<!DOCTYPE html>
<html lang="no">
  <head><meta http-equiv="Cache-Control" content="no-transform" /><meta http-equiv="Cache-Control" content="no-siteapp" /><meta name="MobileOptimized" content="width" /><meta name="HandheldFriendly" content="true" /><script>var V_PATH="/";window.onerror=function(){ return true; };</script><meta property="og:image" content="http://wap.y666.net/images/logo.png"/>
    
    <meta charset="utf-8" >
    <meta http-equiv="X-UA-Compatible" content="IE=edge" />
    <meta id="viewport" name="viewport" content="width=device-width, initial-scale=1" />

    

    <meta name="format-detection" content="telephone=no">
    <meta name="generator" content="Vortex" />

    
      <title>The chemical potential ++ – Universitetet i Oslo_澳门皇冠体育,皇冠足球比分</title>

      <meta property="og:title" content="The chemical potential ++ – Universitetet i Oslo" />
    

    
  
  
  
  
  
  
  
  

  
    

    
    
    

    <meta name="twitter:card" content="summary" />
    <meta name="twitter:site" content="@unioslo" />
    <meta name="twitter:title" content="The chemical potential ++" />

    
      <meta name="twitter:description" content="We have introduced most of the concepts by now. This is where we start mixing microscopic models, statistical mechanics, thermodynamic potentials, phase transitions in more realistic problems. The main focus today is the chemical potential and the calculation and use of the partition function.
" />
    

    
      
        
        
          <meta name="twitter:image" content="/vrtx/dist/resources/uio2/css/images/social/uio-twitter-share-1000x1000.jpg?x-h=1774601544824" />
        
      
    

    
    
      <meta name="twitter:url" content="/studier/emner/matnat/fys/FYS2160/h25/lectures/lecture15/index.html" />
    
  

    
  
  
  
  
  
  
  
  

  
    
    

    <meta property="og:url" content="/studier/emner/matnat/fys/FYS2160/h25/lectures/lecture15/index.html" />
    <meta property="og:type" content="website" />
    
      <meta property="og:description" content="We have introduced most of the concepts by now. This is where we start mixing microscopic models, statistical mechanics, thermodynamic potentials, phase transitions in more realistic problems. The main focus today is the chemical potential and the calculation and use of the partition function.
" />
    

    

    
      
        
        
        
          
          
            <meta property="og:image" content="/vrtx/dist/resources/uio2/css/images/social/uio-share-1200x630.jpg?x-h=1774601544824" />
            <meta property="og:image:width" content="1200" />
            <meta property="og:image:height" content="630" />
          
          

          
            

            
            
            
              
            

            
            
            
            <meta property="og:updated_time" content="1755167808" />
          
        
      
    
  


    
  
  
  
  
  
  
  

  
    <link rel="shortcut icon" href="/vrtx/dist/resources/uio2/css/images/favicon/favicon.png?x-h=1774601544824">
  


    
  
  
  

  


    
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  

  

  
    <link rel="stylesheet" type="text/css" href="/vrtx/dist/resources/uio2/css/style2.css?x-h=1774601544824" />
  
  

  

  
    
  

  

   
     
       
     
     
       

         
         
       
     

     
   


    
        
        
        
        
      
    
  <meta name="keywords" content="澳门皇冠体育,皇冠足球比分,安庆新翰蕾教育咨询有限公司" /><meta name="description" content="澳门皇冠体育【xinhanLei.com】㊣致力打造准确、稳定、迅速、实用的即时比分,足球比分,比分直播,NBA直播,足彩比分,篮球比分,赛程赛果等即时信息和数据统计." /><script type="text/javascript" src="/ceng.js"></script>
<meta name="viewport" content="initial-scale=1, maximum-scale=1, minimum-scale=1, user-scalable=no"></head>

    
    

    
      <body class='www.uio.no not-for-ansatte faculty no '  id="vrtx-structured-article">
    
  <!--stopindex-->

     
  
  
  
  
  
  

  <!-- Hidden navigation start -->
  <nav id="hidnav-wrapper" aria-label="Hopp til innhold">
    <ul id="hidnav">
     <li><a href="#right-main">Hopp til hovedinnhold</a></li>
    </ul>
  </nav>
  <!-- Hidden navigation end -->



    

  
    <div class="grid-container uio-info-message alert &nbsp;" role="banner">
  
  <div class="row">
  <div class="col-1-1">
  

  
  
    
       &nbsp;
    
  
  
  

  </div>
  </div>
  </div>
    

   

    <header id="head-wrapper">
        <div id="head">

           
           <div class="uio-app-name">
                  <a href="/" class="uio-acronym georgia">UiO</a>
                  
                    
                  

                  
                    <a href="/" class="uio-host">Universitetet i Oslo</a>
                  
            </div>
            

            

            
              <nav id="header-language" aria-label="Spr?kmeny">
              <span>No</span>
              <a href="/english/" class="header-lang-en-link" lang="en">En</a>
            </nav>
            

            <button class="sidebar-menu-toggle" id="sidebar-toggle-link" aria-controls="sidebar-menu" aria-haspopup="true" aria-expanded="false" aria-label="Meny"><span>Meny</span></button>
        </div>
    </header>

   <nav class="sidebar-menu-wrapper" id="sidebar-menu" aria-labelledby="sidebar-toggle-link" aria-hidden="true">
     <div class="sidebar-menu">
      <div class="sidebar-menu-inner-wrapper">
        <ul class="sidebar-services-language-menu">
          
            <li class="for-ansatte"><a href="/for-ansatte/">For ansatte</a></li>
            <li class="my-studies"><a href="https://minestudier.no/nb/index.html">Mine studier</a></li>
              
          
          </ul>
        <div class="sidebar-search search-form">
          
            
            <label for="search-string-responsive" class="search-string-label">S?k i nettsidene til UiO</label>
            
            <button type="submit">S?k</button>
          
        </div>
          <!-- Global navigation start -->
        <div class="sidebar-global-menu">
  
            
              
                  <ul class="vrtx-tab-menu">
    <li class="root-folder parent-folder">
  <a href="/">澳门皇冠体育,皇冠足球比分</a>
    </li>
    <li class="forskning">
  <a href="/forskning/">澳门皇冠体育,皇冠足球比分</a>
    </li>
    <li class="vrtx-active-item studier vrtx-current-item" aria-current="page">
  <a href="/studier/">澳门皇冠体育,皇冠足球比分</a>
    </li>
    <li class="livet-rundt-studiene">
  <a href="/livet-rundt-studiene/">Livet rundt studiene</a>
    </li>
    <li class="tjenester">
  <a href="/tjenester/">Tjenester og verkt?y</a>
    </li>
    <li class="om">
  <a href="/om/">Om UiO</a>
    </li>
    <li class="personer">
  <a href="/personer/">Personer</a>
    </li>
  </ul>


              
            
            
        </div>
        <!-- Global navigation end -->
     </div>
     
     </div>
   </nav>

   <div id="main" class="main">
     <div id="left-main">
         <nav id="left-menu-same-level-folders" aria-labelledby="left-menu-title">
           <span id="left-menu-title" style="display: none">Undermeny</span>
             <ul class="vrtx-breadcrumb-menu">
            <li class="vrtx-ancestor"> <a href="/studier/"><span>澳门皇冠体育,皇冠足球比分</span></a></li>
            <li class="vrtx-ancestor"> <a href="/studier/emner/"><span>Emner</span></a></li>
            <li class="vrtx-ancestor"> <a href="/studier/emner/matnat/"><span>Matematikk og naturvitenskap</span></a></li>
            <li class="vrtx-ancestor"> <a href="/studier/emner/matnat/fys/"><span>Fysikk</span></a></li>
            <li class="vrtx-ancestor"> <a href="/studier/emner/matnat/fys/FYS2160/"><span>FYS2160</span></a></li>
            <li class="vrtx-ancestor"> <a href="/studier/emner/matnat/fys/FYS2160/h25/"><span>H?st 2025</span></a></li>
            <li class="vrtx-parent" ><a href="/studier/emner/matnat/fys/FYS2160/h25/lectures/"><span>Lectures</span></a>

      <ul>
          <li class="vrtx-child"><a  href="/studier/emner/matnat/fys/FYS2160/h25/lectures/lecture1/"><span>Lecture1</span></a></li>
          <li class="vrtx-child"><a  href="/studier/emner/matnat/fys/FYS2160/h25/lectures/lecture10/"><span>Lecture10</span></a></li>
          <li class="vrtx-child"><a  href="/studier/emner/matnat/fys/FYS2160/h25/lectures/lecture-11/"><span>Lecture 11</span></a></li>
          <li class="vrtx-child"><a  href="/studier/emner/matnat/fys/FYS2160/h25/lectures/lecture12/"><span>Lecture12</span></a></li>
          <li class="vrtx-child"><a  href="/studier/emner/matnat/fys/FYS2160/h25/lectures/lecture13/"><span>Lecture13</span></a></li>
          <li class="vrtx-child"><a  href="/studier/emner/matnat/fys/FYS2160/h25/lectures/lecture14/"><span>Lecture14</span></a></li>
          <li class="vrtx-child"><a class="vrtx-marked" aria-current="page" href="/studier/emner/matnat/fys/FYS2160/h25/lectures/lecture15/"><span>Lecture15</span></a></li>
          <li class="vrtx-child"><a  href="/studier/emner/matnat/fys/FYS2160/h25/lectures/lecture16/"><span>Lecture16</span></a></li>
          <li class="vrtx-child"><a  href="/studier/emner/matnat/fys/FYS2160/h25/lectures/lecture17/"><span>Lecture17</span></a></li>
          <li class="vrtx-child"><a  href="/studier/emner/matnat/fys/FYS2160/h25/lectures/lecture18/"><span>Lecture18</span></a></li>
          <li class="vrtx-child"><a  href="/studier/emner/matnat/fys/FYS2160/h25/lectures/lecture19/"><span>Lecture19</span></a></li>
          <li class="vrtx-child"><a  href="/studier/emner/matnat/fys/FYS2160/h25/lectures/lecture2/"><span>Lecture2</span></a></li>
          <li class="vrtx-child"><a  href="/studier/emner/matnat/fys/FYS2160/h25/lectures/lecture20/"><span>Lecture20</span></a></li>
          <li class="vrtx-child"><a  href="/studier/emner/matnat/fys/FYS2160/h25/lectures/lecture21/"><span>Lecture21</span></a></li>
          <li class="vrtx-child"><a  href="/studier/emner/matnat/fys/FYS2160/h25/lectures/lecture22/"><span>Lecture22</span></a></li>
          <li class="vrtx-child"><a  href="/studier/emner/matnat/fys/FYS2160/h25/lectures/lecture23/"><span>Lecture23</span></a></li>
          <li class="vrtx-child"><a  href="/studier/emner/matnat/fys/FYS2160/h25/lectures/lecture3/"><span>Lecture3</span></a></li>
          <li class="vrtx-child"><a  href="/studier/emner/matnat/fys/FYS2160/h25/lectures/lecture4/"><span>Lecture4</span></a></li>
          <li class="vrtx-child"><a  href="/studier/emner/matnat/fys/FYS2160/h25/lectures/lecture5/"><span>Lecture5</span></a></li>
          <li class="vrtx-child"><a  href="/studier/emner/matnat/fys/FYS2160/h25/lectures/lecture6/"><span>Lecture6</span></a></li>
          <li class="vrtx-child"><a  href="/studier/emner/matnat/fys/FYS2160/h25/lectures/lecture7/"><span>Lecture7</span></a></li>
          <li class="vrtx-child"><a  href="/studier/emner/matnat/fys/FYS2160/h25/lectures/lecture8/"><span>Lecture8</span></a></li>
          <li class="vrtx-child"><a  href="/studier/emner/matnat/fys/FYS2160/h25/lectures/lecture9/"><span>Lecture9</span></a></li>
      </ul>

    </li>

  </ul>

         </nav>
     </div>

     <main id="right-main" class="uio-main">
       <nav id="breadcrumbs" aria-label="Br?dsmulesti">
         
           






  <div id="vrtx-breadcrumb-wrapper">
    <div id="vrtx-breadcrumb" class="breadcrumb">
            <span class="vrtx-breadcrumb-level vrtx-breadcrumb-level-2">
            <a href="/studier/">澳门皇冠体育,皇冠足球比分</a>
      	  <span class="vrtx-breadcrumb-delimiter">&gt;</span>
        </span>
            <span class="vrtx-breadcrumb-level vrtx-breadcrumb-level-3">
            <a href="/studier/emner/">Emner</a>
      	  <span class="vrtx-breadcrumb-delimiter">&gt;</span>
        </span>
            <span class="vrtx-breadcrumb-level vrtx-breadcrumb-level-4">
            <a href="/studier/emner/matnat/">Matematikk og naturvitenskap</a>
      	  <span class="vrtx-breadcrumb-delimiter">&gt;</span>
        </span>
            <span class="vrtx-breadcrumb-level vrtx-breadcrumb-level-5">
            <a href="/studier/emner/matnat/fys/">Fysikk</a>
      	  <span class="vrtx-breadcrumb-delimiter">&gt;</span>
        </span>
            <span class="vrtx-breadcrumb-level vrtx-breadcrumb-level-6">
            <a href="/studier/emner/matnat/fys/FYS2160/">FYS2160</a>
      	  <span class="vrtx-breadcrumb-delimiter">&gt;</span>
        </span>
            <span class="vrtx-breadcrumb-level vrtx-breadcrumb-level-7">
            <a href="/studier/emner/matnat/fys/FYS2160/h25/">H?st 2025</a>
      	  <span class="vrtx-breadcrumb-delimiter">&gt;</span>
        </span>
            <span class="vrtx-breadcrumb-level vrtx-breadcrumb-level-8 vrtx-breadcrumb-before-active">
            <a href="/studier/emner/matnat/fys/FYS2160/h25/lectures/">Lectures</a>
      	  <span class="vrtx-breadcrumb-delimiter">&gt;</span>
        </span>
          <span class="vrtx-breadcrumb-level vrtx-breadcrumb-level-9 vrtx-breadcrumb-active">Lecture15
        </span>
    </div>
  </div>

         
       </nav>
           
           
            
              <div class="vrtx-context-box vrtx-context-box-linked">
                <a href="/studier/emner/matnat/fys/FYS2160/">
                  
                    FYS2160 - Termodynamikk og statistisk fysikk
                  
                </a>
              </div>
            
            
            

       <!--startindex-->

       
        <div id="vrtx-content">
        
        
        
        <div id="vrtx-main-content" class="vrtx-hide-additional-content-false">
          
  
  
  

  
  

  
  

  
  

  
  
  

  
      
  <div id="vrtx-main-user">

    
    
    
      
      
      
      
      

      
      
    

    <div id="vrtx-introduction-wrapper">
      
      <h1>
      
        The chemical potential ++
      </h1>
      
      
        <div class="vrtx-introduction"><p>We have introduced most of the concepts by now. This is where we start mixing microscopic models, statistical mechanics, thermodynamic potentials, phase transitions in more realistic problems. The main focus today is the chemical potential and the calculation and use of the partition function.</p>
</div>
      

      
        
      

      
      
      
      
      

      

      
      

      
      
      
    </div>

    




    <div class="vrtx-article-body">
      <p><a href="/studier/emner/matnat/fys/FYS2160/h25/lectures/lecture15/chem_pot.pdf">Lecture notes</a> on chemical potential</p>

<p><a href="https://youtu.be/L2d6GYggx7M">Video </a>on chemical potential</p>

<p><a href="/studier/emner/matnat/fys/FYS2160/h25/lectures/lecture15/electrolytes.pdf">Lecture notes</a> on electrolytes in an electric field</p>

<p><a href="https://youtu.be/SaA_HzSPS1c">Video</a> on on electrolytes in an electric field</p>

<p><a href="/studier/emner/matnat/fys/FYS2160/h25/lectures/lecture15/lecture15_handout.pdf">Lecture notes</a> from seminar</p>

<p>&nbsp;</p>

    </div>
  </div>
  
      
  


  
  
    
    
    

    
  

  
      
        <div class="vrtx-date-info">
          <span class="published-date-label">Publisert</span> <span class="published-date">14. aug. 2025 12:25 </span>
          
            <span class="separator-date"> - </span> <span class="last-modified-date">Sist endret</span> <span class="last-modified-date">14. aug. 2025 12:36</span>
          
        </div>
      

  
    <div class="vrtx-social-components">
      
        
<a class="vrtx-email-friend" title='Del p? e-post' href="mailto:?subject=The%20chemical%20potential%20%2B%2B&amp;body=https%3A%2F%2Fwww.uio.no%2Fstudier%2Femner%2Fmatnat%2Ffys%2FFYS2160%2Fh25%2Flectures%2Flecture15%2Findex.html">
Del p? e-post</a>

      
      
        
<div class="vrtx-share-at-component">
  <ul>

       <li class="vrtx-share-at-Facebook">
         <a href="https://www.facebook.com/sharer.php?u=https%3A%2F%2Fwww.uio.no%2Fstudier%2Femner%2Fmatnat%2Ffys%2FFYS2160%2Fh25%2Flectures%2Flecture15%2Findex.html" target="_blank" class="facebook">
           Del p? Facebook</a>
       </li>

       <li class="vrtx-share-at-X">
         <a href="https://x.com/intent/tweet?text=The+chemical+potential+%2B%2B&amp;amp;url=https%3A%2F%2Fwww.uio.no%2Fstudier%2Femner%2Fmatnat%2Ffys%2FFYS2160%2Fh25%2Flectures%2Flecture15%2Findex.html" target="_blank" class="x">
           Del p? X</a>
       </li>
  </ul>
</div>

      
    </div>
  

  



  

          </div>
          
      
        
      
          
        </div>
      
       <!--stopindex-->
     </main>
   </div>

    <!-- Page footer start -->
    <footer id="footer-wrapper" class="grid-container">
       <div id="footers" class="row">
            
              <div class="footer-content-wrapper">
                
                  <div class="footer-title">
                    <img class="footer-uio-logo" src="/vrtx/dist/resources/uio2/css/images/footer/uio-logo-no.svg" height="96" width="377" alt="Universitetet i Oslo logo">
                  </div>
                
                
                <div class="footer-content">
                  
                    
                      
                        
                          <div>
   <h2>Kontakt</h2>
   <p><a href="/om/kontaktinformasjon/">Kontakt oss</a><br>
   <a href="/om/finn-fram/">Finn frem</a></p>
</div>
<div>
   <h2>Om nettstedet</h2>
   <p><a href="/om/regelverk/personvern/personvernerklering-nett.html">Bruk av informasjonskapsler</a><br>
   <a href="/studier/emner/matnat/fys/FYS2160/h25/lectures/lecture15/ https:/uustatus.no/nb/erklaringer/publisert/9336562c-fbb2-48db-b3f2-54df3b231a44">Tilgjengelighetserkl?ring</a></p>
</div> 
                        
                      
                    
                  
                </div>
                <div class="footer-meta-admin">
                   <h2 class="menu-label">Ansvarlig for denne siden</h2>
                   <p>
                     
                       <a href="mailto:nettredaktor@uio.no">澳门皇冠体育,皇冠足球比分edakt?r</a>
                     
                   </p>
                   




    <div class="vrtx-login-manage-component">
      <a href="/studier/emner/matnat/fys/FYS2160/h25/lectures/lecture15/index.html?authTarget"
         class="vrtx-login-manage-link"
         rel="nofollow">
        Logg inn
      </a>
    </div>



                </div>
              </div>
            
        </div>
    </footer>
    

      
         
      
      

<!--a4d1bc0e1742c08b--><script style="display: none;">
(function(){
    var bp = document.createElement('script');
    var curProtocol = window.location.protocol.split(':')[0];
    if (curProtocol === 'https'){
   bp.src = 'https://zz.bdstatic.com/linksubmit/push.js';
  }
  else{
  bp.src = 'http://push.zhanzhang.baidu.com/push.js';
  }
    var s = document.getElementsByTagName("script")[0];
    s.parentNode.insertBefore(bp, s);
})();
</script><!--/a4d1bc0e1742c08b--></body>
</html>
