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Display information for equation id:math.2512.2 on revision:2512
* Page found: Phasenübergänge (eq math.2512.2)
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Hash: c08d01c8dc9f53582e2af805f827ccef
TeX (original user input):
\begin{align}
& {{\left( \frac{\partial f}{\partial v} \right)}_{T}}=-p \\
& \Rightarrow \int_{v\acute{\ }}^{v\acute{\ }\acute{\ }}{{}}\left( \frac{\partial f}{\partial v} \right)dv+\left( v\acute{\ }\acute{\ }-v\acute{\ } \right)P=0 \\
& \left( v\acute{\ }\acute{\ }-v\acute{\ } \right)P=-\int_{v\acute{\ }}^{v\acute{\ }\acute{\ }}{{}}\left( \frac{\partial f}{\partial v} \right)dv=\int_{v\acute{\ }}^{v\acute{\ }\acute{\ }}{{}}pdv \\
\end{align}
TeX (checked):
{\begin{aligned}&{{\left({\frac {\partial f}{\partial v}}\right)}_{T}}=-p\\&\Rightarrow \int _{v{\acute {\ }}}^{v{\acute {\ }}{\acute {\ }}}{}\left({\frac {\partial f}{\partial v}}\right)dv+\left(v{\acute {\ }}{\acute {\ }}-v{\acute {\ }}\right)P=0\\&\left(v{\acute {\ }}{\acute {\ }}-v{\acute {\ }}\right)P=-\int _{v{\acute {\ }}}^{v{\acute {\ }}{\acute {\ }}}{}\left({\frac {\partial f}{\partial v}}\right)dv=\int _{v{\acute {\ }}}^{v{\acute {\ }}{\acute {\ }}}{}pdv\\\end{aligned}}
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<math xmlns="http://www.w3.org/1998/Math/MathML" class="mwe-math-element mwe-math-element-inline"><mrow data-mjx-texclass="ORD"><mstyle displaystyle="true" scriptlevel="0"><mtable displaystyle="true"><mtr><mtd class="mwe-math-columnalign-r"></mtd><mtd class="mwe-math-columnalign-l"><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"><mi>T</mi></mrow></msub><mo stretchy="false">=</mo><mo stretchy="false">−</mo><mi>p</mi></mtd></mtr><mtr><mtd class="mwe-math-columnalign-r"></mtd><mtd class="mwe-math-columnalign-l"><mo stretchy="false">⇒</mo><msubsup><mo stretchy="false">∫</mo><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mi>v</mi><mover><mtext> </mtext><mo data-mjx-pseudoscript="true">´</mo></mover></mrow></mrow><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mi>v</mi><mover><mtext> </mtext><mo data-mjx-pseudoscript="true">´</mo></mover><mover><mtext> </mtext><mo data-mjx-pseudoscript="true">´</mo></mover></mrow></mrow></msubsup><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><mi>d</mi><mi>v</mi><mo stretchy="false">+</mo><mrow data-mjx-texclass="INNER"><mo data-mjx-texclass="OPEN">(</mo><mi>v</mi><mover><mtext> </mtext><mo data-mjx-pseudoscript="true">´</mo></mover><mover><mtext> </mtext><mo data-mjx-pseudoscript="true">´</mo></mover><mo stretchy="false">−</mo><mi>v</mi><mover><mtext> </mtext><mo data-mjx-pseudoscript="true">´</mo></mover><mo data-mjx-texclass="CLOSE">)</mo></mrow><mi>P</mi><mo stretchy="false">=</mo><mn>0</mn></mtd></mtr><mtr><mtd class="mwe-math-columnalign-r"></mtd><mtd class="mwe-math-columnalign-l"><mrow data-mjx-texclass="INNER"><mo data-mjx-texclass="OPEN">(</mo><mi>v</mi><mover><mtext> </mtext><mo data-mjx-pseudoscript="true">´</mo></mover><mover><mtext> </mtext><mo data-mjx-pseudoscript="true">´</mo></mover><mo stretchy="false">−</mo><mi>v</mi><mover><mtext> </mtext><mo data-mjx-pseudoscript="true">´</mo></mover><mo data-mjx-texclass="CLOSE">)</mo></mrow><mi>P</mi><mo stretchy="false">=</mo><mo stretchy="false">−</mo><msubsup><mo stretchy="false">∫</mo><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mi>v</mi><mover><mtext> </mtext><mo data-mjx-pseudoscript="true">´</mo></mover></mrow></mrow><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mi>v</mi><mover><mtext> </mtext><mo data-mjx-pseudoscript="true">´</mo></mover><mover><mtext> </mtext><mo data-mjx-pseudoscript="true">´</mo></mover></mrow></mrow></msubsup><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><mi>d</mi><mi>v</mi><mo stretchy="false">=</mo><msubsup><mo stretchy="false">∫</mo><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mi>v</mi><mover><mtext> </mtext><mo data-mjx-pseudoscript="true">´</mo></mover></mrow></mrow><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mi>v</mi><mover><mtext> </mtext><mo data-mjx-pseudoscript="true">´</mo></mover><mover><mtext> </mtext><mo data-mjx-pseudoscript="true">´</mo></mover></mrow></mrow></msubsup><mi>p</mi><mi>d</mi><mi>v</mi></mtd></mtr><mtr><mtd class="mwe-math-columnalign-r"></mtd></mtr></mtable></mstyle></mrow></math>
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