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Display information for equation id:math.2446.12 on revision:2446

* Page found: Thermodynamischer Limes (eq math.2446.12)

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TeX (original user input): 

\begin{align}

& S\left( U,V,{{{\bar{N}}}^{\alpha }} \right)=\frac{\partial S}{\partial U}U+\frac{\partial S}{\partial V}V+\frac{\partial S}{\partial {{{\bar{N}}}^{\alpha }}}{{{\bar{N}}}^{\alpha }}=\frac{1}{T}U+\frac{p}{T}V-\frac{{{\mu }_{\alpha }}}{T}{{{\bar{N}}}^{\alpha }} \\

& \frac{\partial S}{\partial U}=\frac{1}{T} \\

& \frac{\partial S}{\partial V}=\frac{p}{T} \\

& \frac{\partial S}{\partial {{{\bar{N}}}^{\alpha }}}=-\frac{{{\mu }_{\alpha }}}{T} \\

\end{align}

TeX (checked): 

{\begin{aligned}&S\left(U,V,{{\bar {N}}^{\alpha }}\right)={\frac {\partial S}{\partial U}}U+{\frac {\partial S}{\partial V}}V+{\frac {\partial S}{\partial {{\bar {N}}^{\alpha }}}}{{\bar {N}}^{\alpha }}={\frac {1}{T}}U+{\frac {p}{T}}V-{\frac {{\mu }_{\alpha }}{T}}{{\bar {N}}^{\alpha }}\\&{\frac {\partial S}{\partial U}}={\frac {1}{T}}\\&{\frac {\partial S}{\partial V}}={\frac {p}{T}}\\&{\frac {\partial S}{\partial {{\bar {N}}^{\alpha }}}}=-{\frac {{\mu }_{\alpha }}{T}}\\\end{aligned}}

LaTeXML (experimentell; verwendet MathML) rendering

MathML (33.894 KB / 3.655 KB) :

S ⁢ ( U , V , N ¯ α ) = ∂ ⁡ S ∂ ⁡ U ⁢ U + ∂ ⁡ S ∂ ⁡ V ⁢ V + ∂ ⁡ S ∂ ⁡ N ¯ α ⁢ N ¯ α = 1 T ⁢ U + p T ⁢ V - μ α T ⁢ N ¯ α ∂ ⁡ S ∂ ⁡ U = 1 T ∂ ⁡ S ∂ ⁡ V = p T ∂ ⁡ S ∂ ⁡ N ¯ α = - μ α T absent 𝑆 𝑈 𝑉 superscript ¯ 𝑁 𝛼 𝑆 𝑈 𝑈 𝑆 𝑉 𝑉 𝑆 superscript ¯ 𝑁 𝛼 superscript ¯ 𝑁 𝛼 1 𝑇 𝑈 𝑝 𝑇 𝑉 subscript 𝜇 𝛼 𝑇 superscript ¯ 𝑁 𝛼 absent 𝑆 𝑈 1 𝑇 absent 𝑆 𝑉 𝑝 𝑇 absent 𝑆 superscript ¯ 𝑁 𝛼 subscript 𝜇 𝛼 𝑇 {\displaystyle{\displaystyle\begin{aligned} \par&\displaystyle S\left(U,V,{{{% \bar{N}}}^{\alpha}}\right)=\frac{\partial S}{\partial U}U+\frac{\partial S}{% \partial V}V+\frac{\partial S}{\partial{{{\bar{N}}}^{\alpha}}}{{{\bar{N}}}^{% \alpha}}=\frac{1}{T}U+\frac{p}{T}V-\frac{{{\mu}_{\alpha}}}{T}{{{\bar{N}}}^{% \alpha}}\\ \par&\displaystyle\frac{\partial S}{\partial U}=\frac{1}{T}\\ \par&\displaystyle\frac{\partial S}{\partial V}=\frac{p}{T}\\ \par&\displaystyle\frac{\partial S}{\partial{{{\bar{N}}}^{\alpha}}}=-\frac{{{% \mu}_{\alpha}}}{T}\\ \par\end{aligned}}}

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MathML (4.183 KB / 472 B) :

S(U,V,N¯α)=∂S∂UU+∂S∂VV+∂S∂N¯αN¯α=1TU+pTV−μαTN¯α∂S∂U=1T∂S∂V=pT∂S∂N¯α=−μαT

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Calculated based on the variables occurring on the entire Thermodynamischer Limes page

Identifiers

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