GermanWikipedia - /page/entry.mu

<!DOCTYPE html>

<title>Grauer Körper</title>

</head>

<h1 id="firstHeading" class="firstHeading mw-first-heading"><span class="mw-page-title-main">Grauer Körper</span></h1>

</header>

</div>

<p>Ein <b>grauer Körper</b> im Sinne der <a href="Strahlung" title="Strahlung">Strahlungsphysik</a> ist ein Körper, dessen <a href="Grenzfl%C3%A4che" title="Grenzfläche">Oberfläche</a> auftreffende Strahlung nicht vollständig <a href="Absorption_(Physik)" title="Absorption (Physik)">absorbiert</a> und dementsprechend auch nicht bei einer gegebenen <a href="Temperatur" title="Temperatur">Temperatur</a> die maximale Strahlung (<a href="Schwarzk%C3%B6rperstrahlung" class="mw-redirect" title="Schwarzkörperstrahlung">Schwarzkörperstrahlung</a>) emittiert (siehe <a href="Plancksches_Strahlungsgesetz" title="Plancksches Strahlungsgesetz">plancksches Strahlungsgesetz</a>). Er hat jedoch einen <a href="Wellenl%C3%A4nge" title="Wellenlänge">wellenlängen</a><i>unabhängigen</i> <a href="Emissionsgrad" title="Emissionsgrad">Emissions-</a> bzw. <a href="Absorptionsgrad" title="Absorptionsgrad">Absorptionsgrad</a> – er erscheint „grau“, wobei sich die fehlende „Farbe“ nicht auf den sichtbaren, sondern auf den für die Messung relevanten Bereich des <a href="Elektromagnetisches_Spektrum" title="Elektromagnetisches Spektrum">Spektrums</a> bezieht.

</p><p>Aufgrund des <a href="Wiensches_Verschiebungsgesetz" title="Wiensches Verschiebungsgesetz">wienschen Verschiebungsgesetzes</a> führt ein wellenlängenabhängiger spektraler Emissionsgrad zu einem temperaturabhängigen Gesamt-Emissionsgrad. Bei vielen Materialien und in großen Temperaturbereichen ist die Temperaturabhängigkeit von <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 \varepsilon _{T}}">

<msub>

</mrow>

</msub>

</mstyle>

</mrow>

<annotation encoding="application/x-tex">{\displaystyle \varepsilon _{T}}</annotation>

</semantics>

</math></span><img src="./_assets_/eb734a37dd21ce173a46342d1cc64c92/e5e9b8363853fbd87677d5186fc3277392649e52.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:2.473ex; height:2.009ex;" alt="{\displaystyle \varepsilon _{T}}" loading="lazy"></span> jedoch so gering, dass man sie vernachlässigen kann.

</p><p>Aber es gibt auch Ausnahmen: bei <a href="Metall" class="mw-redirect" title="Metall">Metalloberflächen</a> wirkt sich die Änderung der <a href="Spektralverteilung" class="mw-redirect" title="Spektralverteilung">Spektralverteilung</a> bei tiefen Temperaturen so aus, dass das <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 \varepsilon _{T}}">

<msub>

</mrow>

</msub>

</mstyle>

</mrow>

<annotation encoding="application/x-tex">{\displaystyle \varepsilon _{T}}</annotation>

</semantics>

</math></span><img src="./_assets_/eb734a37dd21ce173a46342d1cc64c92/e5e9b8363853fbd87677d5186fc3277392649e52.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:2.473ex; height:2.009ex;" alt="{\displaystyle \varepsilon _{T}}" loading="lazy"></span> fast temperatur<a href="Proportional" class="mw-redirect" title="Proportional">proportional</a> ist. Dadurch ist die Abstrahlung nicht nur proportional zu <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^{4}}">

<msup>

</mrow>

</msup>

</mstyle>

</mrow>

<annotation encoding="application/x-tex">{\displaystyle T^{4}}</annotation>

</semantics>

</math></span><img src="./_assets_/eb734a37dd21ce173a46342d1cc64c92/ca7236f42486c0b248a18b57907170e46fdf6f2e.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:2.774ex; height:2.676ex;" alt="{\displaystyle T^{4}}" loading="lazy"></span>, sondern fast proportional zu <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^{5}}">

<msup>

</mrow>

</msup>

</mstyle>

</mrow>

<annotation encoding="application/x-tex">{\displaystyle T^{5}}</annotation>

</semantics>

</math></span><img src="./_assets_/eb734a37dd21ce173a46342d1cc64c92/5faa08e3daf65c0aee7c5587ed7968076ee0342c.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:2.774ex; height:2.676ex;" alt="{\displaystyle T^{5}}" loading="lazy"></span>.

</p><p>Der Zahlenwert, wie „grau“ die Oberfläche ist, wird durch den <a href="Absorptionskoeffizient" title="Absorptionskoeffizient">Absorptionskoeffizienten</a> ausgedrückt – in dem entsprechenden Zusammenhang auch als Emissionskoeffizient <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 \varepsilon }">

</mstyle>

</mrow>

<annotation encoding="application/x-tex">{\displaystyle \varepsilon }</annotation>

</semantics>

</math></span><img src="./_assets_/eb734a37dd21ce173a46342d1cc64c92/a30c89172e5b88edbd45d3e2772c7f5e562e5173.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.083ex; height:1.676ex;" alt="{\displaystyle \varepsilon }" loading="lazy"></span> bezeichnet:

</p>

</mstyle>

</mrow>

<annotation encoding="application/x-tex">{\displaystyle 0<\varepsilon <1}</annotation>

</semantics>

</math></span><img src="./_assets_/eb734a37dd21ce173a46342d1cc64c92/a62c0bbc36352f492bde6217430cfe342032487d.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:9.605ex; height:2.176ex;" alt="{\displaystyle 0<\varepsilon <1}" loading="lazy"></span></dd></dl>

<p>ohne dass die idealen Werte erreicht werden können:

</p>

</mstyle>

</mrow>

<annotation encoding="application/x-tex">{\displaystyle \varepsilon =0}</annotation>

</semantics>

</math></span><img src="./_assets_/eb734a37dd21ce173a46342d1cc64c92/0cbe653d369abd71fc0be98efbf59e9edc1bdfb2.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:5.344ex; height:2.176ex;" alt="{\displaystyle \varepsilon =0}" loading="lazy"></span> wäre ein idealer weißer Körper</li>

</mstyle>

</mrow>

<annotation encoding="application/x-tex">{\displaystyle \varepsilon =1}</annotation>

</semantics>

</math></span><img src="./_assets_/eb734a37dd21ce173a46342d1cc64c92/1753afd2efa95ce60e70983a02a58bea70cc7b1d.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:5.344ex; height:2.176ex;" alt="{\displaystyle \varepsilon =1}" loading="lazy"></span> wäre der ideale <a href="Schwarzer_K%C3%B6rper" title="Schwarzer Körper">schwarze Körper</a>.</li></ul>

<p>In der Realität (und damit abweichend von grauen Körpern) hängt <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 \varepsilon }">

</mstyle>

</mrow>

<annotation encoding="application/x-tex">{\displaystyle \varepsilon }</annotation>

</semantics>

</math></span><img src="./_assets_/eb734a37dd21ce173a46342d1cc64c92/a30c89172e5b88edbd45d3e2772c7f5e562e5173.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.083ex; height:1.676ex;" alt="{\displaystyle \varepsilon }" loading="lazy"></span> meist ab von der Wellenlänge <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 \lambda }">

</mstyle>

</mrow>

<annotation encoding="application/x-tex">{\displaystyle \lambda }</annotation>

</semantics>

</math></span><img src="./_assets_/eb734a37dd21ce173a46342d1cc64c92/b43d0ea3c9c025af1be9128e62a18fa74bedda2a.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.355ex; height:2.176ex;" alt="{\displaystyle \lambda }" loading="lazy"></span> bzw. der <a href="Frequenz" title="Frequenz">Frequenz</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 \nu }">

</mstyle>

</mrow>

<annotation encoding="application/x-tex">{\displaystyle \nu }</annotation>

</semantics>

</math></span><img src="./_assets_/eb734a37dd21ce173a46342d1cc64c92/c15bbbb971240cf328aba572178f091684585468.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.232ex; height:1.676ex;" alt="{\displaystyle \nu }" loading="lazy"></span> der Strahlung:

</p>

<msub>

</mrow>

</msub>

</mstyle>

</mrow>

<annotation encoding="application/x-tex">{\displaystyle \varepsilon _{\lambda }:=\varepsilon (\lambda )}</annotation>

</semantics>

</math></span><img src="./_assets_/eb734a37dd21ce173a46342d1cc64c92/237bd73f7d9d7d6b6c7196cd80b62d5633bca847.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:10.267ex; height:2.843ex;" alt="{\displaystyle \varepsilon _{\lambda }:=\varepsilon (\lambda )}" loading="lazy"></span></dd>

<msub>

</mrow>

</msub>

</mstyle>

</mrow>

<annotation encoding="application/x-tex">{\displaystyle \varepsilon _{\nu }:=\varepsilon (\nu )}</annotation>

</semantics>

</math></span><img src="./_assets_/eb734a37dd21ce173a46342d1cc64c92/4218d404af10cd12253b3b412a2fd91fd3502ffa.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:10.057ex; height:2.843ex;" alt="{\displaystyle \varepsilon _{\nu }:=\varepsilon (\nu )}" loading="lazy"></span></dd></dl>

<p>Dadurch wird aus dem <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^{4}}">

<msup>

</mrow>

</msup>

</mstyle>

</mrow>

<annotation encoding="application/x-tex">{\displaystyle T^{4}}</annotation>

</semantics>

</math></span><img src="./_assets_/eb734a37dd21ce173a46342d1cc64c92/ca7236f42486c0b248a18b57907170e46fdf6f2e.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:2.774ex; height:2.676ex;" alt="{\displaystyle T^{4}}" loading="lazy"></span>-Gesetz beim schwarzen Körper

</p>

<msup>

</mrow>

</msup>

<msup>

</mrow>

</msup>

</mstyle>

</mrow>

<annotation encoding="application/x-tex">{\displaystyle M^{o}=\sigma \cdot T^{4}}</annotation>

</semantics>

</math></span><img src="./_assets_/eb734a37dd21ce173a46342d1cc64c92/8932de5aaa1c8f9ad19e5ba9e9d2c834250d3493.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:12.41ex; height:2.676ex;" alt="{\displaystyle M^{o}=\sigma \cdot T^{4}}" loading="lazy"></span> wegen <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 I(\nu )\cdot \mathrm {d} \nu \cdot \mathrm {d} \Omega ={\frac {2\cdot h\cdot \nu ^{3}}{c^{2}}}{\frac {1}{e^{\left({\frac {h\cdot \nu }{k\cdot T}}\right)}-1}}\mathrm {d} \nu \cdot \mathrm {d} \Omega }">

</mrow>

</mrow>

<mfrac>

<mrow>

<msup>

</mrow>

</msup>

</mrow>

<msup>

</mrow>

</msup>

</mfrac>

</mrow>

<mfrac>

<mrow>

<msup>

<mrow>

<mfrac>

<mrow>

</mrow>

<mrow>

</mrow>

</mfrac>

</mrow>

</mrow>

</msup>

</mrow>

</mfrac>

</mrow>

</mrow>

</mrow>

</mstyle>

</mrow>

<annotation encoding="application/x-tex">{\displaystyle I(\nu )\cdot \mathrm {d} \nu \cdot \mathrm {d} \Omega ={\frac {2\cdot h\cdot \nu ^{3}}{c^{2}}}{\frac {1}{e^{\left({\frac {h\cdot \nu }{k\cdot T}}\right)}-1}}\mathrm {d} \nu \cdot \mathrm {d} \Omega }</annotation>

</semantics>

</math></span><img src="./_assets_/eb734a37dd21ce173a46342d1cc64c92/2153c4ff51e4f9d8609f97c89149e52320d2a9fb.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -3.671ex; width:43.306ex; height:7.509ex;" alt="{\displaystyle I(\nu )\cdot \mathrm {d} \nu \cdot \mathrm {d} \Omega ={\frac {2\cdot h\cdot \nu ^{3}}{c^{2}}}{\frac {1}{e^{\left({\frac {h\cdot \nu }{k\cdot T}}\right)}-1}}\mathrm {d} \nu \cdot \mathrm {d} \Omega }" loading="lazy"></span></dd></dl>

<p>für den grauen Körper (reale Oberflächen):

</p>

<msub>

</mrow>

</msub>

</mrow>

</mrow>

</msubsup>

<msub>

</mrow>

</msub>

<msup>

</mrow>

</msup>

</mstyle>

</mrow>

<annotation encoding="application/x-tex">{\displaystyle M_{\varepsilon _{T}}^{o}=\varepsilon _{T}\cdot \sigma \cdot T^{4}}</annotation>

</semantics>

</math></span><img src="./_assets_/eb734a37dd21ce173a46342d1cc64c92/e094ef324539a4173925e886debd81b56a8a0c42.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.005ex; width:17.389ex; height:3.343ex;" alt="{\displaystyle M_{\varepsilon _{T}}^{o}=\varepsilon _{T}\cdot \sigma \cdot T^{4}}" loading="lazy"></span> wegen <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 I_{\varepsilon _{\nu }}(\nu )\cdot \mathrm {d} \nu \cdot \mathrm {d} \Omega =\varepsilon _{\nu }{\frac {2\cdot h\cdot \nu ^{3}}{c^{2}}}{\frac {1}{e^{\left({\frac {h\cdot \nu }{k\cdot T}}\right)}-1}}\mathrm {d} \nu \cdot \mathrm {d} \Omega }">

<msub>

<msub>

</mrow>

</msub>

</mrow>

</msub>

</mrow>

</mrow>

<msub>

</mrow>

</msub>

<mfrac>

<mrow>

<msup>

</mrow>

</msup>

</mrow>

<msup>

</mrow>

</msup>

</mfrac>

</mrow>

<mfrac>

<mrow>

<msup>

<mrow>

<mfrac>

<mrow>

</mrow>

<mrow>

</mrow>

</mfrac>

</mrow>

</mrow>

</msup>

</mrow>

</mfrac>

</mrow>

</mrow>

</mrow>

</mstyle>

</mrow>

<annotation encoding="application/x-tex">{\displaystyle I_{\varepsilon _{\nu }}(\nu )\cdot \mathrm {d} \nu \cdot \mathrm {d} \Omega =\varepsilon _{\nu }{\frac {2\cdot h\cdot \nu ^{3}}{c^{2}}}{\frac {1}{e^{\left({\frac {h\cdot \nu }{k\cdot T}}\right)}-1}}\mathrm {d} \nu \cdot \mathrm {d} \Omega }</annotation>

</semantics>

</math></span><img src="./_assets_/eb734a37dd21ce173a46342d1cc64c92/dbc75f788237def25d9e294ffdc3a980b4b82045.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -3.671ex; width:47.215ex; height:7.509ex;" alt="{\displaystyle I_{\varepsilon _{\nu }}(\nu )\cdot \mathrm {d} \nu \cdot \mathrm {d} \Omega =\varepsilon _{\nu }{\frac {2\cdot h\cdot \nu ^{3}}{c^{2}}}{\frac {1}{e^{\left({\frac {h\cdot \nu }{k\cdot T}}\right)}-1}}\mathrm {d} \nu \cdot \mathrm {d} \Omega }" loading="lazy"></span></dd></dl>

<p>Dabei entspricht <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 \varepsilon _{T}}">

<msub>

</mrow>

</msub>

</mstyle>

</mrow>

<annotation encoding="application/x-tex">{\displaystyle \varepsilon _{T}}</annotation>

</semantics>

</math></span><img src="./_assets_/eb734a37dd21ce173a46342d1cc64c92/e5e9b8363853fbd87677d5186fc3277392649e52.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:2.473ex; height:2.009ex;" alt="{\displaystyle \varepsilon _{T}}" loading="lazy"></span> den <a href="Gewichtetes_Mittel" class="mw-redirect" title="Gewichtetes Mittel">gewichteten Mitteln</a> von <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 \varepsilon _{\nu }}">

<msub>

</mrow>

</msub>

</mstyle>

</mrow>

<annotation encoding="application/x-tex">{\displaystyle \varepsilon _{\nu }}</annotation>

</semantics>

</math></span><img src="./_assets_/eb734a37dd21ce173a46342d1cc64c92/3e5d46e9e71d8e8e99ad8c3fc1f8ad9702d137a3.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:2.187ex; height:2.009ex;" alt="{\displaystyle \varepsilon _{\nu }}" loading="lazy"></span> bzw. <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 \varepsilon _{\lambda }}">

<msub>

</mrow>

</msub>

</mstyle>

</mrow>

<annotation encoding="application/x-tex">{\displaystyle \varepsilon _{\lambda }}</annotation>

</semantics>

</math></span><img src="./_assets_/eb734a37dd21ce173a46342d1cc64c92/045f26e97a400b884417ae3cbadaf8b6d336e5e1.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:2.274ex; height:2.009ex;" alt="{\displaystyle \varepsilon _{\lambda }}" loading="lazy"></span>, die gleich groß sind:

</p>

<msub>

</mrow>

</msub>

<mfrac>

<mrow>

</mrow>

</mrow>

</munderover>

<msub>

</mrow>

</msub>

</mrow>

</mrow>

</mrow>

<mrow>

</mrow>

</mrow>

</munderover>

</mrow>

</mrow>

</mrow>

</mfrac>

</mrow>

<mfrac>

<mrow>

</mrow>

</mrow>

</munderover>

<msub>

</mrow>

</msub>

</mrow>

</mrow>

</mrow>

<mrow>

</mrow>

</mrow>

</munderover>

</mrow>

</mrow>

</mrow>

</mfrac>

</mrow>

</mstyle>

</mrow>

<annotation encoding="application/x-tex">{\displaystyle \varepsilon _{T}={\frac {\int \int \limits _{0}^{\infty }\varepsilon _{\nu }\cdot I(\nu )\cdot \mathrm {d} \nu \cdot \mathrm {d} \Omega }{\int \int \limits _{0}^{\infty }I(\nu )\cdot \mathrm {d} \nu \cdot \mathrm {d} \Omega }}={\frac {\int \int \limits _{0}^{\infty }\varepsilon _{\lambda }\cdot I(\lambda )\cdot \mathrm {d} \lambda \cdot \mathrm {d} \Omega }{\int \int \limits _{0}^{\infty }I(\lambda )\cdot \mathrm {d} \lambda \cdot \mathrm {d} \Omega }}}</annotation>

</semantics>

</math></span><img src="./_assets_/eb734a37dd21ce173a46342d1cc64c92/1768417a755286340b35f36493dfc546de400424.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -6.005ex; width:52.628ex; height:13.176ex;" alt="{\displaystyle \varepsilon _{T}={\frac {\int \int \limits _{0}^{\infty }\varepsilon _{\nu }\cdot I(\nu )\cdot \mathrm {d} \nu \cdot \mathrm {d} \Omega }{\int \int \limits _{0}^{\infty }I(\nu )\cdot \mathrm {d} \nu \cdot \mathrm {d} \Omega }}={\frac {\int \int \limits _{0}^{\infty }\varepsilon _{\lambda }\cdot I(\lambda )\cdot \mathrm {d} \lambda \cdot \mathrm {d} \Omega }{\int \int \limits _{0}^{\infty }I(\lambda )\cdot \mathrm {d} \lambda \cdot \mathrm {d} \Omega }}}" loading="lazy"></span></dd></dl></div><div><div class="zim-footer">

Dieser Artikel wurde von <a class="external text" title="Zuletzt bearbeitet am 2022-12-10" href="https://de.wikipedia.org/wiki/?title=Grauer_K%C3%B6rper&oldid=228744898">Wikipedia</a> herausgegeben. Der Text ist unter <a class="external text" href="https://creativecommons.org/licenses/by-sa/4.0/deed.de">Creative Commons Attribution-Share Alike 4.0</a> verfügbar, sofern nicht anders angegeben. Für die Mediendateien können zusätzliche Bedingungen gelten.

</div>

</div></div>

</div>

</main>

</div>

</body></html>