Isobaric cubic expansion coefficient

Values for calculation

Inverse reduced temperature

$τ$

Cross derivative of $ γ $ with respect to $ π $ and temperature $ τ $

$γ_{πτ}$

Derivative of $ γ $ with respect to the dimensionless pressure $ π $

$γ_π$

The water temperature

$T$ $\mathrm{°C}$

Reduced pressure

$π$

Derivative of $ γ^r $ with respect to the dimensionless pressure $ π $

$γ^r_π$

Cross derivative of $ γ^r $ with respect to $ π $ and temperature $ τ $

$γ^r_{πτ}$

Derivative of $ φ $ with respect to the dimensionless density $ δ $

$φ_δ$

Cross derivative of $ φ $ with respect to $ δ $ and temperature $ τ $

$φ_{δτ}$

Reduced density

$δ$

Second partial derivative of $ φ $ with respect to $ δ $

$φ_{δδ}$

Region

$\text{Region}$

$\text{if }\ \text{Region}= 1$

$$α_ν=\cfrac{1-\cfrac{τ\cdot γ_{πτ}}{γ_π}}{\left(T+273.15\right)}$$

$\text{else if }\ \text{Region}= 2$

$$α_ν=\cfrac{1+π\cdot γ^r_π-τ\cdot π\cdot γ^r_{πτ}}{\left(1+π\cdot γ^r_π\right)\cdot\left(T+273.15\right)}$$

$\text{else if }\ \text{Region}= 3$

$$α_ν=\cfrac{φ_δ-τ\cdot φ_{δτ}}{\left(2\cdot φ_δ+δ\cdot φ_{δδ}\right)\cdot \left(T+273.15\right)}$$

$\text{else if }\ \text{Region}= 5$

$$α_ν=\cfrac{1+π\cdot γ^r_π-τ\cdot π\cdot γ^r_{πτ}}{\left(1+π\cdot γ^r_π\right)\cdot\left(T+273.15\right)}$$

$\text{else}$

$$α_ν=0$$

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