Wechseln zu: Navigation, Suche

General

Display information for equation id:50 on page id:457

* Page found: Reale Gase (eq 50) (force rerendering)

Occurences on the following pages:

   Reale Gase Eq: 50
TeX (as stored in database):
\begin{align}
 
& {{\left( \frac{\partial {{c}_{v}}}{\partial v} \right)}_{T}}=\frac{{{\partial }^{2}}u}{\partial T\partial v}=\frac{\partial }{\partial T}\left( \frac{a}{{{v}^{2}}} \right)=0 \\
 
& \Rightarrow {{c}_{v}}={{c}_{v}}(T) \\
 
\end{align}
MathML (10.559 KB / 1.739 KB) :
(cvv)T=2uTv=T(av2)=0subscriptsubscriptcvvTsuperscript2uTvTasuperscriptv20\displaystyle{{\left(\frac{\partial{{c}_{{v}}}}{\partial v}\right)}_{{T}}}=% \frac{{{\partial}^{{2}}}u}{\partial T\partial v}=\frac{\partial}{\partial T}% \left(\frac{a}{{{v}^{{2}}}}\right)=0
cv=cv(T)fragmentsnormal-⇒subscriptcvsubscriptcvfragmentsnormal-(Tnormal-)\displaystyle\Rightarrow{{c}_{{v}}}={{c}_{{v}}}(T)

SVG (0 B / 8 B) :
PNG (0 B / 8 B) :
Hash : 916173fd654a3c80f252cbf0a8110ff7

Similar pages

Calculataed based on the variables occuring on the entire Reale Gase page

  1. Thermodynamische Potenziale similarity 4.9793279%
  2. Phasenübergänge similarity 4.93780699%
  3. Der harmonische Oszillator similarity 4.58120513%
  4. Räumliche Isotropie similarity 4.46212637%
  5. Das ideale Gas similarity 4.29754729%
  6. Das ideale Fermigas similarity 4.28713403%
  7. Klassisch- mechanische Gleichgewichtsverteilungen similarity 4.1859383%
  8. Kanonisches Enseble similarity 4.10721776%
  9. Elektrische Multipolentwicklung similarity 4.00254052%
  10. Symmetrien und Erhaltungsgrößen similarity 3.94209876%

Variables

12 results

  • mo (1/22/1479)
  • mi u (1/20/1504)
  • mi c (3/37/2835)
  • mi v (6/211/3347)
  • mi a (1/37/5608)
  • mo (7/133/7333)
  • mo (6/142/9643)
  • mi T (4/142/10589)
  • mo = (4/144/18270)
  • mo ( (3/169/18822)
  • mo ) (3/169/18905)
  • mo (2/419/59187)

MathML


<table class="equationgroup ltx_align">
 
<tr id="S0.Ex1" class="equation baseline">
<td class="eqpad"/>
<td colspan="1" class="td right" style="text-align:right;"/>
<td colspan="1" class="td left" style="text-align:left;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\displaystyle{{\left(\frac{\partial{{c}_{{v}}}}{\partial v}\right)}_{{T}}}=%&#10;\frac{{{\partial}^{{2}}}u}{\partial T\partial v}=\frac{\partial}{\partial T}%&#10;\left(\frac{a}{{{v}^{{2}}}}\right)=0" id="S0.Ex1.m2.1" display="inline" xref="S0.Ex1.m2.1.cmml"><semantics id="S0.Ex1.m2.1a" xref="S0.Ex1.m2.1.cmml"><mrow id="S0.Ex1.m2.1.14" xref="S0.Ex1.m2.1.14.cmml"><msub id="S0.Ex1.m2.1.14.2" xref="S0.Ex1.m2.1.14.2.cmml"><mrow id="S0.Ex1.m2.1.2" xref="S0.Ex1.m2.1.2.cmml"><mo id="S0.Ex1.m2.1.2a" xref="S0.Ex1.m2.1.2.cmml">(</mo><mstyle displaystyle="true" id="S0.Ex1.m2.1.2b" xref="S0.Ex1.m2.1.2.cmml"><mfrac id="S0.Ex1.m2.1.2c" xref="S0.Ex1.m2.1.2.cmml"><mrow id="S0.Ex1.m2.1.2.2" xref="S0.Ex1.m2.1.2.2.cmml"><mo id="S0.Ex1.m2.1.2.2.1" xref="S0.Ex1.m2.1.2.2.1.cmml"></mo><mo id="S0.Ex1.m2.1.2.2a" xref="S0.Ex1.m2.1.2.2.cmml"></mo><msub id="S0.Ex1.m2.1.2.2.4" xref="S0.Ex1.m2.1.2.2.4.cmml"><mi id="S0.Ex1.m2.1.2.2.2" xref="S0.Ex1.m2.1.2.2.2.cmml">c</mi><mi id="S0.Ex1.m2.1.2.2.3.1" xref="S0.Ex1.m2.1.2.2.3.1.cmml">v</mi></msub></mrow><mrow id="S0.Ex1.m2.1.2.3" xref="S0.Ex1.m2.1.2.3.cmml"><mo id="S0.Ex1.m2.1.2.3.1" xref="S0.Ex1.m2.1.2.3.1.cmml"></mo><mo id="S0.Ex1.m2.1.2.3a" xref="S0.Ex1.m2.1.2.3.cmml"></mo><mi id="S0.Ex1.m2.1.2.3.2" xref="S0.Ex1.m2.1.2.3.2.cmml">v</mi></mrow></mfrac></mstyle><mo id="S0.Ex1.m2.1.2d" xref="S0.Ex1.m2.1.2.cmml">)</mo></mrow><mi id="S0.Ex1.m2.1.4.1" xref="S0.Ex1.m2.1.4.1.cmml">T</mi></msub><mo id="S0.Ex1.m2.1.5" xref="S0.Ex1.m2.1.5.cmml">=</mo><mstyle displaystyle="true" id="S0.Ex1.m2.1.6" xref="S0.Ex1.m2.1.6.cmml"><mfrac id="S0.Ex1.m2.1.6a" xref="S0.Ex1.m2.1.6.cmml"><mrow id="S0.Ex1.m2.1.6.2" xref="S0.Ex1.m2.1.6.2.cmml"><msup id="S0.Ex1.m2.1.6.2.4" xref="S0.Ex1.m2.1.6.2.4.cmml"><mo id="S0.Ex1.m2.1.6.2.1" xref="S0.Ex1.m2.1.6.2.1.cmml"></mo><mn id="S0.Ex1.m2.1.6.2.2.1" xref="S0.Ex1.m2.1.6.2.2.1.cmml">2</mn></msup><mo id="S0.Ex1.m2.1.6.2a" xref="S0.Ex1.m2.1.6.2.cmml"></mo><mi id="S0.Ex1.m2.1.6.2.3" xref="S0.Ex1.m2.1.6.2.3.cmml">u</mi></mrow><mrow id="S0.Ex1.m2.1.6.3" xref="S0.Ex1.m2.1.6.3.cmml"><mrow id="S0.Ex1.m2.1.6.3.6" xref="S0.Ex1.m2.1.6.3.6.cmml"><mo id="S0.Ex1.m2.1.6.3.1" xref="S0.Ex1.m2.1.6.3.1.cmml"></mo><mo id="S0.Ex1.m2.1.6.3.6a" xref="S0.Ex1.m2.1.6.3.6.cmml"></mo><mi id="S0.Ex1.m2.1.6.3.2" xref="S0.Ex1.m2.1.6.3.2.cmml">T</mi></mrow><mo id="S0.Ex1.m2.1.6.3.5" xref="S0.Ex1.m2.1.6.3.5.cmml"></mo><mrow id="S0.Ex1.m2.1.6.3.7" xref="S0.Ex1.m2.1.6.3.7.cmml"><mo id="S0.Ex1.m2.1.6.3.3" xref="S0.Ex1.m2.1.6.3.3.cmml"></mo><mo id="S0.Ex1.m2.1.6.3.7a" xref="S0.Ex1.m2.1.6.3.7.cmml"></mo><mi id="S0.Ex1.m2.1.6.3.4" xref="S0.Ex1.m2.1.6.3.4.cmml">v</mi></mrow></mrow></mfrac></mstyle><mo id="S0.Ex1.m2.1.7" xref="S0.Ex1.m2.1.7.cmml">=</mo><mrow id="S0.Ex1.m2.1.14.3" xref="S0.Ex1.m2.1.14.3.cmml"><mstyle displaystyle="true" id="S0.Ex1.m2.1.8" xref="S0.Ex1.m2.1.8.cmml"><mfrac id="S0.Ex1.m2.1.8a" xref="S0.Ex1.m2.1.8.cmml"><mo id="S0.Ex1.m2.1.8.2" xref="S0.Ex1.m2.1.8.2.cmml"></mo><mrow id="S0.Ex1.m2.1.8.3" xref="S0.Ex1.m2.1.8.3.cmml"><mo id="S0.Ex1.m2.1.8.3.1" xref="S0.Ex1.m2.1.8.3.1.cmml"></mo><mo id="S0.Ex1.m2.1.8.3a" xref="S0.Ex1.m2.1.8.3.cmml"></mo><mi id="S0.Ex1.m2.1.8.3.2" xref="S0.Ex1.m2.1.8.3.2.cmml">T</mi></mrow></mfrac></mstyle><mo id="S0.Ex1.m2.1.14.3.1" xref="S0.Ex1.m2.1.14.3.1.cmml"></mo><mrow id="S0.Ex1.m2.1.10" xref="S0.Ex1.m2.1.10.cmml"><mo id="S0.Ex1.m2.1.10a" xref="S0.Ex1.m2.1.10.cmml">(</mo><mstyle displaystyle="true" id="S0.Ex1.m2.1.10b" xref="S0.Ex1.m2.1.10.cmml"><mfrac id="S0.Ex1.m2.1.10c" xref="S0.Ex1.m2.1.10.cmml"><mi id="S0.Ex1.m2.1.10.2" xref="S0.Ex1.m2.1.10.2.cmml">a</mi><msup id="S0.Ex1.m2.1.10.3" xref="S0.Ex1.m2.1.10.3.cmml"><mi id="S0.Ex1.m2.1.10.3.1" xref="S0.Ex1.m2.1.10.3.1.cmml">v</mi><mn id="S0.Ex1.m2.1.10.3.2.1" xref="S0.Ex1.m2.1.10.3.2.1.cmml">2</mn></msup></mfrac></mstyle><mo id="S0.Ex1.m2.1.10d" xref="S0.Ex1.m2.1.10.cmml">)</mo></mrow></mrow><mo id="S0.Ex1.m2.1.12" xref="S0.Ex1.m2.1.12.cmml">=</mo><mn id="S0.Ex1.m2.1.13" xref="S0.Ex1.m2.1.13.cmml">0</mn></mrow><annotation-xml id="S0.Ex1.m2.1.cmml" encoding="MathML-Content" xref="S0.Ex1.m2.1"><apply id="S0.Ex1.m2.1.14.cmml" xref="S0.Ex1.m2.1.14"><and id="S0.Ex1.m2.1.14a.cmml" xref="S0.Ex1.m2.1.14"/><apply id="S0.Ex1.m2.1.14b.cmml" xref="S0.Ex1.m2.1.14"><eq id="S0.Ex1.m2.1.5.cmml" xref="S0.Ex1.m2.1.5"/><apply id="S0.Ex1.m2.1.14.2.cmml" xref="S0.Ex1.m2.1.14.2"><csymbol cd="ambiguous" id="S0.Ex1.m2.1.14.2.1.cmml">subscript</csymbol><apply id="S0.Ex1.m2.1.2.cmml" xref="S0.Ex1.m2.1.2"><divide id="S0.Ex1.m2.1.2.1.cmml"/><apply id="S0.Ex1.m2.1.2.2.cmml" xref="S0.Ex1.m2.1.2.2"><partialdiff id="S0.Ex1.m2.1.2.2.1.cmml" xref="S0.Ex1.m2.1.2.2.1"/><apply id="S0.Ex1.m2.1.2.2.4.cmml" xref="S0.Ex1.m2.1.2.2.4"><csymbol cd="ambiguous" id="S0.Ex1.m2.1.2.2.4.1.cmml">subscript</csymbol><ci id="S0.Ex1.m2.1.2.2.2.cmml" xref="S0.Ex1.m2.1.2.2.2">c</ci><ci id="S0.Ex1.m2.1.2.2.3.1.cmml" xref="S0.Ex1.m2.1.2.2.3.1">v</ci></apply></apply><apply id="S0.Ex1.m2.1.2.3.cmml" xref="S0.Ex1.m2.1.2.3"><partialdiff id="S0.Ex1.m2.1.2.3.1.cmml" xref="S0.Ex1.m2.1.2.3.1"/><ci id="S0.Ex1.m2.1.2.3.2.cmml" xref="S0.Ex1.m2.1.2.3.2">v</ci></apply></apply><ci id="S0.Ex1.m2.1.4.1.cmml" xref="S0.Ex1.m2.1.4.1">T</ci></apply><apply id="S0.Ex1.m2.1.6.cmml" xref="S0.Ex1.m2.1.6"><divide id="S0.Ex1.m2.1.6.1.cmml"/><apply id="S0.Ex1.m2.1.6.2.cmml" xref="S0.Ex1.m2.1.6.2"><apply id="S0.Ex1.m2.1.6.2.4.cmml" xref="S0.Ex1.m2.1.6.2.4"><csymbol cd="ambiguous" id="S0.Ex1.m2.1.6.2.4.1.cmml">superscript</csymbol><partialdiff id="S0.Ex1.m2.1.6.2.1.cmml" xref="S0.Ex1.m2.1.6.2.1"/><cn type="integer" id="S0.Ex1.m2.1.6.2.2.1.cmml" xref="S0.Ex1.m2.1.6.2.2.1">2</cn></apply><ci id="S0.Ex1.m2.1.6.2.3.cmml" xref="S0.Ex1.m2.1.6.2.3">u</ci></apply><apply id="S0.Ex1.m2.1.6.3.cmml" xref="S0.Ex1.m2.1.6.3"><times id="S0.Ex1.m2.1.6.3.5.cmml" xref="S0.Ex1.m2.1.6.3.5"/><apply id="S0.Ex1.m2.1.6.3.6.cmml" xref="S0.Ex1.m2.1.6.3.6"><partialdiff id="S0.Ex1.m2.1.6.3.1.cmml" xref="S0.Ex1.m2.1.6.3.1"/><ci id="S0.Ex1.m2.1.6.3.2.cmml" xref="S0.Ex1.m2.1.6.3.2">T</ci></apply><apply id="S0.Ex1.m2.1.6.3.7.cmml" xref="S0.Ex1.m2.1.6.3.7"><partialdiff id="S0.Ex1.m2.1.6.3.3.cmml" xref="S0.Ex1.m2.1.6.3.3"/><ci id="S0.Ex1.m2.1.6.3.4.cmml" xref="S0.Ex1.m2.1.6.3.4">v</ci></apply></apply></apply></apply><apply id="S0.Ex1.m2.1.14c.cmml" xref="S0.Ex1.m2.1.14"><eq id="S0.Ex1.m2.1.7.cmml" xref="S0.Ex1.m2.1.7"/><share href="#S0.Ex1.m2.1.6.cmml" id="S0.Ex1.m2.1.14d.cmml" xref="S0.Ex1.m2.1.14"/><apply id="S0.Ex1.m2.1.14.3.cmml" xref="S0.Ex1.m2.1.14.3"><times id="S0.Ex1.m2.1.14.3.1.cmml" xref="S0.Ex1.m2.1.14.3.1"/><apply id="S0.Ex1.m2.1.8.cmml" xref="S0.Ex1.m2.1.8"><divide id="S0.Ex1.m2.1.8.1.cmml"/><partialdiff id="S0.Ex1.m2.1.8.2.cmml" xref="S0.Ex1.m2.1.8.2"/><apply id="S0.Ex1.m2.1.8.3.cmml" xref="S0.Ex1.m2.1.8.3"><partialdiff id="S0.Ex1.m2.1.8.3.1.cmml" xref="S0.Ex1.m2.1.8.3.1"/><ci id="S0.Ex1.m2.1.8.3.2.cmml" xref="S0.Ex1.m2.1.8.3.2">T</ci></apply></apply><apply id="S0.Ex1.m2.1.10.cmml" xref="S0.Ex1.m2.1.10"><divide id="S0.Ex1.m2.1.10.1.cmml"/><ci id="S0.Ex1.m2.1.10.2.cmml" xref="S0.Ex1.m2.1.10.2">a</ci><apply id="S0.Ex1.m2.1.10.3.cmml" xref="S0.Ex1.m2.1.10.3"><csymbol cd="ambiguous" id="S0.Ex1.m2.1.10.3.3.cmml">superscript</csymbol><ci id="S0.Ex1.m2.1.10.3.1.cmml" xref="S0.Ex1.m2.1.10.3.1">v</ci><cn type="integer" id="S0.Ex1.m2.1.10.3.2.1.cmml" xref="S0.Ex1.m2.1.10.3.2.1">2</cn></apply></apply></apply></apply><apply id="S0.Ex1.m2.1.14e.cmml" xref="S0.Ex1.m2.1.14"><eq id="S0.Ex1.m2.1.12.cmml" xref="S0.Ex1.m2.1.12"/><share href="#S0.Ex1.m2.1.14.3.cmml" id="S0.Ex1.m2.1.14f.cmml" xref="S0.Ex1.m2.1.14"/><cn type="integer" id="S0.Ex1.m2.1.13.cmml" xref="S0.Ex1.m2.1.13">0</cn></apply></apply></annotation-xml><annotation id="S0.Ex1.m2.1b" encoding="application/x-tex" xref="S0.Ex1.m2.1.cmml">\displaystyle{{\left(\frac{\partial{{c}_{{v}}}}{\partial v}\right)}_{{T}}}=%
\frac{{{\partial}^{{2}}}u}{\partial T\partial v}=\frac{\partial}{\partial T}%
\left(\frac{a}{{{v}^{{2}}}}\right)=0</annotation></semantics></math></td>
<td class="eqpad"/></tr>
<tr id="S0.Ex2" class="equation baseline">
<td class="eqpad"/>
<td colspan="1" class="td right" style="text-align:right;"/>
<td colspan="1" class="td left" style="text-align:left;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\displaystyle\Rightarrow{{c}_{{v}}}={{c}_{{v}}}(T)" id="S0.Ex2.m2.1" display="inline" xref="S0.Ex2.m2.1.cmml"><semantics id="S0.Ex2.m2.1a" xref="S0.Ex2.m2.1.cmml"><mrow id="S0.Ex2.m2.1b" xref="S0.Ex2.m2.1.cmml"><mo id="S0.Ex2.m2.1.1" xref="S0.Ex2.m2.1.1.cmml"></mo><msub id="S0.Ex2.m2.1.10" xref="S0.Ex2.m2.1.10.cmml"><mi id="S0.Ex2.m2.1.2" xref="S0.Ex2.m2.1.2.cmml">c</mi><mi id="S0.Ex2.m2.1.3.1" xref="S0.Ex2.m2.1.3.1.cmml">v</mi></msub><mo id="S0.Ex2.m2.1.4" xref="S0.Ex2.m2.1.4.cmml">=</mo><msub id="S0.Ex2.m2.1.11" xref="S0.Ex2.m2.1.11.cmml"><mi id="S0.Ex2.m2.1.5" xref="S0.Ex2.m2.1.5.cmml">c</mi><mi id="S0.Ex2.m2.1.6.1" xref="S0.Ex2.m2.1.6.1.cmml">v</mi></msub><mrow id="S0.Ex2.m2.1.12" xref="S0.Ex2.m2.1.12.cmml"><mo id="S0.Ex2.m2.1.7" xref="S0.Ex2.m2.1.7.cmml">(</mo><mi id="S0.Ex2.m2.1.8">T</mi><mo id="S0.Ex2.m2.1.9" xref="S0.Ex2.m2.1.9.cmml">)</mo></mrow></mrow><annotation-xml id="S0.Ex2.m2.1.cmml" encoding="MathML-Content" xref="S0.Ex2.m2.1"><cerror id="S0.Ex2.m2.1a.cmml" xref="S0.Ex2.m2.1"><csymbol cd="ambiguous" id="S0.Ex2.m2.1b.cmml" xref="S0.Ex2.m2.1">fragments</csymbol><ci id="S0.Ex2.m2.1.1.cmml" xref="S0.Ex2.m2.1.1">normal-⇒</ci><apply id="S0.Ex2.m2.1.10.cmml" xref="S0.Ex2.m2.1.10"><csymbol cd="ambiguous" id="S0.Ex2.m2.1.10.1.cmml">subscript</csymbol><ci id="S0.Ex2.m2.1.2.cmml" xref="S0.Ex2.m2.1.2">c</ci><ci id="S0.Ex2.m2.1.3.1.cmml" xref="S0.Ex2.m2.1.3.1">v</ci></apply><eq id="S0.Ex2.m2.1.4.cmml" xref="S0.Ex2.m2.1.4"/><apply id="S0.Ex2.m2.1.11.cmml" xref="S0.Ex2.m2.1.11"><csymbol cd="ambiguous" id="S0.Ex2.m2.1.11.1.cmml">subscript</csymbol><ci id="S0.Ex2.m2.1.5.cmml" xref="S0.Ex2.m2.1.5">c</ci><ci id="S0.Ex2.m2.1.6.1.cmml" xref="S0.Ex2.m2.1.6.1">v</ci></apply><cerror id="S0.Ex2.m2.1.12.cmml" xref="S0.Ex2.m2.1.12"><csymbol cd="ambiguous" id="S0.Ex2.m2.1.12a.cmml" xref="S0.Ex2.m2.1.12">fragments</csymbol><ci id="S0.Ex2.m2.1.7.cmml" xref="S0.Ex2.m2.1.7">normal-(</ci><csymbol cd="unknown" id="S0.Ex2.m2.1.12b.cmml" xref="S0.Ex2.m2.1.12">T</csymbol><ci id="S0.Ex2.m2.1.9.cmml" xref="S0.Ex2.m2.1.9">normal-)</ci></cerror></cerror></annotation-xml><annotation id="S0.Ex2.m2.1c" encoding="application/x-tex" xref="S0.Ex2.m2.1.cmml">\displaystyle\Rightarrow{{c}_{{v}}}={{c}_{{v}}}(T)</annotation></semantics></math></td>
<td class="eqpad"/></tr>
</table>