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Display information for equation id:math.2467.9 on revision:2467
* Page found: Thermodynamische Potenziale (eq math.2467.9)
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Hash: dc0ec550f95b7b30d3a44d85145d6ce8
TeX (original user input):
\begin{align}
* & dF\left( T,V,N \right)=dU-TdS-SdT=TdS-pdV+\mu dN-TdS-SdT=\mu dN-pdV-SdT \\
* & {{\left( \frac{\partial F}{\partial T} \right)}_{V,N}}=-S \\
* & {{\left( \frac{\partial F}{\partial V} \right)}_{T,N}}=-p \\
* & {{\left( \frac{\partial F}{\partial N} \right)}_{T,V}}=\mu \\
* \end{align}
TeX (checked):
{\begin{aligned}*&dF\left(T,V,N\right)=dU-TdS-SdT=TdS-pdV+\mu dN-TdS-SdT=\mu dN-pdV-SdT\\*&{{\left({\frac {\partial F}{\partial T}}\right)}_{V,N}}=-S\\*&{{\left({\frac {\partial F}{\partial V}}\right)}_{T,N}}=-p\\*&{{\left({\frac {\partial F}{\partial N}}\right)}_{T,V}}=\mu \\*\end{aligned}}
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<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><mo>*</mo></mtd><mtd><mi>d</mi><mi>F</mi><mrow data-mjx-texclass="INNER"><mo data-mjx-texclass="OPEN">(</mo><mi>T</mi><mo>,</mo><mi>V</mi><mo>,</mo><mi>N</mi><mo data-mjx-texclass="CLOSE">)</mo></mrow><mo>=</mo><mi>d</mi><mi>U</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>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>μ</mi><mi>d</mi><mi>N</mi><mo>−</mo><mi>p</mi><mi>d</mi><mi>V</mi><mo>−</mo><mi>S</mi><mi>d</mi><mi>T</mi></mtd></mtr><mtr><mtd><mo>*</mo></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>F</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>V</mi><mo>,</mo><mi>N</mi></mrow></mrow></msub><mo>=</mo><mo>−</mo><mi>S</mi></mtd></mtr><mtr><mtd><mo>*</mo></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>F</mi></mrow></mrow><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mi>∂</mi><mi>V</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><mo>−</mo><mi>p</mi></mtd></mtr><mtr><mtd><mo>*</mo></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>F</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>V</mi></mrow></mrow></msub><mo>=</mo><mi>μ</mi></mtd></mtr><mtr><mtd><mo>*</mo></mtd></mtr></mtable></mrow></mstyle></mrow></math>
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