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Display information for equation id:math.2555.97 on revision:2555

* Page found: Das ideale Fermigas (eq math.2555.97)

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Das ideale Fermigas Eq: math.2555.97

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TeX (original user input):

\begin{align}

& \bar{N}=V{{N}_{C}}\xi \left[ 1-{{2}^{-\frac{3}{2}}}\frac{{\bar{N}}}{V{{N}_{C}}} \right] \\

& \Rightarrow \xi ={{e}^{\frac{\mu }{kT}}}\approx \frac{{\bar{N}}}{V{{N}_{C}}}\left[ 1+{{2}^{-\frac{3}{2}}}\frac{{\bar{N}}}{V{{N}_{C}}} \right] \\

& \Rightarrow U\approx V{{N}_{C}}\frac{3}{2}kT{{e}^{\frac{\mu }{kT}}}\left[ 1-{{e}^{\frac{\mu }{kT}}}\frac{1}{{{2}^{\frac{5}{2}}}} \right]\approx \frac{3}{2}kT\bar{N}\left[ 1+{{2}^{-\frac{3}{2}}}\frac{{\bar{N}}}{V{{N}_{C}}} \right]\left[ 1-\frac{1}{{{2}^{\frac{5}{2}}}}\frac{{\bar{N}}}{V{{N}_{C}}} \right] \\

\end{align}

TeX (checked):

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

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MathML (5.922 KB / 545 B) :

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

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Translations to Computer Algebra Systems

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Identifiers

$\bar{N}$

$V$

$N_{C}$

$ξ$

$\bar{N}$

$V$

$N_{C}$

$ξ$

$e$

$μ$

$k$

$T$

$\bar{N}$

$V$

$N_{C}$

$\bar{N}$

$V$

$N_{C}$

$U$

$V$

$N_{C}$

$k$

$T$

$e$

$μ$

$k$

$T$

$e$

$μ$

$k$

$T$

$k$

$T$

$\bar{N}$

$\bar{N}$

$V$

$N_{C}$

$\bar{N}$

$V$

$N_{C}$

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