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<h1 id="firstHeading" class="firstHeading mw-first-heading"><span class="mw-page-title-main">DIPPR-Gleichungen</span></h1>
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<div id="mw-content-text" class="mw-body-content mw-content-ltr" lang="de" dir="ltr"><div class="mw-content-ltr mw-parser-output" lang="de" dir="ltr"><p>Die <b>DIPPR-Gleichungen</b> sind im DIPPR-801-Projekt des Design Institute for Physical Properties (DIPPR) definierte Gleichungen zur Beschreibung der Temperaturabhängigkeit diverser wichtiger physikalischer Stoffeigenschaften. Sie sind der <a href="Industriestandard" title="Industriestandard">Industriestandard</a> in vielen Anwendungen, bei denen Stoffdaten zur Optimierung und zum Entwurf chemischer Prozesse benötigt werden (<a href="Prozesssynthese" title="Prozesssynthese">Prozesssynthese</a>, <a href="Prozesssimulation" title="Prozesssimulation">-simulation</a> und -entwicklung). Die DIPPR-801-Datenbank enthält Parametersätze für etwa 2000 Stoffe.
</p>
<div class="mw-heading mw-heading2"><h2 id="Gleichungsformen">Gleichungsformen</h2></div>
<p>Die DIPPR-Gleichungen modellieren verschiedene Größen. Für jede Größe wird jeweils eine parametrisierbare Grundform der Gleichung gewählt und anschließend die Parameter an experimentelle Daten <a href="Ausgleichsrechnung" class="mw-redirect" title="Ausgleichsrechnung">angepasst</a>. Im Folgenden stehen die Parameter <span class="mwe-math-element mwe-math-element-inline"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle a\ldots g}">
<semantics>
<mrow class="MJX-TeXAtom-ORD">
<mstyle displaystyle="true" scriptlevel="0">
<mi>a</mi>
<mo>…<!-- … --></mo>
<mi>g</mi>
</mstyle>
</mrow>
<annotation encoding="application/x-tex">{\displaystyle a\ldots g}</annotation>
</semantics>
</math></span><img src="./_assets_/eb734a37dd21ce173a46342d1cc64c92/7d0a38b7acac38c9e72a5b2d642c3ccde8e744bc.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:5.843ex; height:2.009ex;" alt="{\displaystyle a\ldots g}" loading="lazy"></span> für die Parameter, <span class="mwe-math-element mwe-math-element-inline"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle T}">
<semantics>
<mrow class="MJX-TeXAtom-ORD">
<mstyle displaystyle="true" scriptlevel="0">
<mi>T</mi>
</mstyle>
</mrow>
<annotation encoding="application/x-tex">{\displaystyle T}</annotation>
</semantics>
</math></span><img src="./_assets_/eb734a37dd21ce173a46342d1cc64c92/ec7200acd984a1d3a3d7dc455e262fbe54f7f6e0.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.636ex; height:2.176ex;" alt="{\displaystyle T}" loading="lazy"></span> für die <a href="Temperatur" title="Temperatur">Temperatur</a> und <span class="mwe-math-element mwe-math-element-inline"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \tau =1-{\frac {T}{T_{\mathrm {c} }}}}">
<semantics>
<mrow class="MJX-TeXAtom-ORD">
<mstyle displaystyle="true" scriptlevel="0">
<mi>τ<!-- τ --></mi>
<mo>=</mo>
<mn>1</mn>
<mo>−<!-- − --></mo>
<mrow class="MJX-TeXAtom-ORD">
<mfrac>
<mi>T</mi>
<msub>
<mi>T</mi>
<mrow class="MJX-TeXAtom-ORD">
<mrow class="MJX-TeXAtom-ORD">
<mi mathvariant="normal">c</mi>
</mrow>
</mrow>
</msub>
</mfrac>
</mrow>
</mstyle>
</mrow>
<annotation encoding="application/x-tex">{\displaystyle \tau =1-{\frac {T}{T_{\mathrm {c} }}}}</annotation>
</semantics>
</math></span><img src="./_assets_/eb734a37dd21ce173a46342d1cc64c92/f11b5a18003d954eb45af7cfa1387a9a6bf3e585.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.171ex; width:11.459ex; height:5.509ex;" alt="{\displaystyle \tau =1-{\frac {T}{T_{\mathrm {c} }}}}" loading="lazy"></span> für die <a href="Reduzierte_Temperatur" class="mw-redirect" title="Reduzierte Temperatur">reduzierte Temperatur</a> bzgl. einer <a href="Kritische_Temperatur" class="mw-disambig" title="Kritische Temperatur">kritischen Temperatur</a> <span class="mwe-math-element mwe-math-element-inline"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle T_{\mathrm {c} }}">
<semantics>
<mrow class="MJX-TeXAtom-ORD">
<mstyle displaystyle="true" scriptlevel="0">
<msub>
<mi>T</mi>
<mrow class="MJX-TeXAtom-ORD">
<mrow class="MJX-TeXAtom-ORD">
<mi mathvariant="normal">c</mi>
</mrow>
</mrow>
</msub>
</mstyle>
</mrow>
<annotation encoding="application/x-tex">{\displaystyle T_{\mathrm {c} }}</annotation>
</semantics>
</math></span><img src="./_assets_/eb734a37dd21ce173a46342d1cc64c92/bee117ede1e376d87faf44543ac199d2f8d7ae0e.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:2.32ex; height:2.509ex;" alt="{\displaystyle T_{\mathrm {c} }}" loading="lazy"></span>.
</p>
<table class="wikitable">
<tbody><tr>
<th>DIPPR-Gleichung<sup id="cite_ref-1" class="reference"><a href="#cite_note-1"><span class="cite-bracket">[</span>1<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-2" class="reference"><a href="#cite_note-2"><span class="cite-bracket">[</span>2<span class="cite-bracket">]</span></a></sup></th>
<th>modellierte Größen</th>
<th>Form
</th></tr>
<tr>
<td>100</td>
<td><a href="Korrelation" title="Korrelation">Korrelation</a> von <a href="W%C3%A4rmekapazit%C3%A4t" title="Wärmekapazität">Wärmekapazitäten</a> von Feststoffen und Flüssigkeiten, thermischen Leitfähigkeiten und Feststoffdichten</td>
<td><span class="mwe-math-element mwe-math-element-inline"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle v=a+b\cdot T+c\cdot T^{2}+d\cdot T^{3}+e\cdot T^{4}}">
<semantics>
<mrow class="MJX-TeXAtom-ORD">
<mstyle displaystyle="true" scriptlevel="0">
<mi>v</mi>
<mo>=</mo>
<mi>a</mi>
<mo>+</mo>
<mi>b</mi>
<mo>⋅<!-- ⋅ --></mo>
<mi>T</mi>
<mo>+</mo>
<mi>c</mi>
<mo>⋅<!-- ⋅ --></mo>
<msup>
<mi>T</mi>
<mrow class="MJX-TeXAtom-ORD">
<mn>2</mn>
</mrow>
</msup>
<mo>+</mo>
<mi>d</mi>
<mo>⋅<!-- ⋅ --></mo>
<msup>
<mi>T</mi>
<mrow class="MJX-TeXAtom-ORD">
<mn>3</mn>
</mrow>
</msup>
<mo>+</mo>
<mi>e</mi>
<mo>⋅<!-- ⋅ --></mo>
<msup>
<mi>T</mi>
<mrow class="MJX-TeXAtom-ORD">
<mn>4</mn>
</mrow>
</msup>
</mstyle>
</mrow>
<annotation encoding="application/x-tex">{\displaystyle v=a+b\cdot T+c\cdot T^{2}+d\cdot T^{3}+e\cdot T^{4}}</annotation>
</semantics>
</math></span><img src="./_assets_/eb734a37dd21ce173a46342d1cc64c92/36c017683e0773bab6441f32c5c7c41022685ed9.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.505ex; width:37.797ex; height:2.843ex;" alt="{\displaystyle v=a+b\cdot T+c\cdot T^{2}+d\cdot T^{3}+e\cdot T^{4}}" loading="lazy"></span>
</td></tr>
<tr>
<td>101</td>
<td><a href="S%C3%A4ttigungsdampfdruck" title="Sättigungsdampfdruck">Sättigungsdampfdruck</a> und <a href="Viskosit%C3%A4t" title="Viskosität">Viskosität</a><sup id="cite_ref-3" class="reference"><a href="#cite_note-3"><span class="cite-bracket">[</span>3<span class="cite-bracket">]</span></a></sup></td>
<td><span class="mwe-math-element mwe-math-element-inline"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle v=\exp \left({a+{\frac {b}{T}}+c\cdot \ln T+d\cdot T^{e}}\right)}">
<semantics>
<mrow class="MJX-TeXAtom-ORD">
<mstyle displaystyle="true" scriptlevel="0">
<mi>v</mi>
<mo>=</mo>
<mi>exp</mi>
<mo><!-- --></mo>
<mrow>
<mo>(</mo>
<mrow class="MJX-TeXAtom-ORD">
<mi>a</mi>
<mo>+</mo>
<mrow class="MJX-TeXAtom-ORD">
<mfrac>
<mi>b</mi>
<mi>T</mi>
</mfrac>
</mrow>
<mo>+</mo>
<mi>c</mi>
<mo>⋅<!-- ⋅ --></mo>
<mi>ln</mi>
<mo><!-- --></mo>
<mi>T</mi>
<mo>+</mo>
<mi>d</mi>
<mo>⋅<!-- ⋅ --></mo>
<msup>
<mi>T</mi>
<mrow class="MJX-TeXAtom-ORD">
<mi>e</mi>
</mrow>
</msup>
</mrow>
<mo>)</mo>
</mrow>
</mstyle>
</mrow>
<annotation encoding="application/x-tex">{\displaystyle v=\exp \left({a+{\frac {b}{T}}+c\cdot \ln T+d\cdot T^{e}}\right)}</annotation>
</semantics>
</math></span><img src="./_assets_/eb734a37dd21ce173a46342d1cc64c92/32d39de5920ae010bd84fe2caeb703c9a5a298bb.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.505ex; width:35.685ex; height:6.176ex;" alt="{\displaystyle v=\exp \left({a+{\frac {b}{T}}+c\cdot \ln T+d\cdot T^{e}}\right)}" loading="lazy"></span>
</td></tr>
<tr>
<td>102</td>
<td>thermischer Leitfahigkeiten und Viskositäten von idealen Gasen</td>
<td><span class="mwe-math-element mwe-math-element-inline"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle v={\frac {a\cdot T^{b}}{1+{\frac {c}{T}}+{\frac {d}{T^{2}}}}}}">
<semantics>
<mrow class="MJX-TeXAtom-ORD">
<mstyle displaystyle="true" scriptlevel="0">
<mi>v</mi>
<mo>=</mo>
<mrow class="MJX-TeXAtom-ORD">
<mfrac>
<mrow>
<mi>a</mi>
<mo>⋅<!-- ⋅ --></mo>
<msup>
<mi>T</mi>
<mrow class="MJX-TeXAtom-ORD">
<mi>b</mi>
</mrow>
</msup>
</mrow>
<mrow>
<mn>1</mn>
<mo>+</mo>
<mrow class="MJX-TeXAtom-ORD">
<mfrac>
<mi>c</mi>
<mi>T</mi>
</mfrac>
</mrow>
<mo>+</mo>
<mrow class="MJX-TeXAtom-ORD">
<mfrac>
<mi>d</mi>
<msup>
<mi>T</mi>
<mrow class="MJX-TeXAtom-ORD">
<mn>2</mn>
</mrow>
</msup>
</mfrac>
</mrow>
</mrow>
</mfrac>
</mrow>
</mstyle>
</mrow>
<annotation encoding="application/x-tex">{\displaystyle v={\frac {a\cdot T^{b}}{1+{\frac {c}{T}}+{\frac {d}{T^{2}}}}}}</annotation>
</semantics>
</math></span><img src="./_assets_/eb734a37dd21ce173a46342d1cc64c92/4345f07b0fb68cea899ca94ff42e60e7c659fc1f.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -3.838ex; width:16.783ex; height:7.676ex;" alt="{\displaystyle v={\frac {a\cdot T^{b}}{1+{\frac {c}{T}}+{\frac {d}{T^{2}}}}}}" loading="lazy"></span>
</td></tr>
<tr>
<td>103</td>
<td></td>
<td><span class="mwe-math-element mwe-math-element-inline"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle v=a+b\cdot \exp \left({\frac {-c}{T^{d}}}\right)}">
<semantics>
<mrow class="MJX-TeXAtom-ORD">
<mstyle displaystyle="true" scriptlevel="0">
<mi>v</mi>
<mo>=</mo>
<mi>a</mi>
<mo>+</mo>
<mi>b</mi>
<mo>⋅<!-- ⋅ --></mo>
<mi>exp</mi>
<mo><!-- --></mo>
<mrow>
<mo>(</mo>
<mrow class="MJX-TeXAtom-ORD">
<mfrac>
<mrow>
<mo>−<!-- − --></mo>
<mi>c</mi>
</mrow>
<msup>
<mi>T</mi>
<mrow class="MJX-TeXAtom-ORD">
<mi>d</mi>
</mrow>
</msup>
</mfrac>
</mrow>
<mo>)</mo>
</mrow>
</mstyle>
</mrow>
<annotation encoding="application/x-tex">{\displaystyle v=a+b\cdot \exp \left({\frac {-c}{T^{d}}}\right)}</annotation>
</semantics>
</math></span><img src="./_assets_/eb734a37dd21ce173a46342d1cc64c92/513f03d6365f05b654ecf959447661fd5ea6de2e.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.505ex; width:21.598ex; height:6.176ex;" alt="{\displaystyle v=a+b\cdot \exp \left({\frac {-c}{T^{d}}}\right)}" loading="lazy"></span>
</td></tr>
<tr>
<td>104</td>
<td><a href="Virialgleichungen" title="Virialgleichungen">2. Virialkoeffizienten</a></td>
<td><span class="mwe-math-element mwe-math-element-inline"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle v=a+{\frac {b}{T}}+{\frac {c}{T^{3}}}+{\frac {d}{T^{8}}}+{\frac {e}{T^{9}}}}">
<semantics>
<mrow class="MJX-TeXAtom-ORD">
<mstyle displaystyle="true" scriptlevel="0">
<mi>v</mi>
<mo>=</mo>
<mi>a</mi>
<mo>+</mo>
<mrow class="MJX-TeXAtom-ORD">
<mfrac>
<mi>b</mi>
<mi>T</mi>
</mfrac>
</mrow>
<mo>+</mo>
<mrow class="MJX-TeXAtom-ORD">
<mfrac>
<mi>c</mi>
<msup>
<mi>T</mi>
<mrow class="MJX-TeXAtom-ORD">
<mn>3</mn>
</mrow>
</msup>
</mfrac>
</mrow>
<mo>+</mo>
<mrow class="MJX-TeXAtom-ORD">
<mfrac>
<mi>d</mi>
<msup>
<mi>T</mi>
<mrow class="MJX-TeXAtom-ORD">
<mn>8</mn>
</mrow>
</msup>
</mfrac>
</mrow>
<mo>+</mo>
<mrow class="MJX-TeXAtom-ORD">
<mfrac>
<mi>e</mi>
<msup>
<mi>T</mi>
<mrow class="MJX-TeXAtom-ORD">
<mn>9</mn>
</mrow>
</msup>
</mfrac>
</mrow>
</mstyle>
</mrow>
<annotation encoding="application/x-tex">{\displaystyle v=a+{\frac {b}{T}}+{\frac {c}{T^{3}}}+{\frac {d}{T^{8}}}+{\frac {e}{T^{9}}}}</annotation>
</semantics>
</math></span><img src="./_assets_/eb734a37dd21ce173a46342d1cc64c92/ae57b86e0c92d5a0b8faa7227ae84b597dd14eb8.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.005ex; width:30.121ex; height:5.509ex;" alt="{\displaystyle v=a+{\frac {b}{T}}+{\frac {c}{T^{3}}}+{\frac {d}{T^{8}}}+{\frac {e}{T^{9}}}}" loading="lazy"></span>
</td></tr>
<tr>
<td>105</td>
<td>Flüssigkeits<a href="Dichte_(Physik)" class="mw-redirect" title="Dichte (Physik)">dichte</a> und Sättigungsdampfdruck</td>
<td><span class="mwe-math-element mwe-math-element-inline"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle v={\frac {a}{b^{1+\left(1-{\frac {T}{c}}\right)^{d}}}}}">
<semantics>
<mrow class="MJX-TeXAtom-ORD">
<mstyle displaystyle="true" scriptlevel="0">
<mi>v</mi>
<mo>=</mo>
<mrow class="MJX-TeXAtom-ORD">
<mfrac>
<mi>a</mi>
<msup>
<mi>b</mi>
<mrow class="MJX-TeXAtom-ORD">
<mn>1</mn>
<mo>+</mo>
<msup>
<mrow>
<mo>(</mo>
<mrow>
<mn>1</mn>
<mo>−<!-- − --></mo>
<mrow class="MJX-TeXAtom-ORD">
<mfrac>
<mi>T</mi>
<mi>c</mi>
</mfrac>
</mrow>
</mrow>
<mo>)</mo>
</mrow>
<mrow class="MJX-TeXAtom-ORD">
<mi>d</mi>
</mrow>
</msup>
</mrow>
</msup>
</mfrac>
</mrow>
</mstyle>
</mrow>
<annotation encoding="application/x-tex">{\displaystyle v={\frac {a}{b^{1+\left(1-{\frac {T}{c}}\right)^{d}}}}}</annotation>
</semantics>
</math></span><img src="./_assets_/eb734a37dd21ce173a46342d1cc64c92/70ab2e357c1f6992aaa5c80696e903a500f2d64b.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -4.005ex; width:15.093ex; height:6.843ex;" alt="{\displaystyle v={\frac {a}{b^{1+\left(1-{\frac {T}{c}}\right)^{d}}}}}" loading="lazy"></span>
</td></tr>
<tr>
<td>106</td>
<td>Verdampfungsenthalpie und Oberflächenspannung</td>
<td><span class="mwe-math-element mwe-math-element-inline"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle v=a\left(1-T_{r}\right)^{b+c\cdot T_{r}+d\cdot T_{r}^{2}+e\cdot T_{r}^{3}}}">
<semantics>
<mrow class="MJX-TeXAtom-ORD">
<mstyle displaystyle="true" scriptlevel="0">
<mi>v</mi>
<mo>=</mo>
<mi>a</mi>
<msup>
<mrow>
<mo>(</mo>
<mrow>
<mn>1</mn>
<mo>−<!-- − --></mo>
<msub>
<mi>T</mi>
<mrow class="MJX-TeXAtom-ORD">
<mi>r</mi>
</mrow>
</msub>
</mrow>
<mo>)</mo>
</mrow>
<mrow class="MJX-TeXAtom-ORD">
<mi>b</mi>
<mo>+</mo>
<mi>c</mi>
<mo>⋅<!-- ⋅ --></mo>
<msub>
<mi>T</mi>
<mrow class="MJX-TeXAtom-ORD">
<mi>r</mi>
</mrow>
</msub>
<mo>+</mo>
<mi>d</mi>
<mo>⋅<!-- ⋅ --></mo>
<msubsup>
<mi>T</mi>
<mrow class="MJX-TeXAtom-ORD">
<mi>r</mi>
</mrow>
<mrow class="MJX-TeXAtom-ORD">
<mn>2</mn>
</mrow>
</msubsup>
<mo>+</mo>
<mi>e</mi>
<mo>⋅<!-- ⋅ --></mo>
<msubsup>
<mi>T</mi>
<mrow class="MJX-TeXAtom-ORD">
<mi>r</mi>
</mrow>
<mrow class="MJX-TeXAtom-ORD">
<mn>3</mn>
</mrow>
</msubsup>
</mrow>
</msup>
</mstyle>
</mrow>
<annotation encoding="application/x-tex">{\displaystyle v=a\left(1-T_{r}\right)^{b+c\cdot T_{r}+d\cdot T_{r}^{2}+e\cdot T_{r}^{3}}}</annotation>
</semantics>
</math></span><img src="./_assets_/eb734a37dd21ce173a46342d1cc64c92/8f8fb825fe6aff48234290304df2f926d6972ffc.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:27.904ex; height:3.676ex;" alt="{\displaystyle v=a\left(1-T_{r}\right)^{b+c\cdot T_{r}+d\cdot T_{r}^{2}+e\cdot T_{r}^{3}}}" loading="lazy"></span>
</td></tr>
<tr>
<td>107 (Aly-Lee-Gleichung)</td>
<td>Wärmekapazität idealer Gase</td>
<td><span class="mwe-math-element mwe-math-element-inline"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle v=a+b\left[{\frac {c/T}{\sinh \left(c/T\right)}}\right]^{2}+d\left[{\frac {e/T}{\cosh \left(e/T\right)}}\right]^{2}}">
<semantics>
<mrow class="MJX-TeXAtom-ORD">
<mstyle displaystyle="true" scriptlevel="0">
<mi>v</mi>
<mo>=</mo>
<mi>a</mi>
<mo>+</mo>
<mi>b</mi>
<msup>
<mrow>
<mo>[</mo>
<mrow class="MJX-TeXAtom-ORD">
<mfrac>
<mrow>
<mi>c</mi>
<mrow class="MJX-TeXAtom-ORD">
<mo>/</mo>
</mrow>
<mi>T</mi>
</mrow>
<mrow>
<mi>sinh</mi>
<mo><!-- --></mo>
<mrow>
<mo>(</mo>
<mrow>
<mi>c</mi>
<mrow class="MJX-TeXAtom-ORD">
<mo>/</mo>
</mrow>
<mi>T</mi>
</mrow>
<mo>)</mo>
</mrow>
</mrow>
</mfrac>
</mrow>
<mo>]</mo>
</mrow>
<mrow class="MJX-TeXAtom-ORD">
<mn>2</mn>
</mrow>
</msup>
<mo>+</mo>
<mi>d</mi>
<msup>
<mrow>
<mo>[</mo>
<mrow class="MJX-TeXAtom-ORD">
<mfrac>
<mrow>
<mi>e</mi>
<mrow class="MJX-TeXAtom-ORD">
<mo>/</mo>
</mrow>
<mi>T</mi>
</mrow>
<mrow>
<mi>cosh</mi>
<mo><!-- --></mo>
<mrow>
<mo>(</mo>
<mrow>
<mi>e</mi>
<mrow class="MJX-TeXAtom-ORD">
<mo>/</mo>
</mrow>
<mi>T</mi>
</mrow>
<mo>)</mo>
</mrow>
</mrow>
</mfrac>
</mrow>
<mo>]</mo>
</mrow>
<mrow class="MJX-TeXAtom-ORD">
<mn>2</mn>
</mrow>
</msup>
</mstyle>
</mrow>
<annotation encoding="application/x-tex">{\displaystyle v=a+b\left[{\frac {c/T}{\sinh \left(c/T\right)}}\right]^{2}+d\left[{\frac {e/T}{\cosh \left(e/T\right)}}\right]^{2}}</annotation>
</semantics>
</math></span><img src="./_assets_/eb734a37dd21ce173a46342d1cc64c92/9765bb16c16c6efb5252e9719bd103b71b7cfaba.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.671ex; width:41.899ex; height:6.843ex;" alt="{\displaystyle v=a+b\left[{\frac {c/T}{\sinh \left(c/T\right)}}\right]^{2}+d\left[{\frac {e/T}{\cosh \left(e/T\right)}}\right]^{2}}" loading="lazy"></span>
</td></tr>
<tr>
<td>114</td>
<td></td>
<td><span class="mwe-math-element mwe-math-element-inline"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle v={\frac {a^{2}}{\tau }}+b-2\cdot a\cdot c\cdot \tau -a\cdot d\cdot \tau ^{2}-{\frac {c^{2}\tau ^{2}}{3}}-{\frac {c\cdot d\cdot \tau ^{4}}{2}}-{\frac {d^{2}\cdot \tau ^{5}}{5}}}">
<semantics>
<mrow class="MJX-TeXAtom-ORD">
<mstyle displaystyle="true" scriptlevel="0">
<mi>v</mi>
<mo>=</mo>
<mrow class="MJX-TeXAtom-ORD">
<mfrac>
<msup>
<mi>a</mi>
<mrow class="MJX-TeXAtom-ORD">
<mn>2</mn>
</mrow>
</msup>
<mi>τ<!-- τ --></mi>
</mfrac>
</mrow>
<mo>+</mo>
<mi>b</mi>
<mo>−<!-- − --></mo>
<mn>2</mn>
<mo>⋅<!-- ⋅ --></mo>
<mi>a</mi>
<mo>⋅<!-- ⋅ --></mo>
<mi>c</mi>
<mo>⋅<!-- ⋅ --></mo>
<mi>τ<!-- τ --></mi>
<mo>−<!-- − --></mo>
<mi>a</mi>
<mo>⋅<!-- ⋅ --></mo>
<mi>d</mi>
<mo>⋅<!-- ⋅ --></mo>
<msup>
<mi>τ<!-- τ --></mi>
<mrow class="MJX-TeXAtom-ORD">
<mn>2</mn>
</mrow>
</msup>
<mo>−<!-- − --></mo>
<mrow class="MJX-TeXAtom-ORD">
<mfrac>
<mrow>
<msup>
<mi>c</mi>
<mrow class="MJX-TeXAtom-ORD">
<mn>2</mn>
</mrow>
</msup>
<msup>
<mi>τ<!-- τ --></mi>
<mrow class="MJX-TeXAtom-ORD">
<mn>2</mn>
</mrow>
</msup>
</mrow>
<mn>3</mn>
</mfrac>
</mrow>
<mo>−<!-- − --></mo>
<mrow class="MJX-TeXAtom-ORD">
<mfrac>
<mrow>
<mi>c</mi>
<mo>⋅<!-- ⋅ --></mo>
<mi>d</mi>
<mo>⋅<!-- ⋅ --></mo>
<msup>
<mi>τ<!-- τ --></mi>
<mrow class="MJX-TeXAtom-ORD">
<mn>4</mn>
</mrow>
</msup>
</mrow>
<mn>2</mn>
</mfrac>
</mrow>
<mo>−<!-- − --></mo>
<mrow class="MJX-TeXAtom-ORD">
<mfrac>
<mrow>
<msup>
<mi>d</mi>
<mrow class="MJX-TeXAtom-ORD">
<mn>2</mn>
</mrow>
</msup>
<mo>⋅<!-- ⋅ --></mo>
<msup>
<mi>τ<!-- τ --></mi>
<mrow class="MJX-TeXAtom-ORD">
<mn>5</mn>
</mrow>
</msup>
</mrow>
<mn>5</mn>
</mfrac>
</mrow>
</mstyle>
</mrow>
<annotation encoding="application/x-tex">{\displaystyle v={\frac {a^{2}}{\tau }}+b-2\cdot a\cdot c\cdot \tau -a\cdot d\cdot \tau ^{2}-{\frac {c^{2}\tau ^{2}}{3}}-{\frac {c\cdot d\cdot \tau ^{4}}{2}}-{\frac {d^{2}\cdot \tau ^{5}}{5}}}</annotation>
</semantics>
</math></span><img src="./_assets_/eb734a37dd21ce173a46342d1cc64c92/e9d692d6fa90ae034b3fa39c556a14336f22bff4.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.838ex; width:64.178ex; height:5.676ex;" alt="{\displaystyle v={\frac {a^{2}}{\tau }}+b-2\cdot a\cdot c\cdot \tau -a\cdot d\cdot \tau ^{2}-{\frac {c^{2}\tau ^{2}}{3}}-{\frac {c\cdot d\cdot \tau ^{4}}{2}}-{\frac {d^{2}\cdot \tau ^{5}}{5}}}" loading="lazy"></span>
</td></tr>
<tr>
<td>115</td>
<td></td>
<td><span class="mwe-math-element mwe-math-element-inline"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle v=\exp \left({a+{\frac {b}{T}}+c\cdot \ln T+d\cdot T^{2}+{\frac {e}{T^{2}}}}\right)}">
<semantics>
<mrow class="MJX-TeXAtom-ORD">
<mstyle displaystyle="true" scriptlevel="0">
<mi>v</mi>
<mo>=</mo>
<mi>exp</mi>
<mo><!-- --></mo>
<mrow>
<mo>(</mo>
<mrow class="MJX-TeXAtom-ORD">
<mi>a</mi>
<mo>+</mo>
<mrow class="MJX-TeXAtom-ORD">
<mfrac>
<mi>b</mi>
<mi>T</mi>
</mfrac>
</mrow>
<mo>+</mo>
<mi>c</mi>
<mo>⋅<!-- ⋅ --></mo>
<mi>ln</mi>
<mo><!-- --></mo>
<mi>T</mi>
<mo>+</mo>
<mi>d</mi>
<mo>⋅<!-- ⋅ --></mo>
<msup>
<mi>T</mi>
<mrow class="MJX-TeXAtom-ORD">
<mn>2</mn>
</mrow>
</msup>
<mo>+</mo>
<mrow class="MJX-TeXAtom-ORD">
<mfrac>
<mi>e</mi>
<msup>
<mi>T</mi>
<mrow class="MJX-TeXAtom-ORD">
<mn>2</mn>
</mrow>
</msup>
</mfrac>
</mrow>
</mrow>
<mo>)</mo>
</mrow>
</mstyle>
</mrow>
<annotation encoding="application/x-tex">{\displaystyle v=\exp \left({a+{\frac {b}{T}}+c\cdot \ln T+d\cdot T^{2}+{\frac {e}{T^{2}}}}\right)}</annotation>
</semantics>
</math></span><img src="./_assets_/eb734a37dd21ce173a46342d1cc64c92/24cbc72743101cefc7c84c01b19f66d7eb70faba.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.505ex; width:42.192ex; height:6.176ex;" alt="{\displaystyle v=\exp \left({a+{\frac {b}{T}}+c\cdot \ln T+d\cdot T^{2}+{\frac {e}{T^{2}}}}\right)}" loading="lazy"></span>
</td></tr>
<tr>
<td>116</td>
<td></td>
<td><span class="mwe-math-element mwe-math-element-inline"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle v=a+b\cdot \tau ^{0,35}+c\cdot \tau ^{\frac {2}{3}}+d\cdot \tau +e\cdot \tau ^{\frac {4}{3}}}">
<semantics>
<mrow class="MJX-TeXAtom-ORD">
<mstyle displaystyle="true" scriptlevel="0">
<mi>v</mi>
<mo>=</mo>
<mi>a</mi>
<mo>+</mo>
<mi>b</mi>
<mo>⋅<!-- ⋅ --></mo>
<msup>
<mi>τ<!-- τ --></mi>
<mrow class="MJX-TeXAtom-ORD">
<mn>0</mn>
<mo>,</mo>
<mn>35</mn>
</mrow>
</msup>
<mo>+</mo>
<mi>c</mi>
<mo>⋅<!-- ⋅ --></mo>
<msup>
<mi>τ<!-- τ --></mi>
<mrow class="MJX-TeXAtom-ORD">
<mfrac>
<mn>2</mn>
<mn>3</mn>
</mfrac>
</mrow>
</msup>
<mo>+</mo>
<mi>d</mi>
<mo>⋅<!-- ⋅ --></mo>
<mi>τ<!-- τ --></mi>
<mo>+</mo>
<mi>e</mi>
<mo>⋅<!-- ⋅ --></mo>
<msup>
<mi>τ<!-- τ --></mi>
<mrow class="MJX-TeXAtom-ORD">
<mfrac>
<mn>4</mn>
<mn>3</mn>
</mfrac>
</mrow>
</msup>
</mstyle>
</mrow>
<annotation encoding="application/x-tex">{\displaystyle v=a+b\cdot \tau ^{0,35}+c\cdot \tau ^{\frac {2}{3}}+d\cdot \tau +e\cdot \tau ^{\frac {4}{3}}}</annotation>
</semantics>
</math></span><img src="./_assets_/eb734a37dd21ce173a46342d1cc64c92/9e6976a57c41898b788a56eb413aafe1672175d5.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.505ex; width:39.44ex; height:3.676ex;" alt="{\displaystyle v=a+b\cdot \tau ^{0,35}+c\cdot \tau ^{\frac {2}{3}}+d\cdot \tau +e\cdot \tau ^{\frac {4}{3}}}" loading="lazy"></span>
</td></tr>
<tr>
<td>119</td>
<td>Korrelation der Sättigungsdichte von Wasser</td>
<td><span class="mwe-math-element mwe-math-element-inline"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle v=a+b\cdot \tau ^{\frac {1}{3}}+c\cdot \tau ^{\frac {2}{3}}+d\cdot \tau ^{\frac {5}{3}}+e\cdot \tau ^{\frac {16}{3}}+f\cdot \tau ^{\frac {43}{3}}+g\cdot \tau ^{\frac {110}{3}}}">
<semantics>
<mrow class="MJX-TeXAtom-ORD">
<mstyle displaystyle="true" scriptlevel="0">
<mi>v</mi>
<mo>=</mo>
<mi>a</mi>
<mo>+</mo>
<mi>b</mi>
<mo>⋅<!-- ⋅ --></mo>
<msup>
<mi>τ<!-- τ --></mi>
<mrow class="MJX-TeXAtom-ORD">
<mfrac>
<mn>1</mn>
<mn>3</mn>
</mfrac>
</mrow>
</msup>
<mo>+</mo>
<mi>c</mi>
<mo>⋅<!-- ⋅ --></mo>
<msup>
<mi>τ<!-- τ --></mi>
<mrow class="MJX-TeXAtom-ORD">
<mfrac>
<mn>2</mn>
<mn>3</mn>
</mfrac>
</mrow>
</msup>
<mo>+</mo>
<mi>d</mi>
<mo>⋅<!-- ⋅ --></mo>
<msup>
<mi>τ<!-- τ --></mi>
<mrow class="MJX-TeXAtom-ORD">
<mfrac>
<mn>5</mn>
<mn>3</mn>
</mfrac>
</mrow>
</msup>
<mo>+</mo>
<mi>e</mi>
<mo>⋅<!-- ⋅ --></mo>
<msup>
<mi>τ<!-- τ --></mi>
<mrow class="MJX-TeXAtom-ORD">
<mfrac>
<mn>16</mn>
<mn>3</mn>
</mfrac>
</mrow>
</msup>
<mo>+</mo>
<mi>f</mi>
<mo>⋅<!-- ⋅ --></mo>
<msup>
<mi>τ<!-- τ --></mi>
<mrow class="MJX-TeXAtom-ORD">
<mfrac>
<mn>43</mn>
<mn>3</mn>
</mfrac>
</mrow>
</msup>
<mo>+</mo>
<mi>g</mi>
<mo>⋅<!-- ⋅ --></mo>
<msup>
<mi>τ<!-- τ --></mi>
<mrow class="MJX-TeXAtom-ORD">
<mfrac>
<mn>110</mn>
<mn>3</mn>
</mfrac>
</mrow>
</msup>
</mstyle>
</mrow>
<annotation encoding="application/x-tex">{\displaystyle v=a+b\cdot \tau ^{\frac {1}{3}}+c\cdot \tau ^{\frac {2}{3}}+d\cdot \tau ^{\frac {5}{3}}+e\cdot \tau ^{\frac {16}{3}}+f\cdot \tau ^{\frac {43}{3}}+g\cdot \tau ^{\frac {110}{3}}}</annotation>
</semantics>
</math></span><img src="./_assets_/eb734a37dd21ce173a46342d1cc64c92/83f79e6eb1fc255d3fcb025adaa27e072d2e57cb.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:59.902ex; height:4.009ex;" alt="{\displaystyle v=a+b\cdot \tau ^{\frac {1}{3}}+c\cdot \tau ^{\frac {2}{3}}+d\cdot \tau ^{\frac {5}{3}}+e\cdot \tau ^{\frac {16}{3}}+f\cdot \tau ^{\frac {43}{3}}+g\cdot \tau ^{\frac {110}{3}}}" loading="lazy"></span>
</td></tr>
</tbody></table>
<p>Gleichungen ohne explizite Nennung einer Eigenschaft werden im Allgemeinen nur für bestimmte Stoffe und Eigenschaften verwendet, wenn die Standardgleichung unzureichend ist.
</p>
<div class="mw-heading mw-heading2"><h2 id="Weblinks">Weblinks</h2></div>
<ul><li><a rel="nofollow" class="external text" href="https://www.aiche.org/dippr/events-products/801-database">DIPPR 801 Database</a></li></ul>
<div class="mw-heading mw-heading2"><h2 id="Einzelnachweise">Einzelnachweise</h2></div>
<ol class="references">
<li id="cite_note-1"><span class="mw-cite-backlink"><a href="#cite_ref-1">↑</a></span> <span class="reference-text"><span class="cite"><a rel="nofollow" class="external text" href="https://chemicals.readthedocs.io/chemicals.dippr.html"><i>DIPPR Fit Equations (chemicals.dippr) — Chemicals 1.1.5 documentation.</i></a> In: <i>readthedocs.io.</i> chemicals.readthedocs.io,<span class="Abrufdatum"> abgerufen am 10. Oktober 2023</span> (englisch).</span><span style="display: none;" class="Z3988" title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Adc&rfr_id=info%3Asid%2Fde.wikipedia.org%3ADIPPR-Gleichungen&rft.title=DIPPR+Fit+Equations+%28chemicals.dippr%29+%E2%80%94+Chemicals+1.1.5+documentation&rft.description=DIPPR+Fit+Equations+%28chemicals.dippr%29+%E2%80%94+Chemicals+1.1.5+documentation&rft.identifier=&rft.publisher=chemicals.readthedocs.io&rft.language=en"> </span></span>
</li>
<li id="cite_note-2"><span class="mw-cite-backlink"><a href="#cite_ref-2">↑</a></span> <span class="reference-text">Katarzyna Staszak, Karolina Wieszczycka, Bartosz Tylkowski: <cite style="font-style:italic">Chemical Technologies and Processes</cite>. Walter de Gruyter & Co KG, 2020, ISBN 978-3-11-065636-7, <span style="white-space:nowrap">S.<span style="display:inline-block;width:.2em"> </span>254</span> (<a rel="nofollow" class="external text" href="https://books.google.com/books?id=EPgdEAAAQBAJ&newbks=0&hl=en">books.google.com</a>).<span class="Z3988" title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rfr_id=info:sid/de.wikipedia.org:DIPPR-Gleichungen&rft.au=Katarzyna+Staszak%2C+Karolina+Wieszczycka%2C+Bartosz+Tylkowski&rft.btitle=Chemical+Technologies+and+Processes&rft.date=2020&rft.genre=book&rft.isbn=9783110656367&rft.pages=254&rft.pub=Walter+de+Gruyter+%26+Co+KG" style="display:none"> </span></span>
</li>
<li id="cite_note-3"><span class="mw-cite-backlink"><a href="#cite_ref-3">↑</a></span> <span class="reference-text">Stefan Rönsch: <cite style="font-style:italic">Anlagenbilanzierung in der Energietechnik: Grundlagen, Gleichungen und Modelle für die Ingenieurpraxis</cite>. Springer, 2015, ISBN 978-3-658-07824-9, <span style="white-space:nowrap">S.<span style="display:inline-block;width:.2em"> </span>154</span>.<span class="Z3988" title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rfr_id=info:sid/de.wikipedia.org:DIPPR-Gleichungen&rft.au=Stefan+R%C3%B6nsch&rft.btitle=Anlagenbilanzierung+in+der+Energietechnik%3A+Grundlagen%2C+Gleichungen+und+Modelle+f%C3%BCr+die+Ingenieurpraxis&rft.date=2015&rft.genre=book&rft.isbn=9783658078249&rft.pages=154&rft.pub=Springer" style="display:none"> </span></span>
</li>
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