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Display information for equation id:math.2528.0 on revision:2528

* Page found: Mehrkomponentige ideale Gase (eq math.2528.0)

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TeX (original user input): 

\begin{align}

& U=\sum\limits_{i}^{{}}{{}}{{n}_{i}}{{u}_{i}}\left( T \right)=\sum\limits_{i}^{{}}{{}}{{n}_{i}}\int_{{{T}_{0}}}^{T}{{}}dT\acute{\ }{{c}_{vi}}\left( T\acute{\ } \right) \\

& S=\sum\limits_{i}^{{}}{{}}{{n}_{i}}{{s}_{i}}\left( T,{{v}_{i}} \right) \\

& {{s}_{i}}\left( T,{{v}_{i}} \right)=\int_{{{T}_{0}}}^{T}{{}}dT\acute{\ }\frac{{{c}_{vi}}\left( T\acute{\ } \right)}{T\acute{\ }}+R\ln \frac{{{v}_{i}}}{{{v}_{0}}} \\

\end{align}

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MathML (37.369 KB / 4.126 KB) :

U = ∑ i n i ⁢ u i ⁢ ( T ) = ∑ i n i ⁢ ∫ T 0 T 𝑑 T ⁢ ´ ⁢ c v ⁢ i ⁢ ( T ⁢ ´ ) S = ∑ i n i ⁢ s i ⁢ ( T , v i ) s i ⁢ ( T , v i ) = ∫ T 0 T 𝑑 T ⁢ ´ ⁢ c v ⁢ i ⁢ ( T ⁢ ´ ) T ⁢ ´ + R ⁢ ln ⁡ v i v 0 absent 𝑈 subscript 𝑖 subscript 𝑛 𝑖 subscript 𝑢 𝑖 𝑇 subscript 𝑖 subscript 𝑛 𝑖 superscript subscript subscript 𝑇 0 𝑇 differential-d 𝑇 ´ absent subscript 𝑐 𝑣 𝑖 𝑇 ´ absent absent 𝑆 subscript 𝑖 subscript 𝑛 𝑖 subscript 𝑠 𝑖 𝑇 subscript 𝑣 𝑖 absent subscript 𝑠 𝑖 𝑇 subscript 𝑣 𝑖 superscript subscript subscript 𝑇 0 𝑇 differential-d 𝑇 ´ absent subscript 𝑐 𝑣 𝑖 𝑇 ´ absent 𝑇 ´ absent 𝑅 subscript 𝑣 𝑖 subscript 𝑣 0 {\displaystyle{\displaystyle\begin{aligned} \par&\displaystyle U=\sum\limits_{% i}{{}}{{n}_{i}}{{u}_{i}}\left(T\right)=\sum\limits_{i}{{}}{{n}_{i}}\int_{{{T}_% {0}}}^{T}{{}}dT\acute{\ }{{c}_{vi}}\left(T\acute{\ }\right)\\ \par&\displaystyle S=\sum\limits_{i}{{}}{{n}_{i}}{{s}_{i}}\left(T,{{v}_{i}}% \right)\\ \par&\displaystyle{{s}_{i}}\left(T,{{v}_{i}}\right)=\int_{{{T}_{0}}}^{T}{{}}dT% \acute{\ }\frac{{{c}_{vi}}\left(T\acute{\ }\right)}{T\acute{\ }}+R\ln\frac{{{v% }_{i}}}{{{v}_{0}}}\\ \par\end{aligned}}}

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MathML (4.208 KB / 552 B) :

U=∑iniui(T)=∑ini∫T0TdT´cvi(T´)S=∑inisi(T,vi)si(T,vi)=∫T0TdT´cvi(T´)T´+Rln⁡viv0

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