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Display information for equation id:math.2461.43 on revision:2461
* Page found: Die Hauptsätze der Thermodynamik (eq math.2461.43)
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Hash: 4f241fe6b18f0ebbf5a76d24d9a23bf1
TeX (original user input):
\begin{align}
& f\left( {{\vartheta }_{1}},{{\vartheta }_{3}} \right)=-\frac{{{Q}_{1}}}{{{Q}_{3}}\acute{\ }}=\left( -\frac{{{Q}_{1}}}{{{Q}_{2}}} \right)\left( -\frac{{{Q}_{2}}\acute{\ }}{{{Q}_{3}}\acute{\ }} \right)=f\left( {{\vartheta }_{1}},{{\vartheta }_{2}} \right)f\left( {{\vartheta }_{2}},{{\vartheta }_{3}} \right) \\
& \Rightarrow f\left( {{\vartheta }_{2}},{{\vartheta }_{3}} \right)=\frac{f\left( {{\vartheta }_{1}},{{\vartheta }_{3}} \right)}{f\left( {{\vartheta }_{1}},{{\vartheta }_{2}} \right)} \\
\end{align}
TeX (checked):
{\begin{aligned}&f\left({{\vartheta }_{1}},{{\vartheta }_{3}}\right)=-{\frac {{Q}_{1}}{{{Q}_{3}}{\acute {\ }}}}=\left(-{\frac {{Q}_{1}}{{Q}_{2}}}\right)\left(-{\frac {{{Q}_{2}}{\acute {\ }}}{{{Q}_{3}}{\acute {\ }}}}\right)=f\left({{\vartheta }_{1}},{{\vartheta }_{2}}\right)f\left({{\vartheta }_{2}},{{\vartheta }_{3}}\right)\\&\Rightarrow f\left({{\vartheta }_{2}},{{\vartheta }_{3}}\right)={\frac {f\left({{\vartheta }_{1}},{{\vartheta }_{3}}\right)}{f\left({{\vartheta }_{1}},{{\vartheta }_{2}}\right)}}\\\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><mi>f</mi><mrow data-mjx-texclass="INNER"><mo data-mjx-texclass="OPEN">(</mo><msub><mi>ϑ</mi><mrow data-mjx-texclass="ORD"><mn>1</mn></mrow></msub><mo>,</mo><msub><mi>ϑ</mi><mrow data-mjx-texclass="ORD"><mn>3</mn></mrow></msub><mo data-mjx-texclass="CLOSE">)</mo></mrow><mo>=</mo><mo>−</mo><mrow data-mjx-texclass="ORD"><mfrac><mrow data-mjx-texclass="ORD"><msub><mi>Q</mi><mrow data-mjx-texclass="ORD"><mn>1</mn></mrow></msub></mrow><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><msub><mi>Q</mi><mrow data-mjx-texclass="ORD"><mn>3</mn></mrow></msub><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mover><mspace width="0.5em"/><mo data-mjx-pseudoscript="true">´</mo></mover></mrow></mrow></mrow></mrow></mfrac></mrow><mo>=</mo><mrow data-mjx-texclass="INNER"><mo data-mjx-texclass="OPEN">(</mo><mo>−</mo><mrow data-mjx-texclass="ORD"><mfrac><mrow data-mjx-texclass="ORD"><msub><mi>Q</mi><mrow data-mjx-texclass="ORD"><mn>1</mn></mrow></msub></mrow><mrow data-mjx-texclass="ORD"><msub><mi>Q</mi><mrow data-mjx-texclass="ORD"><mn>2</mn></mrow></msub></mrow></mfrac></mrow><mo data-mjx-texclass="CLOSE">)</mo></mrow><mrow data-mjx-texclass="INNER"><mo data-mjx-texclass="OPEN">(</mo><mo>−</mo><mrow data-mjx-texclass="ORD"><mfrac><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><msub><mi>Q</mi><mrow data-mjx-texclass="ORD"><mn>2</mn></mrow></msub><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mover><mspace width="0.5em"/><mo data-mjx-pseudoscript="true">´</mo></mover></mrow></mrow></mrow></mrow><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><msub><mi>Q</mi><mrow data-mjx-texclass="ORD"><mn>3</mn></mrow></msub><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mover><mspace width="0.5em"/><mo data-mjx-pseudoscript="true">´</mo></mover></mrow></mrow></mrow></mrow></mfrac></mrow><mo data-mjx-texclass="CLOSE">)</mo></mrow><mo>=</mo><mi>f</mi><mrow data-mjx-texclass="INNER"><mo data-mjx-texclass="OPEN">(</mo><msub><mi>ϑ</mi><mrow data-mjx-texclass="ORD"><mn>1</mn></mrow></msub><mo>,</mo><msub><mi>ϑ</mi><mrow data-mjx-texclass="ORD"><mn>2</mn></mrow></msub><mo data-mjx-texclass="CLOSE">)</mo></mrow><mi>f</mi><mrow data-mjx-texclass="INNER"><mo data-mjx-texclass="OPEN">(</mo><msub><mi>ϑ</mi><mrow data-mjx-texclass="ORD"><mn>2</mn></mrow></msub><mo>,</mo><msub><mi>ϑ</mi><mrow data-mjx-texclass="ORD"><mn>3</mn></mrow></msub><mo data-mjx-texclass="CLOSE">)</mo></mrow></mtd></mtr><mtr><mtd></mtd><mtd><mo>⇒</mo><mi>f</mi><mrow data-mjx-texclass="INNER"><mo data-mjx-texclass="OPEN">(</mo><msub><mi>ϑ</mi><mrow data-mjx-texclass="ORD"><mn>2</mn></mrow></msub><mo>,</mo><msub><mi>ϑ</mi><mrow data-mjx-texclass="ORD"><mn>3</mn></mrow></msub><mo data-mjx-texclass="CLOSE">)</mo></mrow><mo>=</mo><mrow data-mjx-texclass="ORD"><mfrac><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mi>f</mi><mrow data-mjx-texclass="INNER"><mo data-mjx-texclass="OPEN">(</mo><msub><mi>ϑ</mi><mrow data-mjx-texclass="ORD"><mn>1</mn></mrow></msub><mo>,</mo><msub><mi>ϑ</mi><mrow data-mjx-texclass="ORD"><mn>3</mn></mrow></msub><mo data-mjx-texclass="CLOSE">)</mo></mrow></mrow></mrow><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mi>f</mi><mrow data-mjx-texclass="INNER"><mo data-mjx-texclass="OPEN">(</mo><msub><mi>ϑ</mi><mrow data-mjx-texclass="ORD"><mn>1</mn></mrow></msub><mo>,</mo><msub><mi>ϑ</mi><mrow data-mjx-texclass="ORD"><mn>2</mn></mrow></msub><mo data-mjx-texclass="CLOSE">)</mo></mrow></mrow></mrow></mfrac></mrow></mtd></mtr><mtr><mtd></mtd></mtr></mtable></mrow></mstyle></mrow></math>
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