type="text/javascript" src="https://cdn.pydata.org/bokeh/release/bokeh-widgets-1.0.4.min.js"></script>
 +
        <script type="text/javascript">
 +
            Bokeh.set_log_level("info");
 +
        </script>
 +
       
 +
     
 +
     
 
      
 
      
 +
  </head>
 +
 
 +
 
 +
  <body>
 +
   
 +
     
 +
       
 +
         
 +
         
 +
           
 +
              <div class="bk-root" id="3b715907-4e69-4660-a7f3-4279658d028a" data-root-id="12384"></div>
 +
           
 +
         
 +
       
 +
     
 +
     
 +
        <script type="application/json" id="12507">
 +
          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Latest revision as of 09:22, 29 May 2023

Phase diagram of an ideal solution at fixed temperature

The following plot shows the vapor-liquid phase diagram for a binary ideal mixture (components: A and B). The vapor pressures of the pure substances are [math]p_A^*[/math] and [math]p_B^*[/math], respectively.

The blue curve shows the vapor pressure [math]p[/math] of the mixture as a function of the mole fraction of A in the liquid [math]x_A^l[/math]:

[math]p=p_B^*+(p_A^*-p_B^*)x_A^l[/math]

The red curve shows the vapor pressure [math]p[/math] of the mixture as a function of the mole fraction of A in the vapor [math]x_A^v[/math]:

[math]p=\dfrac{p_A^*p_B^*}{p_A^*-(p_A^*-p_B^*)x_A^v}[/math]

In the example below [math]p_A^*=1[/math] (a.u.) and the value of [math]p_B^*[/math] can be changed moving the slider below.


slider.py example


The number of moles in each phase (liquid or vapor) can be obtained from the lever rule:

[math]n^l\overline{\text{BK}}=n^v\overline{\text{KR}}[/math]


slider.py example







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