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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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