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Display information for equation id:math.2569.23 on revision:2569

* Page found: Das Photonengas im Strahlungshohlraum (eq math.2569.23)

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Hash: 70172944acacdf70bc954e9dd06a52d5

TeX (original user input): 

\begin{align}

& F=-kT\ln Z=kT\sum\limits_{\nu }^{{}}{{}}\ln \left( 1-{{e}^{-\frac{h\nu }{kT}}} \right) \\

& p=kT{{\left( \frac{\partial }{\partial V}\ln Z \right)}_{T}}=-kT\sum\limits_{\nu }^{{}}{{}}\frac{\frac{h}{kT}\left( \frac{\partial \nu }{\partial V} \right){{e}^{-\frac{h\nu }{kT}}}}{\left( 1-{{e}^{-\frac{h\nu }{kT}}} \right)} \\

\end{align}

TeX (checked): 

{\begin{aligned}&F=-kT\ln Z=kT\sum \limits _{\nu }^{}{}\ln \left(1-{{e}^{-{\frac {h\nu }{kT}}}}\right)\\&p=kT{{\left({\frac {\partial }{\partial V}}\ln Z\right)}_{T}}=-kT\sum \limits _{\nu }^{}{}{\frac {{\frac {h}{kT}}\left({\frac {\partial \nu }{\partial V}}\right){{e}^{-{\frac {h\nu }{kT}}}}}{\left(1-{{e}^{-{\frac {h\nu }{kT}}}}\right)}}\\\end{aligned}}

LaTeXML (experimentell; verwendet MathML) rendering

MathML (32.466 KB / 3.56 KB) :

F = - k ⁢ T ⁢ ln ⁡ Z = k ⁢ T ⁢ ∑ ν ln ⁡ ( 1 - e - h ⁢ ν k ⁢ T ) p = k ⁢ T ⁢ ( ∂ ∂ ⁡ V ⁢ ln ⁡ Z ) T = - k ⁢ T ⁢ ∑ ν h k ⁢ T ⁢ ( ∂ ⁡ ν ∂ ⁡ V ) ⁢ e - h ⁢ ν k ⁢ T ( 1 - e - h ⁢ ν k ⁢ T ) absent 𝐹 𝑘 𝑇 𝑍 𝑘 𝑇 subscript 𝜈 1 superscript 𝑒 ℎ 𝜈 𝑘 𝑇 absent 𝑝 𝑘 𝑇 subscript 𝑉 𝑍 𝑇 𝑘 𝑇 subscript 𝜈 ℎ 𝑘 𝑇 𝜈 𝑉 superscript 𝑒 ℎ 𝜈 𝑘 𝑇 1 superscript 𝑒 ℎ 𝜈 𝑘 𝑇 {\displaystyle{\displaystyle\begin{aligned} \par&\displaystyle F=-kT\ln Z=kT% \sum\limits_{\nu}{{}}\ln\left(1-{{e}^{-\frac{h\nu}{kT}}}\right)\\ \par&\displaystyle p=kT{{\left(\frac{\partial}{\partial V}\ln Z\right)}_{T}}=-% kT\sum\limits_{\nu}{{}}\frac{\frac{h}{kT}\left(\frac{\partial\nu}{\partial V}% \right){{e}^{-\frac{h\nu}{kT}}}}{\left(1-{{e}^{-\frac{h\nu}{kT}}}\right)}\\ \par\end{aligned}}}

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MathML (3.468 KB / 506 B) :

F=−kTln⁡Z=kT∑νln⁡(1−e−hνkT)p=kT(∂∂Vln⁡Z)T=−kT∑νhkT(∂ν∂V)e−hνkT(1−e−hνkT)

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