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Isothermal compressibility

Values for calculation

$π$
$γ_{ππ}$
$γ_π$
$p$ $\mathrm{Pa}$
$γ^r_{ππ}$
$γ^r_π$
$δ$
$φ_δ$
$φ_{δδ}$
$ρ$ $\mathrm{kg\cdot m^{-3}}$
$R$ $\mathrm{J\cdot kg^{-1}\cdot K^{-1}}$
$T$ $\mathrm{°C}$
$\text{Region}$

Calculation

Isothermal compressibility

$\text{if }\ \text{Region}= 1$
$\text{if }\ \text{Region}= 1$
Equations in LaTeX code
\text{if }\ \text{Region}= 1
$$κ_T=\cfrac{-\cfrac{π\cdot γ_{ππ}}{γ_π}}{p}$$
$κ_T=\cfrac{-\cfrac{π\cdot γ_{ππ}}{γ_π}}{p}$
Equations in LaTeX code
κ_T=\cfrac{-\cfrac{π\cdot γ_{ππ}}{γ_π}}{p}
$\text{else if }\ \text{Region}= 2$
$\text{else if }\ \text{Region}= 2$
Equations in LaTeX code
\text{else if }\ \text{Region}= 2
$$κ_T=\cfrac{1-π^2\cdot γ^r_{ππ}}{\left(1+π\cdot γ^r_π\right)\cdot p}$$
$κ_T=\cfrac{1-π^2\cdot γ^r_{ππ}}{\left(1+π\cdot γ^r_π\right)\cdot p}$
Equations in LaTeX code
κ_T=\cfrac{1-π^2\cdot γ^r_{ππ}}{\left(1+π\cdot γ^r_π\right)\cdot p}
$\text{else if }\ \text{Region}= 3$
$\text{else if }\ \text{Region}= 3$
Equations in LaTeX code
\text{else if }\ \text{Region}= 3
$$κ_T=\cfrac{1}{\left(2\cdot δ\cdot φ_δ+δ^2\cdot φ_{δδ}\right)\cdot ρ\cdot R\cdot\left(T+273.15\right)}$$
$κ_T=\cfrac{1}{\left(2\cdot δ\cdot φ_δ+δ^2\cdot φ_{δδ}\right)\cdot ρ\cdot R\cdot\left(T+273.15\right)}$
Equations in LaTeX code
κ_T=\cfrac{1}{\left(2\cdot δ\cdot φ_δ+δ^2\cdot φ_{δδ}\right)\cdot ρ\cdot R\cdot\left(T+273.15\right)}
$\text{else if }\ \text{Region}= 5$
$\text{else if }\ \text{Region}= 5$
Equations in LaTeX code
\text{else if }\ \text{Region}= 5
$$κ_T=\cfrac{1-π^2\cdot γ^r_{ππ}}{\left(1+π\cdot γ^r_π\right)\cdot p}$$
$κ_T=\cfrac{1-π^2\cdot γ^r_{ππ}}{\left(1+π\cdot γ^r_π\right)\cdot p}$
Equations in LaTeX code
κ_T=\cfrac{1-π^2\cdot γ^r_{ππ}}{\left(1+π\cdot γ^r_π\right)\cdot p}
$\text{else}$
$\text{else}$
Equations in LaTeX code
\text{else}
$$κ_T=0$$
$κ_T=0$
Equations in LaTeX code
κ_T=0
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