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Display information for equation id:math.2284.16 on revision:2284
* Page found: Beispiel des Großkanonischen Ensenbles (eq math.2284.16)
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TeX (original user input):
\begin{align}
& -k\beta \mu ={{\left( \frac{\partial S}{\partial E} \right)}_{V,\bar{N}}} \\
& k{{\partial }_{V}}\ln {{Z}_{gk}}=k\beta p\Rightarrow p=\frac{1}{\beta }{{\partial }_{V}}\ln {{Z}_{gk}} \\
\end{align}
TeX (checked):
{\begin{aligned}&-k\beta \mu ={{\left({\frac {\partial S}{\partial E}}\right)}_{V,{\bar {N}}}}\\&k{{\partial }_{V}}\ln {{Z}_{gk}}=k\beta p\Rightarrow p={\frac {1}{\beta }}{{\partial }_{V}}\ln {{Z}_{gk}}\\\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"><mo stretchy="false">−</mo><mi>k</mi><mi>β</mi><mi>μ</mi><mo stretchy="false">=</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>S</mi></mrow></mrow><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mi>∂</mi><mi>E</mi></mrow></mrow></mfrac></mrow><mo data-mjx-texclass="CLOSE">)</mo></mrow><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mi>V</mi><mo>,</mo><mover><mi>N</mi><mo>¯</mo></mover></mrow></mrow></msub></mtd></mtr><mtr><mtd class="mwe-math-columnalign-r"></mtd><mtd class="mwe-math-columnalign-l"><mi>k</mi><msub><mi>∂</mi><mrow data-mjx-texclass="ORD"><mi>V</mi></mrow></msub><mi>ln</mi><mo>⁡</mo><msub><mi>Z</mi><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mi>g</mi><mi>k</mi></mrow></mrow></msub><mo stretchy="false">=</mo><mi>k</mi><mi>β</mi><mi>p</mi><mo stretchy="false">⇒</mo><mi>p</mi><mo stretchy="false">=</mo><mrow data-mjx-texclass="ORD"><mfrac><mrow data-mjx-texclass="ORD"><mn>1</mn></mrow><mrow data-mjx-texclass="ORD"><mi>β</mi></mrow></mfrac></mrow><msub><mi>∂</mi><mrow data-mjx-texclass="ORD"><mi>V</mi></mrow></msub><mi>ln</mi><mo>⁡</mo><msub><mi>Z</mi><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mi>g</mi><mi>k</mi></mrow></mrow></msub></mtd></mtr><mtr><mtd class="mwe-math-columnalign-r"></mtd></mtr></mtable></mstyle></mrow></math>
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