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Display information for equation id:math.2561.18 on revision:2561

* Page found: Das ideale Bosegas (eq math.2561.18)

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TeX (original user input): 

\begin{align}
  & \bar{N}=\left( 2s+1 \right)\frac{V}{{{\lambda }^{3}}}{{e}^{\frac{\mu }{kT}}}\left[ 1+\frac{1}{{{2}^{\frac{3}{2}}}}\frac{\bar{N}{{\lambda }^{3}}}{V\left( 2s+1 \right)} \right] \\ 
 & \Rightarrow {{e}^{\frac{\mu }{kT}}}\approx \frac{\bar{N}{{\lambda }^{3}}}{V\left( 2s+1 \right)}\left[ 1-\frac{1}{{{2}^{\frac{3}{2}}}}\frac{\bar{N}{{\lambda }^{3}}}{V\left( 2s+1 \right)} \right] \\ 
\end{align}

TeX (checked): 

{\begin{aligned}&{\bar {N}}=\left(2s+1\right){\frac {V}{{\lambda }^{3}}}{{e}^{\frac {\mu }{kT}}}\left[1+{\frac {1}{{2}^{\frac {3}{2}}}}{\frac {{\bar {N}}{{\lambda }^{3}}}{V\left(2s+1\right)}}\right]\\&\Rightarrow {{e}^{\frac {\mu }{kT}}}\approx {\frac {{\bar {N}}{{\lambda }^{3}}}{V\left(2s+1\right)}}\left[1-{\frac {1}{{2}^{\frac {3}{2}}}}{\frac {{\bar {N}}{{\lambda }^{3}}}{V\left(2s+1\right)}}\right]\\\end{aligned}}

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N¯=(2s+1)Vλ3eμkT[1+1232N¯λ3V(2s+1)]⇒eμkT≈N¯λ3V(2s+1)[1−1232N¯λ3V(2s+1)]
<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="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 data-mjx-texclass="ORD"><mfrac><mrow data-mjx-texclass="ORD"><mi>V</mi></mrow><mrow data-mjx-texclass="ORD"><msup><mi>&#x03BB;</mi><mrow data-mjx-texclass="ORD"><mn>3</mn></mrow></msup></mrow></mfrac></mrow><msup><mi>e</mi><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mfrac><mrow data-mjx-texclass="ORD"><mi>&#x03BC;</mi></mrow><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mi>k</mi><mi>T</mi></mrow></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"><mn>1</mn></mrow><mrow data-mjx-texclass="ORD"><msup><mn>2</mn><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></mfrac></mrow><mrow data-mjx-texclass="ORD"><mfrac><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mover><mi>N</mi><mo>¯</mo></mover></mrow></mrow><msup><mi>&#x03BB;</mi><mrow data-mjx-texclass="ORD"><mn>3</mn></mrow></msup></mrow></mrow><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mi>V</mi><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></mfrac></mrow><mo data-mjx-texclass="CLOSE">]</mo></mrow></mtd></mtr><mtr><mtd></mtd><mtd><mo>&#x21D2;</mo><msup><mi>e</mi><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mfrac><mrow data-mjx-texclass="ORD"><mi>&#x03BC;</mi></mrow><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mi>k</mi><mi>T</mi></mrow></mrow></mfrac></mrow></mrow></msup><mo>&#x2248;</mo><mrow data-mjx-texclass="ORD"><mfrac><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mover><mi>N</mi><mo>¯</mo></mover></mrow></mrow><msup><mi>&#x03BB;</mi><mrow data-mjx-texclass="ORD"><mn>3</mn></mrow></msup></mrow></mrow><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mi>V</mi><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></mfrac></mrow><mrow data-mjx-texclass="INNER"><mo data-mjx-texclass="OPEN">[</mo><mn>1</mn><mo>&#x2212;</mo><mrow data-mjx-texclass="ORD"><mfrac><mrow data-mjx-texclass="ORD"><mn>1</mn></mrow><mrow data-mjx-texclass="ORD"><msup><mn>2</mn><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></mfrac></mrow><mrow data-mjx-texclass="ORD"><mfrac><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mover><mi>N</mi><mo>¯</mo></mover></mrow></mrow><msup><mi>&#x03BB;</mi><mrow data-mjx-texclass="ORD"><mn>3</mn></mrow></msup></mrow></mrow><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mi>V</mi><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></mfrac></mrow><mo data-mjx-texclass="CLOSE">]</mo></mrow></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 Bosegas page

Identifiers

  • N¯
  • s
  • V
  • λ
  • e
  • μ
  • k
  • T
  • N¯
  • λ
  • V
  • s
  • e
  • μ
  • k
  • T
  • N¯
  • λ
  • V
  • s
  • N¯
  • λ
  • V
  • s

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