– PhysikWiki

General

Display information for equation id:math.2573.10 on revision:2573

* Page found: Spezifische Wärme zweiatomiger idealer Gase (eq math.2573.10)

Occurrences on the following pages:

Spezifische Wärme zweiatomiger idealer Gase Eq: math.2573.10

Hash: 6aa474f78bd41abada831dbda422b2b5

TeX (original user input):

\begin{align}

& Z=\sum\limits_{t,r,s}^{{}}{{}}\exp \left( -\beta {{E}_{j}} \right)=\sum\limits_{t}^{{}}{{}}\exp \left( -\beta {{E}_{t}} \right)\sum\limits_{r}^{{}}{{}}\exp \left( -\beta {{E}_{r}} \right)\sum\limits_{s}^{{}}{{}}\exp \left( -\beta {{E}_{s}} \right) \\ 

& {{E}_{j}}={{E}_{tj}}+{{E}_{sj}}+{{E}_{rj}} \\

& \sum\limits_{t}^{{}}{{}}\exp \left( -\beta {{E}_{t}} \right)={{Z}_{t}} \\

& \sum\limits_{r}^{{}}{{}}\exp \left( -\beta {{E}_{r}} \right)={{Z}_{r}} \\

& \sum\limits_{s}^{{}}{{}}\exp \left( -\beta {{E}_{s}} \right)={{Z}_{S}} \\

\end{align}

TeX (checked):

{\begin{aligned}&Z=\sum \limits _{t,r,s}^{}{}\exp \left(-\beta {{E}_{j}}\right)=\sum \limits _{t}^{}{}\exp \left(-\beta {{E}_{t}}\right)\sum \limits _{r}^{}{}\exp \left(-\beta {{E}_{r}}\right)\sum \limits _{s}^{}{}\exp \left(-\beta {{E}_{s}}\right)\\&{{E}_{j}}={{E}_{tj}}+{{E}_{sj}}+{{E}_{rj}}\\&\sum \limits _{t}^{}{}\exp \left(-\beta {{E}_{t}}\right)={{Z}_{t}}\\&\sum \limits _{r}^{}{}\exp \left(-\beta {{E}_{r}}\right)={{Z}_{r}}\\&\sum \limits _{s}^{}{}\exp \left(-\beta {{E}_{s}}\right)={{Z}_{S}}\\\end{aligned}}

LaTeXML (experimentell; verwendet MathML) rendering

MathML (0 B / 8 B) :

SVG image empty. Force Re-Rendering

SVG (0 B / 8 B) :

MathML (experimentell; keine Bilder) rendering

MathML (4.068 KB / 466 B) :

\begin{aligned} Z = \sum_{t, r, s}^{} \exp (- β E_{j}) = \sum_{t}^{} \exp (- β E_{t}) \sum_{r}^{} \exp (- β E_{r}) \sum_{s}^{} \exp (- β E_{s}) \\ E_{j} = E_{t j} + E_{s j} + E_{r j} \\ \sum_{t}^{} \exp (- β E_{t}) = Z_{t} \\ \sum_{r}^{} \exp (- β E_{r}) = Z_{r} \\ \sum_{s}^{} \exp (- β E_{s}) = Z_{S} \end{aligned}

<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>Z</mi><mo>=</mo><munderover><mo form="prefix" texclass="OP">&#x2211;</mo><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mi>t</mi><mo>,</mo><mi>r</mi><mo>,</mo><mi>s</mi></mrow></mrow><mrow data-mjx-texclass="ORD"></mrow></munderover><mi>exp</mi><mo>&#x2061;</mo><mrow data-mjx-texclass="INNER"><mo data-mjx-texclass="OPEN">(</mo><mo>&#x2212;</mo><mi>&#x03B2;</mi><msub><mi>E</mi><mrow data-mjx-texclass="ORD"><mi>j</mi></mrow></msub><mo data-mjx-texclass="CLOSE">)</mo></mrow><mo>=</mo><munderover><mo form="prefix" texclass="OP">&#x2211;</mo><mrow data-mjx-texclass="ORD"><mi>t</mi></mrow><mrow data-mjx-texclass="ORD"></mrow></munderover><mi>exp</mi><mo>&#x2061;</mo><mrow data-mjx-texclass="INNER"><mo data-mjx-texclass="OPEN">(</mo><mo>&#x2212;</mo><mi>&#x03B2;</mi><msub><mi>E</mi><mrow data-mjx-texclass="ORD"><mi>t</mi></mrow></msub><mo data-mjx-texclass="CLOSE">)</mo></mrow><munderover><mo form="prefix" texclass="OP">&#x2211;</mo><mrow data-mjx-texclass="ORD"><mi>r</mi></mrow><mrow data-mjx-texclass="ORD"></mrow></munderover><mi>exp</mi><mo>&#x2061;</mo><mrow data-mjx-texclass="INNER"><mo data-mjx-texclass="OPEN">(</mo><mo>&#x2212;</mo><mi>&#x03B2;</mi><msub><mi>E</mi><mrow data-mjx-texclass="ORD"><mi>r</mi></mrow></msub><mo data-mjx-texclass="CLOSE">)</mo></mrow><munderover><mo form="prefix" texclass="OP">&#x2211;</mo><mrow data-mjx-texclass="ORD"><mi>s</mi></mrow><mrow data-mjx-texclass="ORD"></mrow></munderover><mi>exp</mi><mo>&#x2061;</mo><mrow data-mjx-texclass="INNER"><mo data-mjx-texclass="OPEN">(</mo><mo>&#x2212;</mo><mi>&#x03B2;</mi><msub><mi>E</mi><mrow data-mjx-texclass="ORD"><mi>s</mi></mrow></msub><mo data-mjx-texclass="CLOSE">)</mo></mrow></mtd></mtr><mtr><mtd></mtd><mtd><msub><mi>E</mi><mrow data-mjx-texclass="ORD"><mi>j</mi></mrow></msub><mo>=</mo><msub><mi>E</mi><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mi>t</mi><mi>j</mi></mrow></mrow></msub><mo>+</mo><msub><mi>E</mi><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mi>s</mi><mi>j</mi></mrow></mrow></msub><mo>+</mo><msub><mi>E</mi><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mi>r</mi><mi>j</mi></mrow></mrow></msub></mtd></mtr><mtr><mtd></mtd><mtd><munderover><mo form="prefix" texclass="OP">&#x2211;</mo><mrow data-mjx-texclass="ORD"><mi>t</mi></mrow><mrow data-mjx-texclass="ORD"></mrow></munderover><mi>exp</mi><mo>&#x2061;</mo><mrow data-mjx-texclass="INNER"><mo data-mjx-texclass="OPEN">(</mo><mo>&#x2212;</mo><mi>&#x03B2;</mi><msub><mi>E</mi><mrow data-mjx-texclass="ORD"><mi>t</mi></mrow></msub><mo data-mjx-texclass="CLOSE">)</mo></mrow><mo>=</mo><msub><mi>Z</mi><mrow data-mjx-texclass="ORD"><mi>t</mi></mrow></msub></mtd></mtr><mtr><mtd></mtd><mtd><munderover><mo form="prefix" texclass="OP">&#x2211;</mo><mrow data-mjx-texclass="ORD"><mi>r</mi></mrow><mrow data-mjx-texclass="ORD"></mrow></munderover><mi>exp</mi><mo>&#x2061;</mo><mrow data-mjx-texclass="INNER"><mo data-mjx-texclass="OPEN">(</mo><mo>&#x2212;</mo><mi>&#x03B2;</mi><msub><mi>E</mi><mrow data-mjx-texclass="ORD"><mi>r</mi></mrow></msub><mo data-mjx-texclass="CLOSE">)</mo></mrow><mo>=</mo><msub><mi>Z</mi><mrow data-mjx-texclass="ORD"><mi>r</mi></mrow></msub></mtd></mtr><mtr><mtd></mtd><mtd><munderover><mo form="prefix" texclass="OP">&#x2211;</mo><mrow data-mjx-texclass="ORD"><mi>s</mi></mrow><mrow data-mjx-texclass="ORD"></mrow></munderover><mi>exp</mi><mo>&#x2061;</mo><mrow data-mjx-texclass="INNER"><mo data-mjx-texclass="OPEN">(</mo><mo>&#x2212;</mo><mi>&#x03B2;</mi><msub><mi>E</mi><mrow data-mjx-texclass="ORD"><mi>s</mi></mrow></msub><mo data-mjx-texclass="CLOSE">)</mo></mrow><mo>=</mo><msub><mi>Z</mi><mrow data-mjx-texclass="ORD"><mi>S</mi></mrow></msub></mtd></mtr><mtr><mtd></mtd></mtr></mtable></mrow></mstyle></mrow></math>

Translations to Computer Algebra Systems

Translation to Maple

In Maple:

Translation to Mathematica

In Mathematica:

Identifiers

$Z$

$t$

$r$

$s$

$β$

$E_{j}$

$t$

$β$

$E_{t}$

$r$

$β$

$E_{r}$

$s$

$β$

$E_{s}$

$E_{j}$

$E_{t j}$

$E_{s j}$

$E_{r j}$

$t$

$β$

$E_{t}$

$Z_{t}$

$r$

$β$

$E_{r}$

$Z_{r}$

$s$

$β$

$E_{s}$

$Z_{S}$

MathML observations

0results

no statistics present please run the maintenance script ExtractFeatures.php

0 results

General

LaTeXML (experimentell; verwendet MathML) rendering

MathML (experimentell; keine Bilder) rendering

Translations to Computer Algebra Systems

Translation to Maple

Translation to Mathematica

Similar pages

Identifiers

MathML observations

Navigationsmenü

General

LaTeXML (experimentell; verwendet MathML) rendering

MathML (experimentell; keine Bilder) rendering

Translations to Computer Algebra Systems

Translation to Maple

Translation to Mathematica

Similar pages

Identifiers

MathML observations

Navigationsmenü

Suche