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Display information for equation id:math.2510.39 on revision:2510

* Page found: Reale Gase (eq math.2510.39)

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Reale Gase Eq: math.2511.39

Hash: c1d40c828b4604bbb2094ee499becb4c

TeX (original user input):

\begin{align}

& f={{e}^{-\beta \phi }}-1\approx \left\{ \begin{matrix}

-1\quad f\ddot{u}r\,r<d  \\

-\beta \phi \quad f\ddot{u}r\,r>d  \\

\end{matrix} \right. \\

& \Rightarrow B=-\frac{2\pi }{3}{{d}^{3}}-\frac{2\pi }{kT}\int_{d}^{\infty }{{}}dr{{r}^{2}}\phi  \\

& \phi <0 \\

& \Rightarrow B=-\frac{2\pi }{3}{{d}^{3}}-\frac{2\pi }{kT}\int_{d}^{\infty }{{}}dr{{r}^{2}}\phi =-\frac{b}{{{N}_{A}}}+\frac{a}{kT{{N}_{A}}^{2}} \\

\end{align}

TeX (checked):

{\begin{aligned}&f={{e}^{-\beta \phi }}-1\approx \left\{{\begin{matrix}-1\quad f{\ddot {u}}r\,r<d\\-\beta \phi \quad f{\ddot {u}}r\,r>d\\\end{matrix}}\right.\\&\Rightarrow B=-{\frac {2\pi }{3}}{{d}^{3}}-{\frac {2\pi }{kT}}\int _{d}^{\infty }{}dr{{r}^{2}}\phi \\&\phi <0\\&\Rightarrow B=-{\frac {2\pi }{3}}{{d}^{3}}-{\frac {2\pi }{kT}}\int _{d}^{\infty }{}dr{{r}^{2}}\phi =-{\frac {b}{{N}_{A}}}+{\frac {a}{kT{{N}_{A}}^{2}}}\\\end{aligned}}

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\begin{aligned} f = e^{- β ϕ} - 1 \approx {\begin{matrix} - 1 f \ddot{u} r r < d \\ - β ϕ f \ddot{u} r r > d \end{matrix} \\ \Rightarrow B = - \frac{2 π}{3} d^{3} - \frac{2 π}{k T} \int_{d}^{\infty} d r r^{2} ϕ \\ ϕ < 0 \\ \Rightarrow B = - \frac{2 π}{3} d^{3} - \frac{2 π}{k T} \int_{d}^{\infty} d r r^{2} ϕ = - \frac{b}{N_{A}} + \frac{a}{k T {N_{A}}^{2}} \end{aligned}

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Identifiers

$f$

$e$

$β$

$ϕ$

$f$

$\ddot{u}$

$r$

$r$

$d$

$β$

$ϕ$

$f$

$\ddot{u}$

$r$

$r$

$d$

$B$

$π$

$d$

$π$

$k$

$T$

$d$

$r$

$r$

$ϕ$

$ϕ$

$B$

$π$

$d$

$π$

$k$

$T$

$d$

$r$

$r$

$ϕ$

$b$

$N_{A}$

$a$

$k$

$T$

$N_{A}$

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