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Display information for equation id:math.2507.39 on revision:2507
* Page found: Das ideale Gas (eq math.2507.39)
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Hash: fb56b519467a7e78c9a0604282819cab
TeX (original user input):
\begin{align}
& \Rightarrow ds=\frac{1}{T}\left( du+pdv \right)={{c}_{V}}\frac{dT}{T}+R\frac{dv}{v} \\
& \Rightarrow s={{c}_{v}}\ln T+R\ln v+const. \\
\end{align}
TeX (checked):
{\begin{aligned}&\Rightarrow ds={\frac {1}{T}}\left(du+pdv\right)={{c}_{V}}{\frac {dT}{T}}+R{\frac {dv}{v}}\\&\Rightarrow s={{c}_{v}}\ln T+R\ln v+const.\\\end{aligned}}
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MathML (experimentell; keine Bilder) rendering
MathML (1.574 KB / 418 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><mo>⇒</mo><mi>d</mi><mi>s</mi><mo>=</mo><mrow data-mjx-texclass="ORD"><mfrac><mrow data-mjx-texclass="ORD"><mn>1</mn></mrow><mrow data-mjx-texclass="ORD"><mi>T</mi></mrow></mfrac></mrow><mrow data-mjx-texclass="INNER"><mo data-mjx-texclass="OPEN">(</mo><mi>d</mi><mi>u</mi><mo>+</mo><mi>p</mi><mi>d</mi><mi>v</mi><mo data-mjx-texclass="CLOSE">)</mo></mrow><mo>=</mo><msub><mi>c</mi><mrow data-mjx-texclass="ORD"><mi>V</mi></mrow></msub><mrow data-mjx-texclass="ORD"><mfrac><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mi>d</mi><mi>T</mi></mrow></mrow><mrow data-mjx-texclass="ORD"><mi>T</mi></mrow></mfrac></mrow><mo>+</mo><mi>R</mi><mrow data-mjx-texclass="ORD"><mfrac><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mi>d</mi><mi>v</mi></mrow></mrow><mrow data-mjx-texclass="ORD"><mi>v</mi></mrow></mfrac></mrow></mtd></mtr><mtr><mtd></mtd><mtd><mo>⇒</mo><mi>s</mi><mo>=</mo><msub><mi>c</mi><mrow data-mjx-texclass="ORD"><mi>v</mi></mrow></msub><mi>ln</mi><mo>⁡</mo><mi>T</mi><mo>+</mo><mi>R</mi><mi>ln</mi><mo>⁡</mo><mi>v</mi><mo>+</mo><mi>c</mi><mi>o</mi><mi>n</mi><mi>s</mi><mi>t</mi><mo>.</mo></mtd></mtr><mtr><mtd></mtd></mtr></mtable></mrow></mstyle></mrow></math>
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