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Display information for equation id:math.2473.11 on revision:2473

* Page found: Thermodynamische Potenziale (eq math.2473.11)

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TeX (original user input):

\begin{align}
& dH\left( S,p,N \right)=TdS-pdV+\mu dN+pdV+Vdp=\mu dN+TdS+Vdp \\
& {{\left( \frac{\partial H}{\partial S} \right)}_{p,N}}=T \\
& {{\left( \frac{\partial H}{\partial p} \right)}_{S,N}}=V \\
& {{\left( \frac{\partial H}{\partial N} \right)}_{S,p}}=\mu  \\
\end{align}

TeX (checked):

{\begin{aligned}&dH\left(S,p,N\right)=TdS-pdV+\mu dN+pdV+Vdp=\mu dN+TdS+Vdp\\&{{\left({\frac {\partial H}{\partial S}}\right)}_{p,N}}=T\\&{{\left({\frac {\partial H}{\partial p}}\right)}_{S,N}}=V\\&{{\left({\frac {\partial H}{\partial N}}\right)}_{S,p}}=\mu \\\end{aligned}}

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MathML (experimentell; keine Bilder) rendering

MathML (2.526 KB / 431 B) :

dH(S,p,N)=TdSpdV+μdN+pdV+Vdp=μdN+TdS+Vdp(HS)p,N=T(Hp)S,N=V(HN)S,p=μ
<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><mi>d</mi><mi>H</mi><mrow data-mjx-texclass="INNER"><mo data-mjx-texclass="OPEN">(</mo><mi>S</mi><mo>,</mo><mi>p</mi><mo>,</mo><mi>N</mi><mo data-mjx-texclass="CLOSE">)</mo></mrow><mo>=</mo><mi>T</mi><mi>d</mi><mi>S</mi><mo>&#x2212;</mo><mi>p</mi><mi>d</mi><mi>V</mi><mo>+</mo><mi>&#x03BC;</mi><mi>d</mi><mi>N</mi><mo>+</mo><mi>p</mi><mi>d</mi><mi>V</mi><mo>+</mo><mi>V</mi><mi>d</mi><mi>p</mi><mo>=</mo><mi>&#x03BC;</mi><mi>d</mi><mi>N</mi><mo>+</mo><mi>T</mi><mi>d</mi><mi>S</mi><mo>+</mo><mi>V</mi><mi>d</mi><mi>p</mi></mtd></mtr><mtr><mtd></mtd><mtd><msub><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>&#x2202;</mi><mi>H</mi></mrow></mrow><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mi>&#x2202;</mi><mi>S</mi></mrow></mrow></mfrac></mrow><mo data-mjx-texclass="CLOSE">)</mo></mrow><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mi>p</mi><mo>,</mo><mi>N</mi></mrow></mrow></msub><mo>=</mo><mi>T</mi></mtd></mtr><mtr><mtd></mtd><mtd><msub><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>&#x2202;</mi><mi>H</mi></mrow></mrow><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mi>&#x2202;</mi><mi>p</mi></mrow></mrow></mfrac></mrow><mo data-mjx-texclass="CLOSE">)</mo></mrow><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mi>S</mi><mo>,</mo><mi>N</mi></mrow></mrow></msub><mo>=</mo><mi>V</mi></mtd></mtr><mtr><mtd></mtd><mtd><msub><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>&#x2202;</mi><mi>H</mi></mrow></mrow><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mi>&#x2202;</mi><mi>N</mi></mrow></mrow></mfrac></mrow><mo data-mjx-texclass="CLOSE">)</mo></mrow><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mi>S</mi><mo>,</mo><mi>p</mi></mrow></mrow></msub><mo>=</mo><mi>&#x03BC;</mi></mtd></mtr><mtr><mtd></mtd></mtr></mtable></mrow></mstyle></mrow></math>

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Identifiers

  • d
  • H
  • S
  • p
  • N
  • T
  • d
  • S
  • p
  • d
  • V
  • μ
  • d
  • N
  • p
  • d
  • V
  • V
  • d
  • p
  • μ
  • d
  • N
  • T
  • d
  • S
  • V
  • d
  • p
  • H
  • S
  • p
  • N
  • T
  • H
  • p
  • S
  • N
  • V
  • H
  • N
  • S
  • p
  • μ

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