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Atmospheric pressure air

Values for calculation

$p_b$ $\mathrm{Pa}$
$g$ $\mathrm{m/s^2}$
$R$ $\mathrm{J\cdot K^{-1}\cdot kg^{-1}}$
$T$ $\mathrm{K}$
$H$ $\mathrm{m}$
$H_b$ $\mathrm{m}$
$β$ $\mathrm{K\cdot m^{-1}}$
$T_b$ $\mathrm{K}$

Calculation

Atmospheric pressure air

$\text{if }\ β=0$
$\text{if }\ β=0$
Equations in LaTeX code
\text{if }\ β=0
$$p_{air}=p_b\cdot\exp\left[-\cfrac{g}{R\cdot T}\cdot\left(H-H_b\right)\right]$$
$p_{air}=p_b\cdot\exp\left[-\cfrac{g}{R\cdot T}\cdot\left(H-H_b\right)\right]$
Equations in LaTeX code
p_{air}=p_b\cdot\exp\left[-\cfrac{g}{R\cdot T}\cdot\left(H-H_b\right)\right]
$\text{else}$
$\text{else}$
Equations in LaTeX code
\text{else}
$$p_{air}=p_b\cdot\left[1+\cfrac{β}{T_b}\cdot\left(H-H_b\right)\right]^{-g/\left(β\cdot R\right)}$$
$p_{air}=p_b\cdot\left[1+\cfrac{β}{T_b}\cdot\left(H-H_b\right)\right]^{-g/\left(β\cdot R\right)}$
Equations in LaTeX code
p_{air}=p_b\cdot\left[1+\cfrac{β}{T_b}\cdot\left(H-H_b\right)\right]^{-g/\left(β\cdot R\right)}
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