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Display information for equation id:math.2510.57 on revision:2510
* Page found: Reale Gase (eq math.2510.57)
(force rerendering)Occurrences on the following pages:
Hash: 508c5c7e497c350eca8d331f87a506f5
TeX (original user input):
\begin{align}
& 0=dh={{c}_{p}}dT+{{\left( \frac{\partial h}{\partial p} \right)}_{T}}dp \\
& dT<0 \\
& dp<0 \\
& \Rightarrow {{\left( \frac{\partial h}{\partial p} \right)}_{T}}=v-T{{\left( \frac{\partial v}{\partial T} \right)}_{p}}>0 \\
& \Rightarrow T<\frac{2a}{Rb} \\
\end{align}
TeX (checked):
{\begin{aligned}&0=dh={{c}_{p}}dT+{{\left({\frac {\partial h}{\partial p}}\right)}_{T}}dp\\&dT<0\\&dp<0\\&\Rightarrow {{\left({\frac {\partial h}{\partial p}}\right)}_{T}}=v-T{{\left({\frac {\partial v}{\partial T}}\right)}_{p}}>0\\&\Rightarrow T<{\frac {2a}{Rb}}\\\end{aligned}}
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MathML (2.426 KB / 437 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><mn>0</mn><mo>=</mo><mi>d</mi><mi>h</mi><mo>=</mo><msub><mi>c</mi><mrow data-mjx-texclass="ORD"><mi>p</mi></mrow></msub><mi>d</mi><mi>T</mi><mo>+</mo><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>h</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><mi>d</mi><mi>p</mi></mtd></mtr><mtr><mtd></mtd><mtd><mi>d</mi><mi>T</mi><mo><</mo><mn>0</mn></mtd></mtr><mtr><mtd></mtd><mtd><mi>d</mi><mi>p</mi><mo><</mo><mn>0</mn></mtd></mtr><mtr><mtd></mtd><mtd><mo>⇒</mo><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>h</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><mo>=</mo><mi>v</mi><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>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><mn>0</mn></mtd></mtr><mtr><mtd></mtd><mtd><mo>⇒</mo><mi>T</mi><mo><</mo><mrow data-mjx-texclass="ORD"><mfrac><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mn>2</mn><mi>a</mi></mrow></mrow><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mi>R</mi><mi>b</mi></mrow></mrow></mfrac></mrow></mtd></mtr><mtr><mtd></mtd></mtr></mtable></mrow></mstyle></mrow></math>
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