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Display information for equation id:math.2508.50 on revision:2508
* Page found: Reale Gase (eq math.2508.50)
(force rerendering)Occurrences on the following pages:
Hash: f26a89eb666f2e153420527d2f29471d
TeX (original user input):
\begin{align}
& {{\left( \frac{\partial {{c}_{v}}}{\partial v} \right)}_{T}}=\frac{{{\partial }^{2}}u}{\partial T\partial v}=\frac{\partial }{\partial T}\left( \frac{a}{{{v}^{2}}} \right)=0 \\
& \Rightarrow {{c}_{v}}={{c}_{v}}(T) \\
\end{align}
TeX (checked):
{\begin{aligned}&{{\left({\frac {\partial {{c}_{v}}}{\partial v}}\right)}_{T}}={\frac {{{\partial }^{2}}u}{\partial T\partial v}}={\frac {\partial }{\partial T}}\left({\frac {a}{{v}^{2}}}\right)=0\\&\Rightarrow {{c}_{v}}={{c}_{v}}(T)\\\end{aligned}}
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MathML (2.06 KB / 423 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><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><msub><mi>c</mi><mrow data-mjx-texclass="ORD"><mi>v</mi></mrow></msub></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>=</mo><mrow data-mjx-texclass="ORD"><mfrac><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><msup><mi>∂</mi><mrow data-mjx-texclass="ORD"><mn>2</mn></mrow></msup><mi>u</mi></mrow></mrow><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mi>∂</mi><mi>T</mi><mi>∂</mi><mi>v</mi></mrow></mrow></mfrac></mrow><mo>=</mo><mrow data-mjx-texclass="ORD"><mfrac><mrow data-mjx-texclass="ORD"><mi>∂</mi></mrow><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mi>∂</mi><mi>T</mi></mrow></mrow></mfrac></mrow><mrow data-mjx-texclass="INNER"><mo data-mjx-texclass="OPEN">(</mo><mrow data-mjx-texclass="ORD"><mfrac><mrow data-mjx-texclass="ORD"><mi>a</mi></mrow><mrow data-mjx-texclass="ORD"><msup><mi>v</mi><mrow data-mjx-texclass="ORD"><mn>2</mn></mrow></msup></mrow></mfrac></mrow><mo data-mjx-texclass="CLOSE">)</mo></mrow><mo>=</mo><mn>0</mn></mtd></mtr><mtr><mtd></mtd><mtd><mo>⇒</mo><msub><mi>c</mi><mrow data-mjx-texclass="ORD"><mi>v</mi></mrow></msub><mo>=</mo><msub><mi>c</mi><mrow data-mjx-texclass="ORD"><mi>v</mi></mrow></msub><mo stretchy="false">(</mo><mi>T</mi><mo stretchy="false">)</mo></mtd></mtr><mtr><mtd></mtd></mtr></mtable></mrow></mstyle></mrow></math>
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