Jump to navigation Jump to search

General

Display information for equation id:math.2491.49 on revision:2491

* Page found: Gleichgewichtsbedingungen (eq math.2491.49)

(force rerendering)

Occurrences on the following pages:

Hash: 2cb87526bdf8ad7610a4d008d4f9adce

TeX (original user input): 

dF=d\left( U-TS \right)=dU-TdS=!=\delta W=\left( p\acute{\ }\acute{\ }-p\acute{\ }+\frac{2}{r}\sigma  \right)dV\acute{\ }=!=0

TeX (checked): 

dF=d\left(U-TS\right)=dU-TdS=!=\delta W=\left(p{\acute {\ }}{\acute {\ }}-p{\acute {\ }}+{\frac {2}{r}}\sigma \right)dV{\acute {\ }}=!=0

LaTeXML (experimental; uses MathML) rendering

MathML (8.425 KB / 1.451 KB) :

d F = d ( U - T S ) = d U - T d S = ! = δ W = ( p ´ ´ - p ´ + 2 r σ ) d V ´ = ! = 0 fragments d F d fragments ( U T S ) d U T d S δ W fragments ( p ´ absent ´ absent p ´ absent 2 𝑟 σ ) d V ´ absent 0 {\displaystyle{\displaystyle dF=d\left(U-TS\right)=dU-TdS=!=\delta W=\left(p% \acute{\ }\acute{\ }-p\acute{\ }+\frac{2}{r}\sigma\right)dV\acute{\ }=!=0}} 
<math xmlns="http://www.w3.org/1998/Math/MathML" id="p1.1.m1.1" class="ltx_Math" alttext="{\displaystyle{\displaystyle dF=d\left(U-TS\right)=dU-TdS=!=\delta W=\left(p%&#10;\acute{\ }\acute{\ }-p\acute{\ }+\frac{2}{r}\sigma\right)dV\acute{\ }=!=0}}" display="inline">
  <semantics id="p1.1.m1.1a">
    <mrow id="p1.1.m1.1b">
      <mi id="p1.1.m1.1.1" xref="p1.1.m1.1.1.cmml">d</mi>
      <mi id="p1.1.m1.1.2" xref="p1.1.m1.1.2.cmml">F</mi>
      <mo id="p1.1.m1.1.3" xref="p1.1.m1.1.3.cmml">=</mo>
      <mi id="p1.1.m1.1.4" xref="p1.1.m1.1.4.cmml">d</mi>
      <mrow id="p1.1.m1.1.42" xref="p1.1.m1.1.42.cmml">
        <mo id="p1.1.m1.1.5" xref="p1.1.m1.1.5.cmml">(</mo>
        <mi id="p1.1.m1.1.6" xref="p1.1.m1.1.6.cmml">U</mi>
        <mo id="p1.1.m1.1.7" xref="p1.1.m1.1.7.cmml">-</mo>
        <mi id="p1.1.m1.1.8" xref="p1.1.m1.1.8.cmml">T</mi>
        <mi id="p1.1.m1.1.9" xref="p1.1.m1.1.9.cmml">S</mi>
        <mo id="p1.1.m1.1.10" xref="p1.1.m1.1.10.cmml">)</mo>
      </mrow>
      <mo id="p1.1.m1.1.11" xref="p1.1.m1.1.11.cmml">=</mo>
      <mi id="p1.1.m1.1.12" xref="p1.1.m1.1.12.cmml">d</mi>
      <mi id="p1.1.m1.1.13" xref="p1.1.m1.1.13.cmml">U</mi>
      <mo id="p1.1.m1.1.14" xref="p1.1.m1.1.14.cmml">-</mo>
      <mi id="p1.1.m1.1.15" xref="p1.1.m1.1.15.cmml">T</mi>
      <mi id="p1.1.m1.1.16" xref="p1.1.m1.1.16.cmml">d</mi>
      <mi id="p1.1.m1.1.17" xref="p1.1.m1.1.17.cmml">S</mi>
      <mo id="p1.1.m1.1.18" xref="p1.1.m1.1.18.cmml">=</mo>
      <mo lspace="0pt" rspace="3.5pt" id="p1.1.m1.1.19" xref="p1.1.m1.1.19.cmml">!</mo>
      <mo id="p1.1.m1.1.20" xref="p1.1.m1.1.20.cmml">=</mo>
      <mi id="p1.1.m1.1.21" xref="p1.1.m1.1.21.cmml">δ</mi>
      <mi id="p1.1.m1.1.22" xref="p1.1.m1.1.22.cmml">W</mi>
      <mo id="p1.1.m1.1.23" xref="p1.1.m1.1.23.cmml">=</mo>
      <mrow id="p1.1.m1.1.43" xref="p1.1.m1.1.43.cmml">
        <mo id="p1.1.m1.1.24" xref="p1.1.m1.1.24.cmml">(</mo>
        <mi id="p1.1.m1.1.25" xref="p1.1.m1.1.25.cmml">p</mi>
        <mover accent="true" id="p1.1.m1.1.26" xref="p1.1.m1.1.26.cmml">
          <mi id="p1.1.m1.1.26.2" xref="p1.1.m1.1.26.2.cmml"/>
          <mo id="p1.1.m1.1.26.1" xref="p1.1.m1.1.26.1.cmml">´</mo>
        </mover>
        <mover accent="true" id="p1.1.m1.1.27" xref="p1.1.m1.1.27.cmml">
          <mi id="p1.1.m1.1.27.2" xref="p1.1.m1.1.27.2.cmml"/>
          <mo id="p1.1.m1.1.27.1" xref="p1.1.m1.1.27.1.cmml">´</mo>
        </mover>
        <mo id="p1.1.m1.1.28" xref="p1.1.m1.1.28.cmml">-</mo>
        <mi id="p1.1.m1.1.29" xref="p1.1.m1.1.29.cmml">p</mi>
        <mover accent="true" id="p1.1.m1.1.30" xref="p1.1.m1.1.30.cmml">
          <mi id="p1.1.m1.1.30.2" xref="p1.1.m1.1.30.2.cmml"/>
          <mo id="p1.1.m1.1.30.1" xref="p1.1.m1.1.30.1.cmml">´</mo>
        </mover>
        <mo id="p1.1.m1.1.31" xref="p1.1.m1.1.31.cmml">+</mo>
        <mstyle displaystyle="true" id="p1.1.m1.1.32" xref="p1.1.m1.1.32.cmml">
          <mfrac id="p1.1.m1.1.32a" xref="p1.1.m1.1.32.cmml">
            <mn id="p1.1.m1.1.32.2" xref="p1.1.m1.1.32.2.cmml">2</mn>
            <mi id="p1.1.m1.1.32.3" xref="p1.1.m1.1.32.3.cmml">r</mi>
          </mfrac>
        </mstyle>
        <mi id="p1.1.m1.1.33" xref="p1.1.m1.1.33.cmml">σ</mi>
        <mo id="p1.1.m1.1.34" xref="p1.1.m1.1.34.cmml">)</mo>
      </mrow>
      <mi id="p1.1.m1.1.35" xref="p1.1.m1.1.35.cmml">d</mi>
      <mi id="p1.1.m1.1.36" xref="p1.1.m1.1.36.cmml">V</mi>
      <mover accent="true" id="p1.1.m1.1.37" xref="p1.1.m1.1.37.cmml">
        <mi id="p1.1.m1.1.37.2" xref="p1.1.m1.1.37.2.cmml"/>
        <mo id="p1.1.m1.1.37.1" xref="p1.1.m1.1.37.1.cmml">´</mo>
      </mover>
      <mo id="p1.1.m1.1.38" xref="p1.1.m1.1.38.cmml">=</mo>
      <mo lspace="0pt" rspace="3.5pt" id="p1.1.m1.1.39" xref="p1.1.m1.1.39.cmml">!</mo>
      <mo id="p1.1.m1.1.40" xref="p1.1.m1.1.40.cmml">=</mo>
      <mn id="p1.1.m1.1.41" xref="p1.1.m1.1.41.cmml">0</mn>
    </mrow>
    <annotation-xml encoding="MathML-Content" id="p1.1.m1.1c">
      <cerror id="p1.1.m1.1d">
        <csymbol cd="ambiguous" id="p1.1.m1.1e">fragments</csymbol>
        <csymbol cd="unknown" id="p1.1.m1.1.1.cmml" xref="p1.1.m1.1.1">d</csymbol>
        <csymbol cd="unknown" id="p1.1.m1.1.2.cmml" xref="p1.1.m1.1.2">F</csymbol>
        <eq id="p1.1.m1.1.3.cmml" xref="p1.1.m1.1.3"/>
        <csymbol cd="unknown" id="p1.1.m1.1.4.cmml" xref="p1.1.m1.1.4">d</csymbol>
        <cerror id="p1.1.m1.1.42.cmml" xref="p1.1.m1.1.42">
          <csymbol cd="ambiguous" id="p1.1.m1.1.42a.cmml" xref="p1.1.m1.1.42">fragments</csymbol>
          <ci id="p1.1.m1.1.5.cmml" xref="p1.1.m1.1.5">(</ci>
          <csymbol cd="unknown" id="p1.1.m1.1.6.cmml" xref="p1.1.m1.1.6">U</csymbol>
          <minus id="p1.1.m1.1.7.cmml" xref="p1.1.m1.1.7"/>
          <csymbol cd="unknown" id="p1.1.m1.1.8.cmml" xref="p1.1.m1.1.8">T</csymbol>
          <csymbol cd="unknown" id="p1.1.m1.1.9.cmml" xref="p1.1.m1.1.9">S</csymbol>
          <ci id="p1.1.m1.1.10.cmml" xref="p1.1.m1.1.10">)</ci>
        </cerror>
        <eq id="p1.1.m1.1.11.cmml" xref="p1.1.m1.1.11"/>
        <csymbol cd="unknown" id="p1.1.m1.1.12.cmml" xref="p1.1.m1.1.12">d</csymbol>
        <csymbol cd="unknown" id="p1.1.m1.1.13.cmml" xref="p1.1.m1.1.13">U</csymbol>
        <minus id="p1.1.m1.1.14.cmml" xref="p1.1.m1.1.14"/>
        <csymbol cd="unknown" id="p1.1.m1.1.15.cmml" xref="p1.1.m1.1.15">T</csymbol>
        <csymbol cd="unknown" id="p1.1.m1.1.16.cmml" xref="p1.1.m1.1.16">d</csymbol>
        <csymbol cd="unknown" id="p1.1.m1.1.17.cmml" xref="p1.1.m1.1.17">S</csymbol>
        <eq id="p1.1.m1.1.18.cmml" xref="p1.1.m1.1.18"/>
        <factorial id="p1.1.m1.1.19.cmml" xref="p1.1.m1.1.19"/>
        <eq id="p1.1.m1.1.20.cmml" xref="p1.1.m1.1.20"/>
        <csymbol cd="unknown" id="p1.1.m1.1.21.cmml" xref="p1.1.m1.1.21">δ</csymbol>
        <csymbol cd="unknown" id="p1.1.m1.1.22.cmml" xref="p1.1.m1.1.22">W</csymbol>
        <eq id="p1.1.m1.1.23.cmml" xref="p1.1.m1.1.23"/>
        <cerror id="p1.1.m1.1.43.cmml" xref="p1.1.m1.1.43">
          <csymbol cd="ambiguous" id="p1.1.m1.1.43a.cmml" xref="p1.1.m1.1.43">fragments</csymbol>
          <ci id="p1.1.m1.1.24.cmml" xref="p1.1.m1.1.24">(</ci>
          <csymbol cd="unknown" id="p1.1.m1.1.25.cmml" xref="p1.1.m1.1.25">p</csymbol>
          <apply id="p1.1.m1.1.26.cmml" xref="p1.1.m1.1.26">
            <ci id="p1.1.m1.1.26.1.cmml" xref="p1.1.m1.1.26.1">´</ci>
            <csymbol cd="latexml" id="p1.1.m1.1.26.2.cmml" xref="p1.1.m1.1.26.2">absent</csymbol>
          </apply>
          <apply id="p1.1.m1.1.27.cmml" xref="p1.1.m1.1.27">
            <ci id="p1.1.m1.1.27.1.cmml" xref="p1.1.m1.1.27.1">´</ci>
            <csymbol cd="latexml" id="p1.1.m1.1.27.2.cmml" xref="p1.1.m1.1.27.2">absent</csymbol>
          </apply>
          <minus id="p1.1.m1.1.28.cmml" xref="p1.1.m1.1.28"/>
          <csymbol cd="unknown" id="p1.1.m1.1.29.cmml" xref="p1.1.m1.1.29">p</csymbol>
          <apply id="p1.1.m1.1.30.cmml" xref="p1.1.m1.1.30">
            <ci id="p1.1.m1.1.30.1.cmml" xref="p1.1.m1.1.30.1">´</ci>
            <csymbol cd="latexml" id="p1.1.m1.1.30.2.cmml" xref="p1.1.m1.1.30.2">absent</csymbol>
          </apply>
          <plus id="p1.1.m1.1.31.cmml" xref="p1.1.m1.1.31"/>
          <apply id="p1.1.m1.1.32.cmml" xref="p1.1.m1.1.32">
            <divide id="p1.1.m1.1.32.1.cmml" xref="p1.1.m1.1.32"/>
            <cn type="integer" id="p1.1.m1.1.32.2.cmml" xref="p1.1.m1.1.32.2">2</cn>
            <ci id="p1.1.m1.1.32.3.cmml" xref="p1.1.m1.1.32.3">𝑟</ci>
          </apply>
          <csymbol cd="unknown" id="p1.1.m1.1.33.cmml" xref="p1.1.m1.1.33">σ</csymbol>
          <ci id="p1.1.m1.1.34.cmml" xref="p1.1.m1.1.34">)</ci>
        </cerror>
        <csymbol cd="unknown" id="p1.1.m1.1.35.cmml" xref="p1.1.m1.1.35">d</csymbol>
        <csymbol cd="unknown" id="p1.1.m1.1.36.cmml" xref="p1.1.m1.1.36">V</csymbol>
        <apply id="p1.1.m1.1.37.cmml" xref="p1.1.m1.1.37">
          <ci id="p1.1.m1.1.37.1.cmml" xref="p1.1.m1.1.37.1">´</ci>
          <csymbol cd="latexml" id="p1.1.m1.1.37.2.cmml" xref="p1.1.m1.1.37.2">absent</csymbol>
        </apply>
        <eq id="p1.1.m1.1.38.cmml" xref="p1.1.m1.1.38"/>
        <factorial id="p1.1.m1.1.39.cmml" xref="p1.1.m1.1.39"/>
        <eq id="p1.1.m1.1.40.cmml" xref="p1.1.m1.1.40"/>
        <cn type="integer" id="p1.1.m1.1.41.cmml" xref="p1.1.m1.1.41">0</cn>
      </cerror>
    </annotation-xml>
    <annotation encoding="application/x-tex" id="p1.1.m1.1f">{\displaystyle{\displaystyle dF=d\left(U-TS\right)=dU-TdS=!=\delta W=\left(p%
\acute{\ }\acute{\ }-p\acute{\ }+\frac{2}{r}\sigma\right)dV\acute{\ }=!=0}}</annotation>
  </semantics>
</math>

SVG image empty. Force Re-Rendering

SVG (0 B / 8 B) :


MathML (experimental; no images) rendering

MathML (1.465 KB / 363 B) :

dF=d(U−TS)=dU−TdS=!=δW=(p´´−p´+2rσ)dV´=!=0
<math class="mwe-math-element" xmlns="http://www.w3.org/1998/Math/MathML"><mrow data-mjx-texclass="ORD"><mstyle displaystyle="true" scriptlevel="0"><mi>d</mi><mi>F</mi><mo>=</mo><mi>d</mi><mrow data-mjx-texclass="INNER"><mo data-mjx-texclass="OPEN">(</mo><mi>U</mi><mo>&#x2212;</mo><mi>T</mi><mi>S</mi><mo data-mjx-texclass="CLOSE">)</mo></mrow><mo>=</mo><mi>d</mi><mi>U</mi><mo>&#x2212;</mo><mi>T</mi><mi>d</mi><mi>S</mi><mo>=</mo><mi>!</mi><mo>=</mo><mi>&#x03B4;</mi><mi>W</mi><mo>=</mo><mrow data-mjx-texclass="INNER"><mo data-mjx-texclass="OPEN">(</mo><mi>p</mi><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 data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mover><mspace width="0.5em"/><mo data-mjx-pseudoscript="true">´</mo></mover></mrow></mrow><mo>&#x2212;</mo><mi>p</mi><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mover><mspace width="0.5em"/><mo data-mjx-pseudoscript="true">´</mo></mover></mrow></mrow><mo>+</mo><mrow data-mjx-texclass="ORD"><mfrac><mrow data-mjx-texclass="ORD"><mn>2</mn></mrow><mrow data-mjx-texclass="ORD"><mi>r</mi></mrow></mfrac></mrow><mi>&#x03C3;</mi><mo data-mjx-texclass="CLOSE">)</mo></mrow><mi>d</mi><mi>V</mi><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mover><mspace width="0.5em"/><mo data-mjx-pseudoscript="true">´</mo></mover></mrow></mrow><mo>=</mo><mi>!</mi><mo>=</mo><mn>0</mn></mstyle></mrow></math>

Translations to Computer Algebra Systems

Translation to Maple

In Maple:

Translation to Mathematica

In Mathematica:

Similar pages

Calculated based on the variables occurring on the entire Gleichgewichtsbedingungen page

Identifiers

  • d
  • F
  • d
  • U
  • T
  • S
  • d
  • U
  • T
  • d
  • S
  • δ
  • W
  • p
  • ´
  • ´
  • p
  • ´
  • r
  • σ
  • d
  • V
  • ´

MathML observations

0results

0results

no statistics present please run the maintenance script ExtractFeatures.php

0 results

0 results

Retrieved from "http://physikerwelt.de:8080/w/index.php?title=Special:FormulaInfo"