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Isothermal compressibility

Values for calculation

$ \{π\in\mathbb{R}\mid π>0\} $
This set includes all real numbers that are greater than zero. Therefore, it contains only positive numbers. Zero and negative numbers are not included in this set.
$ π $
$ \{γ_{ππ}\in\mathbb{R}\} $
This set includes all real numbers.
$ γ_{ππ} $
$ \{γ_π\in\mathbb{R}\} $
This set includes all real numbers.
$ γ_π $
$ \{p\in\mathbb{R}\mid p>0\} $
This set includes all real numbers that are greater than zero. Therefore, it contains only positive numbers. Zero and negative numbers are not included in this set.
$ p $ $ \mathrm{Pa} $
$ \{γ^r_{ππ}\in\mathbb{R}\} $
This set includes all real numbers.
$ γ^r_{ππ} $
$ \{γ^r_π\in\mathbb{R}\} $
This set includes all real numbers.
$ γ^r_π $
$ \{δ\in\mathbb{R}\mid δ>0\} $
This set includes all real numbers that are greater than zero. Therefore, it contains only positive numbers. Zero and negative numbers are not included in this set.
$ δ $
$ \{φ_δ\in\mathbb{R}\} $
This set includes all real numbers.
$ φ_δ $
$ \{φ_{δδ}\in\mathbb{R}\} $
This set includes all real numbers.
$ φ_{δδ} $
$ \{ρ\in\mathbb{R}\mid ρ>0\} $
This set includes all real numbers that are greater than zero. Therefore, it contains only positive numbers. Zero and negative numbers are not included in this set.
$ ρ $ $ \mathrm{kg\cdot\ m^{-3}} $
$ R $ $ \mathrm{J\cdot\ kg^{-1}\cdot\ K^{-1}} $
$ \{T\in\mathbb{R}\mid T\geq0\} $
This set includes all real numbers that are greater than or equal to zero. Therefore, it contains all positive numbers and zero, but no negative numbers.
$ 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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