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<h1 id="firstHeading" class="firstHeading mw-first-heading"><span class="mw-page-title-main">Luftdichte</span></h1>
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<p>Die <b>Luftdichte</b> <a href="Rho" title="Rho"><i>ρ</i></a> (auch <b><a href="Dichte" title="Dichte">Dichte</a> von <a href="Luft" title="Luft">Luft</a></b> oder <b>Dichte der Luft</b>) gibt an, welche <a href="Masse_(Physik)" title="Masse (Physik)">Masse</a> Luft in einem bestimmten <a href="Volumen" title="Volumen">Volumen</a> enthalten ist. Auf <a href="Meeresspiegel" title="Meeresspiegel">Meeresspiegelhöhe</a> ist die Luft mit rund 1,2041 <a href="Kilogramm" title="Kilogramm">kg</a>/<a href="Kubikmeter" title="Kubikmeter">m³</a> bei 20 <a href="Grad_Celsius" title="Grad Celsius">°C</a> durch die darüber lastende Luftmasse stärker verdichtet als in größerer Höhe.
</p>
<div class="mw-heading mw-heading2"><h2 id="Einflüsse"><span id="Einfl.C3.BCsse"></span>Einflüsse</h2></div>
<p>Luft ist um so dichter, je höher die <a href="Lufts%C3%A4ule" title="Luftsäule">Luftsäule</a> über ihr ist. Darum hat Luft am Boden einen höheren <a href="Luftdruck" title="Luftdruck">Luftdruck</a> als Luft über dem Boden. Eine Faustregel ist, dass der Luftdruck sich pro 5500 Meter Höhe halbiert. Anhand der Luftdichte lässt sich die <a href="Dichteh%C3%B6he" title="Dichtehöhe">Dichtehöhe</a> als Näherung für die <a href="Gel%C3%A4nde" title="Gelände">topografische</a> Höhe bestimmen.<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>
</p><p>Auch die Temperatur beeinflusst die Luftdichte. Dabei spielen der <a href="Atmosph%C3%A4rischer_Temperaturgradient" title="Atmosphärischer Temperaturgradient">atmosphärische Temperaturgradient</a> und <a href="Meteorologisch" class="mw-redirect" title="Meteorologisch">meteorologische</a> Faktoren eine Rolle. In Bodennähe beeinflusst auch das Gelände die Temperatur; etwas höher können <a href="Temperaturinversion" class="mw-redirect" title="Temperaturinversion">Inversionen</a> Temperaturschwankungen verursachen. Wäre die <a href="Temperatur" title="Temperatur">Temperatur</a> in allen Höhen gleich, so würden Luftdruck und Luftdichte gemeinsam mit zunehmender Höhe nach dem <a href="Gasgesetz" class="mw-redirect" title="Gasgesetz">Gesetz für ideale Gase</a> abnehmen (siehe <a href="Barometrische_H%C3%B6henformel" title="Barometrische Höhenformel">barometrische Höhenformel</a>).
</p><p>Die Luftdichte verändert sich auch mit dem Anteil des in ihr enthaltenen <a href="Wasserdampf" title="Wasserdampf">Wasserdampf</a>, weil <a href="Eigenschaften_des_Wassers" title="Eigenschaften des Wassers">Wassermoleküle</a> eine geringere Masse als Stickstoffmoleküle (N<sub>2</sub>) und Sauerstoffmoleküle (O<sub>2</sub>) haben. Mit steigender <a href="Luftfeuchtigkeit" title="Luftfeuchtigkeit">Luftfeuchtigkeit</a> sinkt also die Luftdichte.
</p>
<div class="mw-heading mw-heading2"><h2 id="Berechnung">Berechnung</h2></div>
<p>In erster Näherung kann man die Luft als ein <a href="Ideales_Gas" title="Ideales Gas">ideales Gas</a> betrachten, dessen Dichte ρ (rho) man nach der folgenden <a href="Ideale_Gasgleichung" class="mw-redirect" title="Ideale Gasgleichung">Gleichung für ideale Gase</a> berechnen kann:
</p>
<dl><dd><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 \rho ={\frac {p\cdot M}{R\cdot T}}}">
<semantics>
<mrow class="MJX-TeXAtom-ORD">
<mstyle displaystyle="true" scriptlevel="0">
<mi>ρ<!-- ρ --></mi>
<mo>=</mo>
<mrow class="MJX-TeXAtom-ORD">
<mfrac>
<mrow>
<mi>p</mi>
<mo>⋅<!-- ⋅ --></mo>
<mi>M</mi>
</mrow>
<mrow>
<mi>R</mi>
<mo>⋅<!-- ⋅ --></mo>
<mi>T</mi>
</mrow>
</mfrac>
</mrow>
</mstyle>
</mrow>
<annotation encoding="application/x-tex">{\displaystyle \rho ={\frac {p\cdot M}{R\cdot T}}}</annotation>
</semantics>
</math></span><img src="./_assets_/eb734a37dd21ce173a46342d1cc64c92/72efc7025ede7f4511e076f888581dd48926d86a.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.005ex; width:10.427ex; height:5.509ex;" alt="{\displaystyle \rho ={\frac {p\cdot M}{R\cdot T}}}" loading="lazy"></span><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></dd></dl>
<p>mit
</p>
<ul><li>dem Luftdruck <i>p (<a href="Standardatmosph%C3%A4re" class="mw-redirect" title="Standardatmosphäre">Standard-Atmosphärendruck</a>:</i> <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 p_{0}=1013,25\,{\text{hPa}}}">
<semantics>
<mrow class="MJX-TeXAtom-ORD">
<mstyle displaystyle="true" scriptlevel="0">
<msub>
<mi>p</mi>
<mrow class="MJX-TeXAtom-ORD">
<mn>0</mn>
</mrow>
</msub>
<mo>=</mo>
<mn>1013</mn>
<mo>,</mo>
<mn>25</mn>
<mspace width="thinmathspace"></mspace>
<mrow class="MJX-TeXAtom-ORD">
<mtext>hPa</mtext>
</mrow>
</mstyle>
</mrow>
<annotation encoding="application/x-tex">{\displaystyle p_{0}=1013,25\,{\text{hPa}}}</annotation>
</semantics>
</math></span><img src="./_assets_/eb734a37dd21ce173a46342d1cc64c92/d553cd02dede4fc61cbc549ead57fbcf0271a24b.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; margin-left: -0.089ex; width:17.845ex; height:2.509ex;" alt="{\displaystyle p_{0}=1013,25\,{\text{hPa}}}" loading="lazy"></span><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> <i>)</i>,</li>
<li>der <a href="Molare_Masse" title="Molare Masse">molaren Masse</a> <i>M</i> (<a href="Mittlere_molare_Masse" title="Mittlere molare Masse">mittlere molare Masse</a> der trockenen Luft = <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 {\begin{aligned}\mathrm {28{,}96\ g\cdot mol^{-1}} \end{aligned}}}">
<semantics>
<mrow class="MJX-TeXAtom-ORD">
<mstyle displaystyle="true" scriptlevel="0">
<mrow class="MJX-TeXAtom-ORD">
<mtable columnalign="right left right left right left right left right left right left" rowspacing="3pt" columnspacing="0em 2em 0em 2em 0em 2em 0em 2em 0em 2em 0em" displaystyle="true">
<mtr>
<mtd>
<mrow class="MJX-TeXAtom-ORD">
<mn>28</mn>
<mrow class="MJX-TeXAtom-ORD">
<mo>,</mo>
</mrow>
<mn>96</mn>
<mtext> </mtext>
<mi mathvariant="normal">g</mi>
<mo>⋅<!-- ⋅ --></mo>
<mi mathvariant="normal">m</mi>
<mi mathvariant="normal">o</mi>
<msup>
<mi mathvariant="normal">l</mi>
<mrow class="MJX-TeXAtom-ORD">
<mo>−<!-- − --></mo>
<mn>1</mn>
</mrow>
</msup>
</mrow>
</mtd>
</mtr>
</mtable>
</mrow>
</mstyle>
</mrow>
<annotation encoding="application/x-tex">{\displaystyle {\begin{aligned}\mathrm {28{,}96\ g\cdot mol^{-1}} \end{aligned}}}</annotation>
</semantics>
</math></span><img src="./_assets_/eb734a37dd21ce173a46342d1cc64c92/5dc9690c5d6629541d2f518aab3665bc5ffdfcdf.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.005ex; width:15.548ex; height:3.176ex;" alt="{\displaystyle {\begin{aligned}\mathrm {28{,}96\ g\cdot mol^{-1}} \end{aligned}}}" loading="lazy"></span>),</li>
<li>der <a href="Universelle_Gaskonstante" class="mw-redirect" title="Universelle Gaskonstante">Universellen Gaskonstante</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 R\approx 8,314462618\,{\frac {\text{J}}{{\text{mol}}\cdot {\text{K}}}}}">
<semantics>
<mrow class="MJX-TeXAtom-ORD">
<mstyle displaystyle="true" scriptlevel="0">
<mi>R</mi>
<mo>≈<!-- ≈ --></mo>
<mn>8</mn>
<mo>,</mo>
<mn>314462618</mn>
<mspace width="thinmathspace"></mspace>
<mrow class="MJX-TeXAtom-ORD">
<mfrac>
<mtext>J</mtext>
<mrow>
<mrow class="MJX-TeXAtom-ORD">
<mtext>mol</mtext>
</mrow>
<mo>⋅<!-- ⋅ --></mo>
<mrow class="MJX-TeXAtom-ORD">
<mtext>K</mtext>
</mrow>
</mrow>
</mfrac>
</mrow>
</mstyle>
</mrow>
<annotation encoding="application/x-tex">{\displaystyle R\approx 8,314462618\,{\frac {\text{J}}{{\text{mol}}\cdot {\text{K}}}}}</annotation>
</semantics>
</math></span><img src="./_assets_/eb734a37dd21ce173a46342d1cc64c92/9d983d1174392d8a8dd295b2d66134f177db04d0.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.005ex; width:25.977ex; height:5.343ex;" alt="{\displaystyle R\approx 8,314462618\,{\frac {\text{J}}{{\text{mol}}\cdot {\text{K}}}}}" loading="lazy"></span><sup id="cite_ref-4" class="reference"><a href="#cite_note-4"><span class="cite-bracket">[</span>4<span class="cite-bracket">]</span></a></sup>,</li>
<li>der <a href="Thermodynamische_Temperatur" title="Thermodynamische Temperatur">Temperatur</a> <i>T.</i></li></ul>
<p>Durch Einsetzen der <a href="Spezifische_Gaskonstante" class="mw-redirect" title="Spezifische Gaskonstante">spezifischen Gaskonstante</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 R_{\mathrm {S} }={\tfrac {R}{M}}=287{,}1\ \mathrm {\tfrac {J}{kg\cdot K}} }">
<semantics>
<mrow class="MJX-TeXAtom-ORD">
<mstyle displaystyle="true" scriptlevel="0">
<msub>
<mi>R</mi>
<mrow class="MJX-TeXAtom-ORD">
<mrow class="MJX-TeXAtom-ORD">
<mi mathvariant="normal">S</mi>
</mrow>
</mrow>
</msub>
<mo>=</mo>
<mrow class="MJX-TeXAtom-ORD">
<mstyle displaystyle="false" scriptlevel="0">
<mfrac>
<mi>R</mi>
<mi>M</mi>
</mfrac>
</mstyle>
</mrow>
<mo>=</mo>
<mn>287</mn>
<mrow class="MJX-TeXAtom-ORD">
<mo>,</mo>
</mrow>
<mn>1</mn>
<mtext> </mtext>
<mrow class="MJX-TeXAtom-ORD">
<mstyle displaystyle="false" scriptlevel="0">
<mfrac>
<mi mathvariant="normal">J</mi>
<mrow>
<mi mathvariant="normal">k</mi>
<mi mathvariant="normal">g</mi>
<mo>⋅<!-- ⋅ --></mo>
<mi mathvariant="normal">K</mi>
</mrow>
</mfrac>
</mstyle>
</mrow>
</mstyle>
</mrow>
<annotation encoding="application/x-tex">{\displaystyle R_{\mathrm {S} }={\tfrac {R}{M}}=287{,}1\ \mathrm {\tfrac {J}{kg\cdot K}} }</annotation>
</semantics>
</math></span><img src="./_assets_/eb734a37dd21ce173a46342d1cc64c92/6120d600b2d25dae2e74250297315da792ee6502.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.671ex; width:21.809ex; height:4.176ex;" alt="{\displaystyle R_{\mathrm {S} }={\tfrac {R}{M}}=287{,}1\ \mathrm {\tfrac {J}{kg\cdot K}} }" loading="lazy"></span> für <a href="Trockene_Luft" title="Trockene Luft">trockene Luft</a><sup id="cite_ref-5" class="reference"><a href="#cite_note-5"><span class="cite-bracket">[</span>5<span class="cite-bracket">]</span></a></sup> erhält man:
</p>
<dl><dd><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 \rho ={\frac {p}{R_{\mathrm {S} }\cdot T}}}">
<semantics>
<mrow class="MJX-TeXAtom-ORD">
<mstyle displaystyle="true" scriptlevel="0">
<mi>ρ<!-- ρ --></mi>
<mo>=</mo>
<mrow class="MJX-TeXAtom-ORD">
<mfrac>
<mi>p</mi>
<mrow>
<msub>
<mi>R</mi>
<mrow class="MJX-TeXAtom-ORD">
<mrow class="MJX-TeXAtom-ORD">
<mi mathvariant="normal">S</mi>
</mrow>
</mrow>
</msub>
<mo>⋅<!-- ⋅ --></mo>
<mi>T</mi>
</mrow>
</mfrac>
</mrow>
</mstyle>
</mrow>
<annotation encoding="application/x-tex">{\displaystyle \rho ={\frac {p}{R_{\mathrm {S} }\cdot T}}}</annotation>
</semantics>
</math></span><img src="./_assets_/eb734a37dd21ce173a46342d1cc64c92/b863b224de94f79617db295e07eedeec5f997c13.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.338ex; width:11.362ex; height:5.343ex;" alt="{\displaystyle \rho ={\frac {p}{R_{\mathrm {S} }\cdot T}}}" loading="lazy"></span>.</dd></dl>
<div class="mw-heading mw-heading2"><h2 id="Temperaturabhängigkeit"><span id="Temperaturabh.C3.A4ngigkeit"></span>Temperaturabhängigkeit</h2></div>
<table class="wikitable" style="text-align:center;">
<caption>Luftdichte in Abhängigkeit von der Lufttemperatur unter Normdruck von 1013,25 mbar
</caption>
<tbody><tr class="hintergrundfarbe5" style="vertical-align:top;">
<th>Temperatur<br><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 \vartheta }">
<semantics>
<mrow class="MJX-TeXAtom-ORD">
<mstyle displaystyle="true" scriptlevel="0">
<mi>ϑ<!-- ϑ --></mi>
</mstyle>
</mrow>
<annotation encoding="application/x-tex">{\displaystyle \vartheta }</annotation>
</semantics>
</math></span><img src="./_assets_/eb734a37dd21ce173a46342d1cc64c92/d00eaf197c35bbfa391b9477490a4af955416837.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.374ex; height:2.176ex;" alt="{\displaystyle \vartheta }" loading="lazy"></span> in °C
</th>
<th>Temperatur<br>T in K
</th>
<th>Luftdichte<br><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 \rho }">
<semantics>
<mrow class="MJX-TeXAtom-ORD">
<mstyle displaystyle="true" scriptlevel="0">
<mi>ρ<!-- ρ --></mi>
</mstyle>
</mrow>
<annotation encoding="application/x-tex">{\displaystyle \rho }</annotation>
</semantics>
</math></span><img src="./_assets_/eb734a37dd21ce173a46342d1cc64c92/1f7d439671d1289b6a816e6af7a304be40608d64.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:1.202ex; height:2.176ex;" alt="{\displaystyle \rho }" loading="lazy"></span> in kg/m³
</th>
<th>Anmerkung
</th></tr>
<tr>
<td>+35</td>
<td>308,15</td>
<td>1,1455
</td></tr>
<tr>
<td>+30</td>
<td>303,15</td>
<td>1,1644
</td></tr>
<tr>
<td>+25</td>
<td>298,15</td>
<td>1,1839
</td></tr>
<tr>
<td>+20</td>
<td>293,15</td>
<td>1,2041</td>
<td>Laborbedingungen
</td></tr>
<tr>
<td>+15</td>
<td>288,15</td>
<td>1,2250</td>
<td>Luftfahrt-<a href="Normatmosph%C3%A4re" title="Normatmosphäre">Normatmosphäre</a>
</td></tr>
<tr>
<td>+10</td>
<td>283,15</td>
<td>1,2466
</td></tr>
<tr>
<td>+5</td>
<td>278,15</td>
<td>1,2690
</td></tr>
<tr>
<td>0</td>
<td>273,15</td>
<td>1,2922</td>
<td>physikalische <a href="Normbedingungen" class="mw-redirect" title="Normbedingungen">Normbedingungen</a>
</td></tr>
<tr>
<td>−5</td>
<td>268,15</td>
<td>1,3163
</td></tr>
<tr>
<td>−10</td>
<td>263,15</td>
<td>1,3413
</td></tr>
<tr>
<td>−15</td>
<td>258,15</td>
<td>1,3673
</td></tr>
<tr>
<td>−20</td>
<td>253,15</td>
<td>1,3943
</td></tr>
<tr>
<td>−25</td>
<td>248,15</td>
<td>1,4224
</td></tr></tbody></table>
<div class="mw-heading mw-heading2"><h2 id="Feuchteabhängigkeit"><span id="Feuchteabh.C3.A4ngigkeit"></span>Feuchteabhängigkeit</h2></div>
<p>Eine genauere Dichtebestimmung der Luft erfordert eine Berücksichtigung der <a href="Luftfeuchte" class="mw-redirect" title="Luftfeuchte">Luftfeuchte</a>, da diese die Gaskonstante der Luft verändert:
</p>
<dl><dd><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 R_{\mathrm {f} }={\frac {R_{\mathrm {S} }}{1-\varphi \cdot {\frac {p_{\mathrm {d} }}{p}}\cdot {\Big (}1-{\frac {R_{\mathrm {S} }}{R_{\mathrm {d} }}}{\Big )}}}}">
<semantics>
<mrow class="MJX-TeXAtom-ORD">
<mstyle displaystyle="true" scriptlevel="0">
<msub>
<mi>R</mi>
<mrow class="MJX-TeXAtom-ORD">
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<mi mathvariant="normal">f</mi>
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<mo>=</mo>
<mrow class="MJX-TeXAtom-ORD">
<mfrac>
<msub>
<mi>R</mi>
<mrow class="MJX-TeXAtom-ORD">
<mrow class="MJX-TeXAtom-ORD">
<mi mathvariant="normal">S</mi>
</mrow>
</mrow>
</msub>
<mrow>
<mn>1</mn>
<mo>−<!-- − --></mo>
<mi>φ<!-- φ --></mi>
<mo>⋅<!-- ⋅ --></mo>
<mrow class="MJX-TeXAtom-ORD">
<mfrac>
<msub>
<mi>p</mi>
<mrow class="MJX-TeXAtom-ORD">
<mrow class="MJX-TeXAtom-ORD">
<mi mathvariant="normal">d</mi>
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<mi>p</mi>
</mfrac>
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<mo>⋅<!-- ⋅ --></mo>
<mrow class="MJX-TeXAtom-ORD">
<mrow class="MJX-TeXAtom-ORD">
<mo maxsize="1.623em" minsize="1.623em">(</mo>
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<mn>1</mn>
<mo>−<!-- − --></mo>
<mrow class="MJX-TeXAtom-ORD">
<mfrac>
<msub>
<mi>R</mi>
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<mrow class="MJX-TeXAtom-ORD">
<mi mathvariant="normal">S</mi>
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<msub>
<mi>R</mi>
<mrow class="MJX-TeXAtom-ORD">
<mrow class="MJX-TeXAtom-ORD">
<mi mathvariant="normal">d</mi>
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</mrow>
<mrow class="MJX-TeXAtom-ORD">
<mrow class="MJX-TeXAtom-ORD">
<mo maxsize="1.623em" minsize="1.623em">)</mo>
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</mfrac>
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</mstyle>
</mrow>
<annotation encoding="application/x-tex">{\displaystyle R_{\mathrm {f} }={\frac {R_{\mathrm {S} }}{1-\varphi \cdot {\frac {p_{\mathrm {d} }}{p}}\cdot {\Big (}1-{\frac {R_{\mathrm {S} }}{R_{\mathrm {d} }}}{\Big )}}}}</annotation>
</semantics>
</math></span><img src="./_assets_/eb734a37dd21ce173a46342d1cc64c92/52ae99a8261fe5902919e0d7e8a6ed5565bc894b.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -4.505ex; width:27.761ex; height:8.009ex;" alt="{\displaystyle R_{\mathrm {f} }={\frac {R_{\mathrm {S} }}{1-\varphi \cdot {\frac {p_{\mathrm {d} }}{p}}\cdot {\Big (}1-{\frac {R_{\mathrm {S} }}{R_{\mathrm {d} }}}{\Big )}}}}" loading="lazy"></span></dd></dl>
<p>mit
</p>
<ul><li>der Gaskonstante <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 R_{\mathrm {S} }=287{,}058\,\mathrm {\tfrac {J}{kg\cdot K}} }">
<semantics>
<mrow class="MJX-TeXAtom-ORD">
<mstyle displaystyle="true" scriptlevel="0">
<msub>
<mi>R</mi>
<mrow class="MJX-TeXAtom-ORD">
<mrow class="MJX-TeXAtom-ORD">
<mi mathvariant="normal">S</mi>
</mrow>
</mrow>
</msub>
<mo>=</mo>
<mn>287,058</mn>
<mspace width="thinmathspace"></mspace>
<mrow class="MJX-TeXAtom-ORD">
<mstyle displaystyle="false" scriptlevel="0">
<mfrac>
<mi mathvariant="normal">J</mi>
<mrow>
<mi mathvariant="normal">k</mi>
<mi mathvariant="normal">g</mi>
<mo>⋅<!-- ⋅ --></mo>
<mi mathvariant="normal">K</mi>
</mrow>
</mfrac>
</mstyle>
</mrow>
</mstyle>
</mrow>
<annotation encoding="application/x-tex">{\displaystyle R_{\mathrm {S} }=287{,}058\,\mathrm {\tfrac {J}{kg\cdot K}} }</annotation>
</semantics>
</math></span><img src="./_assets_/eb734a37dd21ce173a46342d1cc64c92/71d3e6ff140f21f6dfc328281da9d08f8cb79010.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.671ex; width:18.279ex; height:4.176ex;" alt="{\displaystyle R_{\mathrm {S} }=287{,}058\,\mathrm {\tfrac {J}{kg\cdot K}} }" loading="lazy"></span> der trockenen Luft</li>
<li>der Gaskonstante <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 R_{\mathrm {d} }=461{,}523\,\mathrm {\tfrac {J}{kg\cdot K}} }">
<semantics>
<mrow class="MJX-TeXAtom-ORD">
<mstyle displaystyle="true" scriptlevel="0">
<msub>
<mi>R</mi>
<mrow class="MJX-TeXAtom-ORD">
<mrow class="MJX-TeXAtom-ORD">
<mi mathvariant="normal">d</mi>
</mrow>
</mrow>
</msub>
<mo>=</mo>
<mn>461,523</mn>
<mspace width="thinmathspace"></mspace>
<mrow class="MJX-TeXAtom-ORD">
<mstyle displaystyle="false" scriptlevel="0">
<mfrac>
<mi mathvariant="normal">J</mi>
<mrow>
<mi mathvariant="normal">k</mi>
<mi mathvariant="normal">g</mi>
<mo>⋅<!-- ⋅ --></mo>
<mi mathvariant="normal">K</mi>
</mrow>
</mfrac>
</mstyle>
</mrow>
</mstyle>
</mrow>
<annotation encoding="application/x-tex">{\displaystyle R_{\mathrm {d} }=461{,}523\,\mathrm {\tfrac {J}{kg\cdot K}} }</annotation>
</semantics>
</math></span><img src="./_assets_/eb734a37dd21ce173a46342d1cc64c92/aa9eed55fef80c48f2c12f6c174f76bad7721b17.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.671ex; width:18.279ex; height:4.176ex;" alt="{\displaystyle R_{\mathrm {d} }=461{,}523\,\mathrm {\tfrac {J}{kg\cdot K}} }" loading="lazy"></span> von <a href="Wasserdampf" title="Wasserdampf">Wasserdampf</a></li>
<li>der <a href="Relative_Luftfeuchtigkeit" class="mw-redirect" title="Relative Luftfeuchtigkeit">relativen Luftfeuchtigkeit</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 \varphi }">
<semantics>
<mrow class="MJX-TeXAtom-ORD">
<mstyle displaystyle="true" scriptlevel="0">
<mi>φ<!-- φ --></mi>
</mstyle>
</mrow>
<annotation encoding="application/x-tex">{\displaystyle \varphi }</annotation>
</semantics>
</math></span><img src="./_assets_/eb734a37dd21ce173a46342d1cc64c92/33ee699558d09cf9d653f6351f9fda0b2f4aaa3e.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:1.52ex; height:2.176ex;" alt="{\displaystyle \varphi }" loading="lazy"></span> (z. B.: 0,76 = 76 %)</li>
<li>dem <a href="S%C3%A4ttigungsdampfdruck" title="Sättigungsdampfdruck">Sättigungsdampfdruck</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 p_{\mathrm {d} }}">
<semantics>
<mrow class="MJX-TeXAtom-ORD">
<mstyle displaystyle="true" scriptlevel="0">
<msub>
<mi>p</mi>
<mrow class="MJX-TeXAtom-ORD">
<mrow class="MJX-TeXAtom-ORD">
<mi mathvariant="normal">d</mi>
</mrow>
</mrow>
</msub>
</mstyle>
</mrow>
<annotation encoding="application/x-tex">{\displaystyle p_{\mathrm {d} }}</annotation>
</semantics>
</math></span><img src="./_assets_/eb734a37dd21ce173a46342d1cc64c92/ebf093b0b61708ecb38730fb834052ad438302be.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; margin-left: -0.089ex; width:2.405ex; height:2.009ex;" alt="{\displaystyle p_{\mathrm {d} }}" loading="lazy"></span> von Wasser in Luft<sup id="cite_ref-6" class="reference"><a href="#cite_note-6"><span class="cite-bracket">[</span>6<span class="cite-bracket">]</span></a></sup></li>
<li>dem Umgebungsdruck <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 p}">
<semantics>
<mrow class="MJX-TeXAtom-ORD">
<mstyle displaystyle="true" scriptlevel="0">
<mi>p</mi>
</mstyle>
</mrow>
<annotation encoding="application/x-tex">{\displaystyle p}</annotation>
</semantics>
</math></span><img src="./_assets_/eb734a37dd21ce173a46342d1cc64c92/81eac1e205430d1f40810df36a0edffdc367af36.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; margin-left: -0.089ex; width:1.259ex; height:2.009ex;" alt="{\displaystyle p}" loading="lazy"></span></li></ul>
<p>Nachdem die Gaskonstante angepasst wurde, kann die Gleichung
</p>
<dl><dd><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 \rho ={\frac {p}{R_{\mathrm {f} }\cdot T}}}">
<semantics>
<mrow class="MJX-TeXAtom-ORD">
<mstyle displaystyle="true" scriptlevel="0">
<mi>ρ<!-- ρ --></mi>
<mo>=</mo>
<mrow class="MJX-TeXAtom-ORD">
<mfrac>
<mi>p</mi>
<mrow>
<msub>
<mi>R</mi>
<mrow class="MJX-TeXAtom-ORD">
<mrow class="MJX-TeXAtom-ORD">
<mi mathvariant="normal">f</mi>
</mrow>
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<mo>⋅<!-- ⋅ --></mo>
<mi>T</mi>
</mrow>
</mfrac>
</mrow>
</mstyle>
</mrow>
<annotation encoding="application/x-tex">{\displaystyle \rho ={\frac {p}{R_{\mathrm {f} }\cdot T}}}</annotation>
</semantics>
</math></span><img src="./_assets_/eb734a37dd21ce173a46342d1cc64c92/e5b2135e5bcdb5e7e15ef108bd4e689a41894914.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.171ex; width:11.06ex; height:5.176ex;" alt="{\displaystyle \rho ={\frac {p}{R_{\mathrm {f} }\cdot T}}}" loading="lazy"></span></dd></dl>
<p>verwendet werden.
</p>
<div class="mw-heading mw-heading2"><h2 id="Kehrwert">Kehrwert</h2></div>
<div class="hauptartikel" role="navigation"><span class="hauptartikel-pfeil" title="siehe" aria-hidden="true" role="presentation">→ </span><i><span class="hauptartikel-text">Hauptartikel</span>: <a href="Spezifisches_Volumen" title="Spezifisches Volumen">spezifisches Volumen</a></i></div>
<p>Der <a href="Kehrwert" title="Kehrwert">reziproke</a> Wert der Dichte, das <a href="Spezifisches_Volumen" title="Spezifisches Volumen">spezifische Volumen</a>, hat in der <a href="Meteorologie" title="Meteorologie">Meteorologie</a> das Formelzeichen <i>α</i> und in der <a href="Thermodynamik" title="Thermodynamik">Thermodynamik</a> das Formelzeichen <i>v</i><sub>Luft</sub>:
</p>
<dl><dd><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 \alpha =v_{\text{Luft}}={\frac {1}{\rho }}}">
<semantics>
<mrow class="MJX-TeXAtom-ORD">
<mstyle displaystyle="true" scriptlevel="0">
<mi>α<!-- α --></mi>
<mo>=</mo>
<msub>
<mi>v</mi>
<mrow class="MJX-TeXAtom-ORD">
<mtext>Luft</mtext>
</mrow>
</msub>
<mo>=</mo>
<mrow class="MJX-TeXAtom-ORD">
<mfrac>
<mn>1</mn>
<mi>ρ<!-- ρ --></mi>
</mfrac>
</mrow>
</mstyle>
</mrow>
<annotation encoding="application/x-tex">{\displaystyle \alpha =v_{\text{Luft}}={\frac {1}{\rho }}}</annotation>
</semantics>
</math></span><img src="./_assets_/eb734a37dd21ce173a46342d1cc64c92/5ed22f32e69d29fbe04c9d86a56ee8b8e2558036.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.338ex; width:14.167ex; height:5.676ex;" alt="{\displaystyle \alpha =v_{\text{Luft}}={\frac {1}{\rho }}}" loading="lazy"></span>.</dd></dl>
<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://www.dwd.de/DE/service/lexikon/Functions/glossar.html?lv3=607748&lv2=101518"><i>Wetter und Klima - Deutscher Wetterdienst - Glossar - L - Luftdichte.</i></a><span class="Abrufdatum"> Abgerufen am 5. Januar 2026</span>.</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%3ALuftdichte&rft.title=Wetter+und+Klima+-+Deutscher+Wetterdienst+-+Glossar+-+L+-+Luftdichte&rft.description=Wetter+und+Klima+-+Deutscher+Wetterdienst+-+Glossar+-+L+-+Luftdichte&rft.identifier=https%3A%2F%2Fwww.dwd.de%2FDE%2Fservice%2Flexikon%2FFunctions%2Fglossar.html%3Flv3%3D607748%26lv2%3D101518"> </span></span>
</li>
<li id="cite_note-2"><span class="mw-cite-backlink"><a href="#cite_ref-2">↑</a></span> <span class="reference-text"><span class="cite"><a rel="nofollow" class="external text" href="https://chem.libretexts.org/Bookshelves/General_Chemistry/Map:_Structure_and_Properties_(Tro)/11:_Gases/11.04:_The_Ideal_Gas_Law"><i>11.4: The Ideal Gas Law.</i></a> 12. Februar 2015,<span class="Abrufdatum"> abgerufen am 2. April 2025</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%3ALuftdichte&rft.title=11.4%3A+The+Ideal+Gas+Law&rft.description=11.4%3A+The+Ideal+Gas+Law&rft.identifier=https%3A%2F%2Fchem.libretexts.org%2FBookshelves%2FGeneral_Chemistry%2FMap%253A_Structure_and_Properties_%28Tro%29%2F11%253A_Gases%2F11.04%253A_The_Ideal_Gas_Law&rft.date=2015-02-12&rft.language=en"> </span></span>
</li>
<li id="cite_note-3"><span class="mw-cite-backlink"><a href="#cite_ref-3">↑</a></span> <span class="reference-text"><span class="cite"><a rel="nofollow" class="external text" href="https://www.dwd.de/DE/service/lexikon/begriffe/S/Standardatmosphaere.html"><i>Wetter und Klima - Deutscher Wetterdienst - Glossar - Standardatmosphäre.</i></a><span class="Abrufdatum"> Abgerufen am 2. April 2025</span>.</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%3ALuftdichte&rft.title=Wetter+und+Klima+-+Deutscher+Wetterdienst+-+Glossar+-+Standardatmosph%C3%A4re&rft.description=Wetter+und+Klima+-+Deutscher+Wetterdienst+-+Glossar+-+Standardatmosph%C3%A4re&rft.identifier=https%3A%2F%2Fwww.dwd.de%2FDE%2Fservice%2Flexikon%2Fbegriffe%2FS%2FStandardatmosphaere.html"> </span></span>
</li>
<li id="cite_note-4"><span class="mw-cite-backlink"><a href="#cite_ref-4">↑</a></span> <span class="reference-text"><span class="cite"><a rel="nofollow" class="external text" href="https://pml.nist.gov/cuu/Constants/"><i>Fundamental Physical Constants from NIST.</i></a><span class="Abrufdatum"> Abgerufen am 2. April 2025</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%3ALuftdichte&rft.title=Fundamental+Physical+Constants+from+NIST&rft.description=Fundamental+Physical+Constants+from+NIST&rft.identifier=https%3A%2F%2Fpml.nist.gov%2Fcuu%2FConstants%2F&rft.language=en"> </span></span>
</li>
<li id="cite_note-5"><span class="mw-cite-backlink"><a href="#cite_ref-5">↑</a></span> <span class="reference-text">Hans-Joachim Kretzschmar, Ingo Kraft: <cite style="font-style:italic">Kleine Formelsammlung Technische Thermodynamik</cite> (= <cite style="font-style:italic">Hanser eLibrary</cite>). 6., überarbeitete Auflage. Hanser, München 2022, ISBN 978-3-446-47321-8, <span style="white-space:nowrap">S.<span style="display:inline-block;width:.2em"> </span>182</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:Luftdichte&rft.au=Hans-Joachim+Kretzschmar%2C+Ingo+Kraft&rft.btitle=Kleine+Formelsammlung+Technische+Thermodynamik&rft.date=2022&rft.edition=6.%2C+%C3%BCberarbeitete+Auflage&rft.genre=book&rft.isbn=9783446473218&rft.pages=182&rft.place=M%C3%BCnchen&rft.pub=Hanser&rft.series=Hanser+eLibrary" style="display:none"> </span></span>
</li>
<li id="cite_note-6"><span class="mw-cite-backlink"><a href="#cite_ref-6">↑</a></span> <span class="reference-text">
<div class="sisterproject" style="margin:0.1em 0 0 0;"><div class="noviewer" style="display:inline-block; line-height:10px; min-width:1.6em; text-align:center;" aria-hidden="true" role="presentation"><span class="mw-default-size" typeof="mw:File"><span title="Wikibooks"></span></span></div><b><a href="https://de.wikibooks.org/wiki/Tabellensammlung_Chemie/_Stoffdaten_Wasser#Sättigungsdampfdruck" class="extiw external" title="b:Tabellensammlung Chemie/ Stoffdaten Wasser">Wikibooks: Datentabelle mit genaueren Formeln</a></b> – Lern- und Lehrmaterialien</div>
<p>tabelliert ist. Es gibt auch <a href="Empirische_Formel" title="Empirische Formel">empirische Formeln</a> unterschiedlicher Genauigkeit wie die <a href="Magnus-Formel" class="mw-redirect" title="Magnus-Formel">Magnus-Formel</a> oder <a href="Antoine-Gleichung" title="Antoine-Gleichung">Antoine-Gleichung</a>.
</p>
</span></li>
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