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Display information for equation id:math.2528.1 on revision:2528
* Page found: Mehrkomponentige ideale Gase (eq math.2528.1)
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Hash: 5e1b4a7aa9d66bc73cd12f60de5abfe8
TeX (original user input):
\begin{align}
& F=U-TS=\sum\limits_{i}^{{}}{{}}{{n}_{i}}\left[ {{u}_{i}}\left( T \right)-T\int_{{{T}_{0}}}^{T}{{}}dT\acute{\ }\frac{{{c}_{vi}}\left( T\acute{\ } \right)}{T\acute{\ }}-RT\ln \frac{{{v}_{i}}}{{{v}_{0}}} \right] \\
& =\sum\limits_{i}^{{}}{{}}{{n}_{i}}\left[ \int_{{{T}_{0}}}^{T}{{}}dT\acute{\ }{{c}_{vi}}\left( T\acute{\ } \right)-T\int_{{{T}_{0}}}^{T}{{}}dT\acute{\ }\frac{{{c}_{vi}}\left( T\acute{\ } \right)}{T\acute{\ }}-RT\ln \frac{V/{{n}_{i}}}{{{v}_{0}}} \right] \\
\end{align}
TeX (checked):
{\begin{aligned}&F=U-TS=\sum \limits _{i}^{}{}{{n}_{i}}\left[{{u}_{i}}\left(T\right)-T\int _{{T}_{0}}^{T}{}dT{\acute {\ }}{\frac {{{c}_{vi}}\left(T{\acute {\ }}\right)}{T{\acute {\ }}}}-RT\ln {\frac {{v}_{i}}{{v}_{0}}}\right]\\&=\sum \limits _{i}^{}{}{{n}_{i}}\left[\int _{{T}_{0}}^{T}{}dT{\acute {\ }}{{c}_{vi}}\left(T{\acute {\ }}\right)-T\int _{{T}_{0}}^{T}{}dT{\acute {\ }}{\frac {{{c}_{vi}}\left(T{\acute {\ }}\right)}{T{\acute {\ }}}}-RT\ln {\frac {V/{{n}_{i}}}{{v}_{0}}}\right]\\\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></mtd><mtd><mi>F</mi><mo>=</mo><mi>U</mi><mo>−</mo><mi>T</mi><mi>S</mi><mo>=</mo><munderover><mo form="prefix" texclass="OP">∑</mo><mrow data-mjx-texclass="ORD"><mi>i</mi></mrow><mrow data-mjx-texclass="ORD"></mrow></munderover><msub><mi>n</mi><mrow data-mjx-texclass="ORD"><mi>i</mi></mrow></msub><mrow data-mjx-texclass="INNER"><mo data-mjx-texclass="OPEN">[</mo><msub><mi>u</mi><mrow data-mjx-texclass="ORD"><mi>i</mi></mrow></msub><mrow data-mjx-texclass="INNER"><mo data-mjx-texclass="OPEN">(</mo><mi>T</mi><mo data-mjx-texclass="CLOSE">)</mo></mrow><mo>−</mo><mi>T</mi><mstyle displaystyle="true" scriptlevel="0"><munderover><mo texclass="OP">∫</mo><mrow data-mjx-texclass="ORD"><msub><mi>T</mi><mrow data-mjx-texclass="ORD"><mn>0</mn></mrow></msub></mrow><mrow data-mjx-texclass="ORD"><mi>T</mi></mrow></munderover></mstyle><mi>d</mi><mi>T</mi><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mover><mspace width="0.5em"/><mo data-mjx-pseudoscript="true">´</mo></mover></mrow></mrow><mrow data-mjx-texclass="ORD"><mfrac><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><msub><mi>c</mi><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mi>v</mi><mi>i</mi></mrow></mrow></msub><mrow data-mjx-texclass="INNER"><mo data-mjx-texclass="OPEN">(</mo><mi>T</mi><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mover><mspace width="0.5em"/><mo data-mjx-pseudoscript="true">´</mo></mover></mrow></mrow><mo data-mjx-texclass="CLOSE">)</mo></mrow></mrow></mrow><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mi>T</mi><mrow 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data-mjx-texclass="ORD"><mn>0</mn></mrow></msub></mrow><mrow data-mjx-texclass="ORD"><mi>T</mi></mrow></munderover></mstyle><mi>d</mi><mi>T</mi><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mover><mspace width="0.5em"/><mo data-mjx-pseudoscript="true">´</mo></mover></mrow></mrow><msub><mi>c</mi><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mi>v</mi><mi>i</mi></mrow></mrow></msub><mrow data-mjx-texclass="INNER"><mo data-mjx-texclass="OPEN">(</mo><mi>T</mi><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mover><mspace width="0.5em"/><mo data-mjx-pseudoscript="true">´</mo></mover></mrow></mrow><mo data-mjx-texclass="CLOSE">)</mo></mrow><mo>−</mo><mi>T</mi><mstyle displaystyle="true" scriptlevel="0"><munderover><mo texclass="OP">∫</mo><mrow data-mjx-texclass="ORD"><msub><mi>T</mi><mrow data-mjx-texclass="ORD"><mn>0</mn></mrow></msub></mrow><mrow data-mjx-texclass="ORD"><mi>T</mi></mrow></munderover></mstyle><mi>d</mi><mi>T</mi><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mover><mspace width="0.5em"/><mo data-mjx-pseudoscript="true">´</mo></mover></mrow></mrow><mrow data-mjx-texclass="ORD"><mfrac><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><msub><mi>c</mi><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mi>v</mi><mi>i</mi></mrow></mrow></msub><mrow data-mjx-texclass="INNER"><mo data-mjx-texclass="OPEN">(</mo><mi>T</mi><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mover><mspace width="0.5em"/><mo data-mjx-pseudoscript="true">´</mo></mover></mrow></mrow><mo data-mjx-texclass="CLOSE">)</mo></mrow></mrow></mrow><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mi>T</mi><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mover><mspace width="0.5em"/><mo data-mjx-pseudoscript="true">´</mo></mover></mrow></mrow></mrow></mrow></mfrac></mrow><mo>−</mo><mi>R</mi><mi>T</mi><mi>ln</mi><mo>⁡</mo><mrow data-mjx-texclass="ORD"><mfrac><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mi>V</mi><mo>/</mo><msub><mi>n</mi><mrow data-mjx-texclass="ORD"><mi>i</mi></mrow></msub></mrow></mrow><mrow data-mjx-texclass="ORD"><msub><mi>v</mi><mrow data-mjx-texclass="ORD"><mn>0</mn></mrow></msub></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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