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Specific internal energy

Values for calculation

$ \{τ\in\mathbb{R}\mid τ>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.
$ τ $
$ \{γ_τ\in\mathbb{R}\} $
This set includes all real numbers.
$ γ_τ $
$ \{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_π\in\mathbb{R}\} $
This set includes all real numbers.
$ γ_π $
$ 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} $
$ \{γ^o_τ\in\mathbb{R}\} $
This set includes all real numbers.
$ γ^o_τ $
$ \{γ^r_τ\in\mathbb{R}\} $
This set includes all real numbers.
$ γ^r_τ $
$ \{γ^o_π\in\mathbb{R}\} $
This set includes all real numbers.
$ γ^o_π $
$ \{γ^r_π\in\mathbb{R}\} $
This set includes all real numbers.
$ γ^r_π $
$ \{φ_τ\in\mathbb{R}\} $
This set includes all real numbers.
$ φ_τ $
$ \text{Region} $

Calculation

Specific internal energy

$\text{if }\ \text{Region}= 1$
$\text{if }\ \text{Region}= 1$
Equations in LaTeX code
\text{if }\ \text{Region}= 1
$$u=\left(τ\cdot γ_τ-π\cdot γ_π\right)\cdot R\cdot\left(T+273.15\right)$$
$u=\left(τ\cdot γ_τ-π\cdot γ_π\right)\cdot R\cdot\left(T+273.15\right)$
Equations in LaTeX code
u=\left(τ\cdot γ_τ-π\cdot γ_π\right)\cdot R\cdot\left(T+273.15\right)
$\text{else if }\ \text{Region}= 2$
$\text{else if }\ \text{Region}= 2$
Equations in LaTeX code
\text{else if }\ \text{Region}= 2
$$u=\left(τ\cdot\left(γ^o_τ+γ^r_τ\right)-π\cdot\left(γ^o_π+γ^r_π\right)\right)\cdot R\cdot\left(T+273.15\right)$$
$u=\left(τ\cdot\left(γ^o_τ+γ^r_τ\right)-π\cdot\left(γ^o_π+γ^r_π\right)\right)\cdot R\cdot\left(T+273.15\right)$
Equations in LaTeX code
u=\left(τ\cdot\left(γ^o_τ+γ^r_τ\right)-π\cdot\left(γ^o_π+γ^r_π\right)\right)\cdot R\cdot\left(T+273.15\right)
$\text{else if }\ \text{Region}= 3$
$\text{else if }\ \text{Region}= 3$
Equations in LaTeX code
\text{else if }\ \text{Region}= 3
$$u=\left(τ\cdot φ_τ\right)\cdot R\cdot\left(T+273.15\right)$$
$u=\left(τ\cdot φ_τ\right)\cdot R\cdot\left(T+273.15\right)$
Equations in LaTeX code
u=\left(τ\cdot φ_τ\right)\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
$$u=\left(τ\cdot\left(γ^o_τ+γ^r_τ\right)-π\cdot\left(γ^o_π+γ^r_π\right)\right)\cdot R\cdot\left(T+273.15\right)$$
$u=\left(τ\cdot\left(γ^o_τ+γ^r_τ\right)-π\cdot\left(γ^o_π+γ^r_π\right)\right)\cdot R\cdot\left(T+273.15\right)$
Equations in LaTeX code
u=\left(τ\cdot\left(γ^o_τ+γ^r_τ\right)-π\cdot\left(γ^o_π+γ^r_π\right)\right)\cdot R\cdot\left(T+273.15\right)
$\text{else}$
$\text{else}$
Equations in LaTeX code
\text{else}
$$u=0$$
$u=0$
Equations in LaTeX code
u=0
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