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Display information for equation id:math.2577.1 on revision:2577

* Page found: Spezifische Wärme von Festkörpern (eq math.2577.1)

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Spezifische Wärme von Festkörpern Eq: math.2577.1

Hash: 91a3b8eec8123c44ed024fc1687adacb

TeX (original user input):

\begin{align}

& {{c}_{Vs}}=3{{N}_{A}}\frac{\partial }{\partial T}\left( \frac{1}{\left[ \exp \left( \frac{\hbar \omega }{kT} \right)-1 \right]}+\frac{1}{2} \right)\hbar \omega =3R\frac{{{\left( \frac{{{\Theta }_{S}}}{T} \right)}^{2}}{{e}^{\left( \frac{{{\Theta }_{S}}}{T} \right)}}}{{{\left( {{e}^{\left( \frac{{{\Theta }_{S}}}{T} \right)}}-1 \right)}^{2}}} \\

& {{\Theta }_{S}}:=\frac{\hbar \omega }{k} \\

\end{align}

TeX (checked):

{\begin{aligned}&{{c}_{Vs}}=3{{N}_{A}}{\frac {\partial }{\partial T}}\left({\frac {1}{\left[\exp \left({\frac {\hbar \omega }{kT}}\right)-1\right]}}+{\frac {1}{2}}\right)\hbar \omega =3R{\frac {{{\left({\frac {{\Theta }_{S}}{T}}\right)}^{2}}{{e}^{\left({\frac {{\Theta }_{S}}{T}}\right)}}}{{\left({{e}^{\left({\frac {{\Theta }_{S}}{T}}\right)}}-1\right)}^{2}}}\\&{{\Theta }_{S}}:={\frac {\hbar \omega }{k}}\\\end{aligned}}

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MathML (3.775 KB / 555 B) :

\begin{aligned} c_{V s} = 3 N_{A} \frac{\partial}{\partial T} (\frac{1}{[\exp (\frac{ℏ ω}{k T}) - 1]} + \frac{1}{2}) ℏ ω = 3 R \frac{{(\frac{Θ_{S}}{T})}^{2} e^{(\frac{Θ_{S}}{T})}}{{(e^{(\frac{Θ_{S}}{T})} - 1)}^{2}} \\ Θ_{S} : = \frac{ℏ ω}{k} \end{aligned}

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Identifiers

$c_{V s}$

$N_{A}$

$T$

$ω$

$k$

$T$

$ω$

$R$

$Θ_{S}$

$T$

$e$

$Θ_{S}$

$T$

$e$

$Θ_{S}$

$T$

$Θ_{S}$

$ω$

$k$

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