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Display information for equation id:math.2561.20 on revision:2561

* Page found: Das ideale Bosegas (eq math.2561.20)

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Das ideale Bosegas Eq: math.2561.20

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TeX (original user input):

\begin{align}
  & U\approx \frac{3}{2}\left( 2s+1 \right)\frac{VkT}{{{\lambda }^{3}}}\xi \left[ 1+\frac{1}{{{2}^{\frac{5}{2}}}}\xi  \right]=\frac{3}{2}\left( 2s+1 \right)kT\frac{V}{{{\lambda }^{3}}}{{e}^{\frac{\mu }{kT}}}\left[ 1+\frac{1}{{{2}^{\frac{5}{2}}}}{{e}^{\frac{\mu }{kT}}} \right]= \\ 
 &  \\ 
 & \Rightarrow U\approx \frac{3}{2}kT\bar{N}\left[ 1-\frac{1}{{{2}^{\frac{5}{2}}}}\frac{{{\lambda }^{3}}}{V\left( 2s+1 \right)}\bar{N} \right] \\ 
\end{align}

TeX (checked):

{\begin{aligned}&U\approx {\frac {3}{2}}\left(2s+1\right){\frac {VkT}{{\lambda }^{3}}}\xi \left[1+{\frac {1}{{2}^{\frac {5}{2}}}}\xi \right]={\frac {3}{2}}\left(2s+1\right)kT{\frac {V}{{\lambda }^{3}}}{{e}^{\frac {\mu }{kT}}}\left[1+{\frac {1}{{2}^{\frac {5}{2}}}}{{e}^{\frac {\mu }{kT}}}\right]=\\&\\&\Rightarrow U\approx {\frac {3}{2}}kT{\bar {N}}\left[1-{\frac {1}{{2}^{\frac {5}{2}}}}{\frac {{\lambda }^{3}}{V\left(2s+1\right)}}{\bar {N}}\right]\\\end{aligned}}

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MathML (4.367 KB / 531 B) :

\begin{aligned} U \approx \frac{3}{2} (2 s + 1) \frac{V k T}{λ^{3}} ξ [1 + \frac{1}{2^{\frac{5}{2}}} ξ] = \frac{3}{2} (2 s + 1) k T \frac{V}{λ^{3}} e^{\frac{μ}{k T}} [1 + \frac{1}{2^{\frac{5}{2}}} e^{\frac{μ}{k T}}] = \\ \Rightarrow U \approx \frac{3}{2} k T \bar{N} [1 - \frac{1}{2^{\frac{5}{2}}} \frac{λ^{3}}{V (2 s + 1)} \bar{N}] \end{aligned}

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Identifiers

$U$

$s$

$V$

$k$

$T$

$λ$

$ξ$

$ξ$

$s$

$k$

$T$

$V$

$λ$

$e$

$μ$

$k$

$T$

$e$

$μ$

$k$

$T$

$U$

$k$

$T$

$\bar{N}$

$λ$

$V$

$s$

$\bar{N}$

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