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Display information for equation id:math.2473.13 on revision:2473
* Page found: Thermodynamische Potenziale (eq math.2473.13)
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Hash: 0bd23106323278319fe4d6efae78d4ff
TeX (original user input):
\begin{align}
& dG\left( T,p,N \right)=TdS-pdV+\mu dN-TdS-SdT+pdV+Vdp=\mu dN-SdT+Vdp \\
& {{\left( \frac{\partial G}{\partial T} \right)}_{p,N}}=-S \\
& {{\left( \frac{\partial G}{\partial p} \right)}_{T,N}}=V \\
& {{\left( \frac{\partial G}{\partial N} \right)}_{T,p}}=\mu \\
\end{align}
TeX (checked):
{\begin{aligned}&dG\left(T,p,N\right)=TdS-pdV+\mu dN-TdS-SdT+pdV+Vdp=\mu dN-SdT+Vdp\\&{{\left({\frac {\partial G}{\partial T}}\right)}_{p,N}}=-S\\&{{\left({\frac {\partial G}{\partial p}}\right)}_{T,N}}=V\\&{{\left({\frac {\partial G}{\partial N}}\right)}_{T,p}}=\mu \\\end{aligned}}
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MathML (2.642 KB / 443 B) :
<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>G</mi><mrow data-mjx-texclass="INNER"><mo data-mjx-texclass="OPEN">(</mo><mi>T</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>−</mo><mi>p</mi><mi>d</mi><mi>V</mi><mo>+</mo><mi>μ</mi><mi>d</mi><mi>N</mi><mo>−</mo><mi>T</mi><mi>d</mi><mi>S</mi><mo>−</mo><mi>S</mi><mi>d</mi><mi>T</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>μ</mi><mi>d</mi><mi>N</mi><mo>−</mo><mi>S</mi><mi>d</mi><mi>T</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>∂</mi><mi>G</mi></mrow></mrow><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mi>∂</mi><mi>T</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><mo>−</mo><mi>S</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>∂</mi><mi>G</mi></mrow></mrow><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mi>∂</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>T</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>∂</mi><mi>G</mi></mrow></mrow><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mi>∂</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>T</mi><mo>,</mo><mi>p</mi></mrow></mrow></msub><mo>=</mo><mi>μ</mi></mtd></mtr><mtr><mtd></mtd></mtr></mtable></mrow></mstyle></mrow></math>
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