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Display information for equation id:math.2508.83 on revision:2508
* Page found: Reale Gase (eq math.2508.83)
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Hash: b7211d5617839e2386c93cf066d26977
TeX (original user input):
\begin{align}
& {{\kappa }_{T}}=-\frac{1}{v}{{\left( \frac{\partial v}{\partial p} \right)}_{T}}\tilde{\ }\frac{1}{{{\left( \frac{\partial p}{\partial v} \right)}_{T}}}=\infty \\
& \alpha =\frac{1}{v}{{\left( \frac{\partial v}{\partial T} \right)}_{p}}=-\frac{{{\left( \frac{\partial p}{\partial T} \right)}_{v}}}{v{{\left( \frac{\partial p}{\partial v} \right)}_{T}}}=\infty \\
& {{c}_{p}}={{c}_{v}}+T{{\left( \frac{\partial p}{\partial T} \right)}_{v}}{{\left( \frac{\partial v}{\partial T} \right)}_{p}}=\infty \\
& {{\left( \frac{\partial v}{\partial T} \right)}_{p}}\to \infty \\
\end{align}
TeX (checked):
{\begin{aligned}&{{\kappa }_{T}}=-{\frac {1}{v}}{{\left({\frac {\partial v}{\partial p}}\right)}_{T}}{\tilde {\ }}{\frac {1}{{\left({\frac {\partial p}{\partial v}}\right)}_{T}}}=\infty \\&\alpha ={\frac {1}{v}}{{\left({\frac {\partial v}{\partial T}}\right)}_{p}}=-{\frac {{\left({\frac {\partial p}{\partial T}}\right)}_{v}}{v{{\left({\frac {\partial p}{\partial v}}\right)}_{T}}}}=\infty \\&{{c}_{p}}={{c}_{v}}+T{{\left({\frac {\partial p}{\partial T}}\right)}_{v}}{{\left({\frac {\partial v}{\partial T}}\right)}_{p}}=\infty \\&{{\left({\frac {\partial v}{\partial T}}\right)}_{p}}\to \infty \\\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><msub><mi>κ</mi><mrow data-mjx-texclass="ORD"><mi>T</mi></mrow></msub><mo>=</mo><mo>−</mo><mrow data-mjx-texclass="ORD"><mfrac><mrow data-mjx-texclass="ORD"><mn>1</mn></mrow><mrow data-mjx-texclass="ORD"><mi>v</mi></mrow></mfrac></mrow><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>v</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"><mi>T</mi></mrow></msub><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mover><mspace width="0.5em"/><mo>~</mo></mover></mrow></mrow><mrow data-mjx-texclass="ORD"><mfrac><mrow data-mjx-texclass="ORD"><mn>1</mn></mrow><mrow data-mjx-texclass="ORD"><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>p</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></mrow></mfrac></mrow><mo>=</mo><mi mathvariant="normal">∞</mi></mtd></mtr><mtr><mtd></mtd><mtd><mi>α</mi><mo>=</mo><mrow data-mjx-texclass="ORD"><mfrac><mrow data-mjx-texclass="ORD"><mn>1</mn></mrow><mrow data-mjx-texclass="ORD"><mi>v</mi></mrow></mfrac></mrow><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>v</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"><mi>p</mi></mrow></msub><mo>=</mo><mo>−</mo><mrow data-mjx-texclass="ORD"><mfrac><mrow data-mjx-texclass="ORD"><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>p</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"><mi>v</mi></mrow></msub></mrow><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mi>v</mi><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>p</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></mrow></mrow></mfrac></mrow><mo>=</mo><mi mathvariant="normal">∞</mi></mtd></mtr><mtr><mtd></mtd><mtd><msub><mi>c</mi><mrow data-mjx-texclass="ORD"><mi>p</mi></mrow></msub><mo>=</mo><msub><mi>c</mi><mrow data-mjx-texclass="ORD"><mi>v</mi></mrow></msub><mo>+</mo><mi>T</mi><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>p</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"><mi>v</mi></mrow></msub><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>v</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"><mi>p</mi></mrow></msub><mo>=</mo><mi mathvariant="normal">∞</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>v</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"><mi>p</mi></mrow></msub><mo accent="false">→</mo><mi mathvariant="normal">∞</mi></mtd></mtr><mtr><mtd></mtd></mtr></mtable></mrow></mstyle></mrow></math>
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