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Display information for equation id:math.2458.61 on revision:2458
* Page found: Die Hauptsätze der Thermodynamik (eq math.2458.61)
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Hash: 2711f93a396f5957ef56d8f88b49222d
TeX (original user input):
\begin{align}
& 0\ge \oint\limits_{{}}{{}}\frac{\delta Q}{T}={{\left. \int_{1}^{2}{{}}\frac{\delta Q}{T} \right|}_{irreversibel}}+\left. \int_{2}^{1}{{}}\frac{\delta {{Q}_{r}}}{T} \right| \\
& \left. \int_{2}^{1}{{}}\frac{\delta {{Q}_{r}}}{T} \right|={{S}_{1}}-{{S}_{2}} \\
& \Leftrightarrow {{S}_{2}}-{{S}_{1}}\ge \int_{1}^{2}{{}}\frac{\delta Q}{T} \\
\end{align}
TeX (checked):
{\begin{aligned}&0\geq \oint \limits _{}{}{\frac {\delta Q}{T}}={{\left.\int _{1}^{2}{}{\frac {\delta Q}{T}}\right|}_{irreversibel}}+\left.\int _{2}^{1}{}{\frac {\delta {{Q}_{r}}}{T}}\right|\\&\left.\int _{2}^{1}{}{\frac {\delta {{Q}_{r}}}{T}}\right|={{S}_{1}}-{{S}_{2}}\\&\Leftrightarrow {{S}_{2}}-{{S}_{1}}\geq \int _{1}^{2}{}{\frac {\delta Q}{T}}\\\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"><mn>0</mn><mo stretchy="false">≥</mo><munder><mo>∮</mo><mrow data-mjx-texclass="ORD"></mrow></munder><mrow data-mjx-texclass="ORD"><mfrac><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mi>δ</mi><mi>Q</mi></mrow></mrow><mrow data-mjx-texclass="ORD"><mi>T</mi></mrow></mfrac></mrow><mo stretchy="false">=</mo><msub><mrow data-mjx-texclass="INNER"><mo data-mjx-texclass="OPEN"></mo><msubsup><mo stretchy="false">∫</mo><mrow data-mjx-texclass="ORD"><mn>1</mn></mrow><mrow data-mjx-texclass="ORD"><mn>2</mn></mrow></msubsup><mrow data-mjx-texclass="ORD"><mfrac><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mi>δ</mi><mi>Q</mi></mrow></mrow><mrow data-mjx-texclass="ORD"><mi>T</mi></mrow></mfrac></mrow><mo data-mjx-texclass="CLOSE">|</mo></mrow><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mi>i</mi><mi>r</mi><mi>r</mi><mi>e</mi><mi>v</mi><mi>e</mi><mi>r</mi><mi>s</mi><mi>i</mi><mi>b</mi><mi>e</mi><mi>l</mi></mrow></mrow></msub><mo stretchy="false">+</mo><mrow data-mjx-texclass="INNER"><mo data-mjx-texclass="OPEN"></mo><msubsup><mo stretchy="false">∫</mo><mrow data-mjx-texclass="ORD"><mn>2</mn></mrow><mrow data-mjx-texclass="ORD"><mn>1</mn></mrow></msubsup><mrow data-mjx-texclass="ORD"><mfrac><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mi>δ</mi><msub><mi>Q</mi><mrow data-mjx-texclass="ORD"><mi>r</mi></mrow></msub></mrow></mrow><mrow data-mjx-texclass="ORD"><mi>T</mi></mrow></mfrac></mrow><mo data-mjx-texclass="CLOSE">|</mo></mrow></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><msubsup><mo stretchy="false">∫</mo><mrow data-mjx-texclass="ORD"><mn>2</mn></mrow><mrow data-mjx-texclass="ORD"><mn>1</mn></mrow></msubsup><mrow data-mjx-texclass="ORD"><mfrac><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mi>δ</mi><msub><mi>Q</mi><mrow data-mjx-texclass="ORD"><mi>r</mi></mrow></msub></mrow></mrow><mrow data-mjx-texclass="ORD"><mi>T</mi></mrow></mfrac></mrow><mo data-mjx-texclass="CLOSE">|</mo></mrow><mo stretchy="false">=</mo><msub><mi>S</mi><mrow data-mjx-texclass="ORD"><mn>1</mn></mrow></msub><mo stretchy="false">−</mo><msub><mi>S</mi><mrow data-mjx-texclass="ORD"><mn>2</mn></mrow></msub></mtd></mtr><mtr><mtd class="mwe-math-columnalign-r"></mtd><mtd class="mwe-math-columnalign-l"><mo stretchy="false">⇔</mo><msub><mi>S</mi><mrow data-mjx-texclass="ORD"><mn>2</mn></mrow></msub><mo stretchy="false">−</mo><msub><mi>S</mi><mrow data-mjx-texclass="ORD"><mn>1</mn></mrow></msub><mo stretchy="false">≥</mo><msubsup><mo stretchy="false">∫</mo><mrow data-mjx-texclass="ORD"><mn>1</mn></mrow><mrow data-mjx-texclass="ORD"><mn>2</mn></mrow></msubsup><mrow data-mjx-texclass="ORD"><mfrac><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mi>δ</mi><mi>Q</mi></mrow></mrow><mrow data-mjx-texclass="ORD"><mi>T</mi></mrow></mfrac></mrow></mtd></mtr><mtr><mtd class="mwe-math-columnalign-r"></mtd></mtr></mtable></mstyle></mrow></math>
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