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* Page found: Phasenübergänge (eq math.2516.2)

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TeX (original user input): 

\begin{align}

& {{\left( \frac{\partial f}{\partial v} \right)}_{T}}=-p \\

& \Rightarrow \int_{v\acute{\ }}^{v\acute{\ }\acute{\ }}{{}}\left( \frac{\partial f}{\partial v} \right)dv+\left( v\acute{\ }\acute{\ }-v\acute{\ } \right)P=0 \\

& \left( v\acute{\ }\acute{\ }-v\acute{\ } \right)P=-\int_{v\acute{\ }}^{v\acute{\ }\acute{\ }}{{}}\left( \frac{\partial f}{\partial v} \right)dv=\int_{v\acute{\ }}^{v\acute{\ }\acute{\ }}{{}}pdv \\

\end{align}

TeX (checked): 

{\begin{aligned}&{{\left({\frac {\partial f}{\partial v}}\right)}_{T}}=-p\\&\Rightarrow \int _{v{\acute {\ }}}^{v{\acute {\ }}{\acute {\ }}}{}\left({\frac {\partial f}{\partial v}}\right)dv+\left(v{\acute {\ }}{\acute {\ }}-v{\acute {\ }}\right)P=0\\&\left(v{\acute {\ }}{\acute {\ }}-v{\acute {\ }}\right)P=-\int _{v{\acute {\ }}}^{v{\acute {\ }}{\acute {\ }}}{}\left({\frac {\partial f}{\partial v}}\right)dv=\int _{v{\acute {\ }}}^{v{\acute {\ }}{\acute {\ }}}{}pdv\\\end{aligned}}

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MathML (39.903 KB / 4.08 KB) :

( ∂ ⁡ f ∂ ⁡ v ) T = - p ⇒ ∫ v ⁢ ´ v ⁢ ´ ⁢ ´ ( ∂ ⁡ f ∂ ⁡ v ) ⁢ 𝑑 v + ( v ⁢ ´ ⁢ ´ - v ⁢ ´ ) ⁢ P = 0 ( v ⁢ ´ ⁢ ´ - v ⁢ ´ ) ⁢ P = - ∫ v ⁢ ´ v ⁢ ´ ⁢ ´ ( ∂ ⁡ f ∂ ⁡ v ) ⁢ 𝑑 v = ∫ v ⁢ ´ v ⁢ ´ ⁢ ´ p ⁢ 𝑑 v absent subscript 𝑓 𝑣 𝑇 𝑝 absent ⇒ absent superscript subscript 𝑣 ´ absent 𝑣 ´ absent ´ absent 𝑓 𝑣 differential-d 𝑣 𝑣 ´ absent ´ absent 𝑣 ´ absent 𝑃 0 absent 𝑣 ´ absent ´ absent 𝑣 ´ absent 𝑃 superscript subscript 𝑣 ´ absent 𝑣 ´ absent ´ absent 𝑓 𝑣 differential-d 𝑣 superscript subscript 𝑣 ´ absent 𝑣 ´ absent ´ absent 𝑝 differential-d 𝑣 {\displaystyle{\displaystyle\begin{aligned} \par&\displaystyle{{\left(\frac{% \partial f}{\partial v}\right)}_{T}}=-p\\ \par&\displaystyle\Rightarrow\int_{v\acute{\ }}^{v\acute{\ }\acute{\ }}{{}}% \left(\frac{\partial f}{\partial v}\right)dv+\left(v\acute{\ }\acute{\ }-v% \acute{\ }\right)P=0\\ \par&\displaystyle\left(v\acute{\ }\acute{\ }-v\acute{\ }\right)P=-\int_{v% \acute{\ }}^{v\acute{\ }\acute{\ }}{{}}\left(\frac{\partial f}{\partial v}% \right)dv=\int_{v\acute{\ }}^{v\acute{\ }\acute{\ }}{{}}pdv\\ \par\end{aligned}}}

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MathML (5.167 KB / 504 B) :

(∂f∂v)T=−p⇒∫v´v´´(∂f∂v)dv+(v´´−v´)P=0(v´´−v´)P=−∫v´v´´(∂f∂v)dv=∫v´v´´pdv

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