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Display information for equation id:math.2528.22 on revision:2528

* Page found: Mehrkomponentige ideale Gase (eq math.2528.22)

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Hash: 935ca3694a9c0d72e76e845e968866b9

TeX (original user input):

\begin{align}

& {{{\tilde{\mu }}}_{i}}(T,p,{{x}_{i}})={{u}_{i}}(T)-T{{c}_{pi}}\ln T+RT+RT\ln p+RT\ln {{x}_{i}} \\

& {{u}_{i}}(T)-T{{c}_{pi}}\ln T+RT:={{\Phi }_{i}}(T) \\

& \Rightarrow {{{\tilde{\mu }}}_{i}}(T,p,{{x}_{i}})={{\Phi }_{i}}(T)+RT\ln ({{x}_{i}}p)={{\Phi }_{i}}(T)+RT\ln ({{p}_{i}}) \\

\end{align}

TeX (checked):

{\begin{aligned}&{{\tilde {\mu }}_{i}}(T,p,{{x}_{i}})={{u}_{i}}(T)-T{{c}_{pi}}\ln T+RT+RT\ln p+RT\ln {{x}_{i}}\\&{{u}_{i}}(T)-T{{c}_{pi}}\ln T+RT:={{\Phi }_{i}}(T)\\&\Rightarrow {{\tilde {\mu }}_{i}}(T,p,{{x}_{i}})={{\Phi }_{i}}(T)+RT\ln({{x}_{i}}p)={{\Phi }_{i}}(T)+RT\ln({{p}_{i}})\\\end{aligned}}

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MathML (experimentell; keine Bilder) rendering

MathML (2.947 KB / 450 B) :

μ~i(T,p,xi)=ui(T)TcpilnT+RT+RTlnp+RTlnxiui(T)TcpilnT+RT:=Φi(T)μ~i(T,p,xi)=Φi(T)+RTln(xip)=Φi(T)+RTln(pi)
<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><msub><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mover><mi>&#x03BC;</mi><mo>~</mo></mover></mrow></mrow><mrow data-mjx-texclass="ORD"><mi>i</mi></mrow></msub><mo stretchy="false">(</mo><mi>T</mi><mo>,</mo><mi>p</mi><mo>,</mo><msub><mi>x</mi><mrow data-mjx-texclass="ORD"><mi>i</mi></mrow></msub><mo stretchy="false">)</mo><mo>=</mo><msub><mi>u</mi><mrow data-mjx-texclass="ORD"><mi>i</mi></mrow></msub><mo stretchy="false">(</mo><mi>T</mi><mo stretchy="false">)</mo><mo>&#x2212;</mo><mi>T</mi><msub><mi>c</mi><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mi>p</mi><mi>i</mi></mrow></mrow></msub><mi>ln</mi><mo>&#x2061;</mo><mi>T</mi><mo>+</mo><mi>R</mi><mi>T</mi><mo>+</mo><mi>R</mi><mi>T</mi><mi>ln</mi><mo>&#x2061;</mo><mi>p</mi><mo>+</mo><mi>R</mi><mi>T</mi><mi>ln</mi><mo>&#x2061;</mo><msub><mi>x</mi><mrow data-mjx-texclass="ORD"><mi>i</mi></mrow></msub></mtd></mtr><mtr><mtd></mtd><mtd><msub><mi>u</mi><mrow data-mjx-texclass="ORD"><mi>i</mi></mrow></msub><mo stretchy="false">(</mo><mi>T</mi><mo stretchy="false">)</mo><mo>&#x2212;</mo><mi>T</mi><msub><mi>c</mi><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mi>p</mi><mi>i</mi></mrow></mrow></msub><mi>ln</mi><mo>&#x2061;</mo><mi>T</mi><mo>+</mo><mi>R</mi><mi>T</mi><mi>:</mi><mo>=</mo><msub><mi mathvariant="normal">&#x03A6;</mi><mrow data-mjx-texclass="ORD"><mi>i</mi></mrow></msub><mo stretchy="false">(</mo><mi>T</mi><mo stretchy="false">)</mo></mtd></mtr><mtr><mtd></mtd><mtd><mo>&#x21D2;</mo><msub><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mover><mi>&#x03BC;</mi><mo>~</mo></mover></mrow></mrow><mrow data-mjx-texclass="ORD"><mi>i</mi></mrow></msub><mo stretchy="false">(</mo><mi>T</mi><mo>,</mo><mi>p</mi><mo>,</mo><msub><mi>x</mi><mrow data-mjx-texclass="ORD"><mi>i</mi></mrow></msub><mo stretchy="false">)</mo><mo>=</mo><msub><mi mathvariant="normal">&#x03A6;</mi><mrow data-mjx-texclass="ORD"><mi>i</mi></mrow></msub><mo stretchy="false">(</mo><mi>T</mi><mo stretchy="false">)</mo><mo>+</mo><mi>R</mi><mi>T</mi><mi>ln</mi><mo>&#x2061;</mo><mo stretchy="false">(</mo><msub><mi>x</mi><mrow data-mjx-texclass="ORD"><mi>i</mi></mrow></msub><mi>p</mi><mo stretchy="false">)</mo><mo>=</mo><msub><mi mathvariant="normal">&#x03A6;</mi><mrow data-mjx-texclass="ORD"><mi>i</mi></mrow></msub><mo stretchy="false">(</mo><mi>T</mi><mo stretchy="false">)</mo><mo>+</mo><mi>R</mi><mi>T</mi><mi>ln</mi><mo>&#x2061;</mo><mo stretchy="false">(</mo><msub><mi>p</mi><mrow data-mjx-texclass="ORD"><mi>i</mi></mrow></msub><mo stretchy="false">)</mo></mtd></mtr><mtr><mtd></mtd></mtr></mtable></mrow></mstyle></mrow></math>

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Identifiers

  • μ~i
  • T
  • p
  • xi
  • ui
  • T
  • T
  • cpi
  • T
  • R
  • T
  • R
  • T
  • p
  • R
  • T
  • xi
  • ui
  • T
  • T
  • cpi
  • T
  • R
  • T
  • Φi
  • T
  • μ~i
  • T
  • p
  • xi
  • Φi
  • T
  • R
  • T
  • xi
  • p
  • Φi
  • T
  • R
  • T
  • pi

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