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Display information for equation id:math.2555.60 on revision:2555

* Page found: Das ideale Fermigas (eq math.2555.60)

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Hash: 4ac5866526fbe51a93e121a621f9b219

TeX (original user input): 

\begin{align}

& \bar{N}=\frac{2}{3}\frac{\left( 2s+1 \right)}{2}\left( \frac{V}{{{h}^{3}}} \right)4\pi {{\left( 2m\mu  \right)}^{\frac{3}{2}}}\left[ 1+\frac{{{\pi }^{2}}}{8}{{\left( \frac{kT}{\mu } \right)}^{2}} \right]=\frac{2}{3}\frac{\left( 2s+1 \right)}{2}\left( \frac{V}{{{h}^{3}}} \right)4\pi {{\left( 2m{{E}_{F}} \right)}^{\frac{3}{2}}} \\

&  \\

\end{align}

TeX (checked): 

{\begin{aligned}&{\bar {N}}={\frac {2}{3}}{\frac {\left(2s+1\right)}{2}}\left({\frac {V}{{h}^{3}}}\right)4\pi {{\left(2m\mu \right)}^{\frac {3}{2}}}\left[1+{\frac {{\pi }^{2}}{8}}{{\left({\frac {kT}{\mu }}\right)}^{2}}\right]={\frac {2}{3}}{\frac {\left(2s+1\right)}{2}}\left({\frac {V}{{h}^{3}}}\right)4\pi {{\left(2m{{E}_{F}}\right)}^{\frac {3}{2}}}\\&\\\end{aligned}}

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MathML (experimentell; keine Bilder) rendering

MathML (3.537 KB / 513 B) :

N¯=23(2s+1)2(Vh3)4π(2mμ)32[1+π28(kTμ)2]=23(2s+1)2(Vh3)4π(2mEF)32
<math class="mwe-math-element" xmlns="http://www.w3.org/1998/Math/MathML"><mrow data-mjx-texclass="ORD"><mstyle displaystyle="true" scriptlevel="0"><mrow data-mjx-texclass="ORD"><mtable columnalign="right left right left right left right left right left right left" columnspacing="0em 2em 0em 2em 0em 2em 0em 2em 0em 2em 0em" displaystyle="true" rowspacing="3pt"><mtr><mtd></mtd><mtd><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mover><mi>N</mi><mo>¯</mo></mover></mrow></mrow><mo>=</mo><mrow data-mjx-texclass="ORD"><mfrac><mrow data-mjx-texclass="ORD"><mn>2</mn></mrow><mrow data-mjx-texclass="ORD"><mn>3</mn></mrow></mfrac></mrow><mrow data-mjx-texclass="ORD"><mfrac><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="INNER"><mo data-mjx-texclass="OPEN">(</mo><mn>2</mn><mi>s</mi><mo>+</mo><mn>1</mn><mo data-mjx-texclass="CLOSE">)</mo></mrow></mrow><mrow data-mjx-texclass="ORD"><mn>2</mn></mrow></mfrac></mrow><mrow data-mjx-texclass="INNER"><mo data-mjx-texclass="OPEN">(</mo><mrow data-mjx-texclass="ORD"><mfrac><mrow data-mjx-texclass="ORD"><mi>V</mi></mrow><mrow data-mjx-texclass="ORD"><msup><mi>h</mi><mrow data-mjx-texclass="ORD"><mn>3</mn></mrow></msup></mrow></mfrac></mrow><mo data-mjx-texclass="CLOSE">)</mo></mrow><mn>4</mn><mi>&#x03C0;</mi><msup><mrow data-mjx-texclass="INNER"><mo data-mjx-texclass="OPEN">(</mo><mn>2</mn><mi>m</mi><mi>&#x03BC;</mi><mo data-mjx-texclass="CLOSE">)</mo></mrow><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mfrac><mrow data-mjx-texclass="ORD"><mn>3</mn></mrow><mrow data-mjx-texclass="ORD"><mn>2</mn></mrow></mfrac></mrow></mrow></msup><mrow data-mjx-texclass="INNER"><mo data-mjx-texclass="OPEN">[</mo><mn>1</mn><mo>+</mo><mrow data-mjx-texclass="ORD"><mfrac><mrow data-mjx-texclass="ORD"><msup><mi>&#x03C0;</mi><mrow data-mjx-texclass="ORD"><mn>2</mn></mrow></msup></mrow><mrow data-mjx-texclass="ORD"><mn>8</mn></mrow></mfrac></mrow><msup><mrow data-mjx-texclass="INNER"><mo data-mjx-texclass="OPEN">(</mo><mrow data-mjx-texclass="ORD"><mfrac><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mi>k</mi><mi>T</mi></mrow></mrow><mrow data-mjx-texclass="ORD"><mi>&#x03BC;</mi></mrow></mfrac></mrow><mo data-mjx-texclass="CLOSE">)</mo></mrow><mrow data-mjx-texclass="ORD"><mn>2</mn></mrow></msup><mo data-mjx-texclass="CLOSE">]</mo></mrow><mo>=</mo><mrow data-mjx-texclass="ORD"><mfrac><mrow data-mjx-texclass="ORD"><mn>2</mn></mrow><mrow data-mjx-texclass="ORD"><mn>3</mn></mrow></mfrac></mrow><mrow data-mjx-texclass="ORD"><mfrac><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="INNER"><mo data-mjx-texclass="OPEN">(</mo><mn>2</mn><mi>s</mi><mo>+</mo><mn>1</mn><mo data-mjx-texclass="CLOSE">)</mo></mrow></mrow><mrow data-mjx-texclass="ORD"><mn>2</mn></mrow></mfrac></mrow><mrow data-mjx-texclass="INNER"><mo data-mjx-texclass="OPEN">(</mo><mrow data-mjx-texclass="ORD"><mfrac><mrow data-mjx-texclass="ORD"><mi>V</mi></mrow><mrow data-mjx-texclass="ORD"><msup><mi>h</mi><mrow data-mjx-texclass="ORD"><mn>3</mn></mrow></msup></mrow></mfrac></mrow><mo data-mjx-texclass="CLOSE">)</mo></mrow><mn>4</mn><mi>&#x03C0;</mi><msup><mrow data-mjx-texclass="INNER"><mo data-mjx-texclass="OPEN">(</mo><mn>2</mn><mi>m</mi><msub><mi>E</mi><mrow data-mjx-texclass="ORD"><mi>F</mi></mrow></msub><mo data-mjx-texclass="CLOSE">)</mo></mrow><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mfrac><mrow data-mjx-texclass="ORD"><mn>3</mn></mrow><mrow data-mjx-texclass="ORD"><mn>2</mn></mrow></mfrac></mrow></mrow></msup></mtd></mtr><mtr><mtd></mtd><mtd></mtd></mtr><mtr><mtd></mtd></mtr></mtable></mrow></mstyle></mrow></math>

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Calculated based on the variables occurring on the entire Das ideale Fermigas page

Identifiers

  • N¯
  • s
  • V
  • h
  • π
  • m
  • μ
  • π
  • k
  • T
  • μ
  • s
  • V
  • h
  • π
  • m
  • EF

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Abgerufen von „https://wiki.physikerwelt.de/wiki/Spezial:Formelinformation“