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Display information for equation id:math.2573.28 on revision:2573

* Page found: Spezifische Wärme zweiatomiger idealer Gase (eq math.2573.28)

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Spezifische Wärme zweiatomiger idealer Gase Eq: math.2573.28

Hash: 7b3b14d53717185fc3c14dc1bf91eefd

TeX (original user input):

\begin{align}

& {{Z}_{r}}\approx 1+3\exp \left( -\frac{2{{\Theta }_{r}}}{T} \right) \\

& \ln {{Z}_{r}}\approx 3\exp \left( -\frac{2{{\Theta }_{r}}}{T} \right) \\

& \Rightarrow {{U}_{r}}\approx Nk{{T}^{2}}\frac{\partial }{\partial T}\left( 3\exp \left( -\frac{2{{\Theta }_{r}}}{T} \right) \right)=6Nk{{\Theta }_{r}}\left( \exp \left( -\frac{2{{\Theta }_{r}}}{T} \right) \right) \\

& \Rightarrow {{c}_{vr}}=12R{{\left( \frac{{{\Theta }_{r}}}{T} \right)}^{2}}\exp \left( -\frac{2{{\Theta }_{r}}}{T} \right) \\

\end{align}

TeX (checked):

{\begin{aligned}&{{Z}_{r}}\approx 1+3\exp \left(-{\frac {2{{\Theta }_{r}}}{T}}\right)\\&\ln {{Z}_{r}}\approx 3\exp \left(-{\frac {2{{\Theta }_{r}}}{T}}\right)\\&\Rightarrow {{U}_{r}}\approx Nk{{T}^{2}}{\frac {\partial }{\partial T}}\left(3\exp \left(-{\frac {2{{\Theta }_{r}}}{T}}\right)\right)=6Nk{{\Theta }_{r}}\left(\exp \left(-{\frac {2{{\Theta }_{r}}}{T}}\right)\right)\\&\Rightarrow {{c}_{vr}}=12R{{\left({\frac {{\Theta }_{r}}{T}}\right)}^{2}}\exp \left(-{\frac {2{{\Theta }_{r}}}{T}}\right)\\\end{aligned}}

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MathML (4.229 KB / 527 B) :

\begin{aligned} Z_{r} \approx 1 + 3 \exp (- \frac{2 Θ_{r}}{T}) \\ \ln Z_{r} \approx 3 \exp (- \frac{2 Θ_{r}}{T}) \\ \Rightarrow U_{r} \approx N k T^{2} \frac{\partial}{\partial T} (3 \exp (- \frac{2 Θ_{r}}{T})) = 6 N k Θ_{r} (\exp (- \frac{2 Θ_{r}}{T})) \\ \Rightarrow c_{v r} = 12 R {(\frac{Θ_{r}}{T})}^{2} \exp (- \frac{2 Θ_{r}}{T}) \end{aligned}

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Identifiers

$Z_{r}$

$Θ_{r}$

$T$

$Z_{r}$

$Θ_{r}$

$T$

$U_{r}$

$N$

$k$

$T$

$T$

$Θ_{r}$

$T$

$N$

$k$

$Θ_{r}$

$Θ_{r}$

$T$

$c_{v r}$

$R$

$Θ_{r}$

$T$

$Θ_{r}$

$T$

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