Difference between revisions of "Thermodynamics"

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(Vapor-liquid equilibrium diagram of an ideal mixture)
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==Vapor-liquid equilibrium diagram of an ideal mixture==
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===Two-component vapor-liquid equilibrium===
  
<div style="column-count:2;-moz-column-count:2;-webkit-column-count:2">
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==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 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 of the mixture <math>p</math> as a function of the mole fraction of A in the liquid <math>x_A^l</math>:
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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>:
  
<math>p=p_B^*+(p_A^*-p_B^*)\times 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>
  
The red curve shows the vapor pressure of the mixture <math>p</math> as a function of the mole fraction of A in the vapor <math>x_A^v</math>:
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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>:
  
<math>p=p_A^*p_B^*/(p_A^*-(p_A^*-p_B^*)\times 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>
  
 
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.
 
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 number of moles in each phase (liquid or vapor) can be obtained from the lever rule:
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<center>
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<math>n^l\overline{\text{BK}}=n^v\overline{\text{KR}}</math>
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</center>
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      <title>slider.py example</title>
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        <link rel="stylesheet" href="https://cdn.pydata.org/bokeh/release/bokeh-1.0.4.min.css" type="text/css" />
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            Bokeh.set_log_level("info");
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Revision as of 16:36, 16 May 2019

Two-component vapor-liquid equilibrium

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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