In Sunday's "60 Minutes" TV program the correspondent descended into a gold mine said to be 2 miles (3 km) deep. What equation describes the air pressure relative to sea level atmospheric pressure?
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2$\begingroup$ Pressure and density of air in mines $\endgroup$– FarcherCommented Nov 14, 2018 at 11:29
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1 Answer
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Barometric formula is the equation which can estimate the pressure at different heights:
$$ p=p_0\cdot\exp\left(-\frac{mgh}{k_BT}\right) $$
The $p_0$ is the reference pressure, $T$ is the temperature in K, $k_B$ is the Boltzmann constant, and $h$ is the height.
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$\begingroup$ Kiitos (thanks) @kalle for the edit of the equation. $\endgroup$ Commented Jan 25, 2019 at 16:52
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1$\begingroup$ This equation suppose constant temperature. It is not the case in a deep mine ? $\endgroup$ Commented Jan 25, 2019 at 16:56
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1$\begingroup$ There are few assumptions. For instanec, this equation gives the pressure of a point with a temperature in equilibrium. $\endgroup$ Commented Jan 25, 2019 at 16:58
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$\begingroup$ And $m$ is what? Probably the mass of a single air molecule. $\endgroup$ Commented Oct 30, 2020 at 11:11
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$\begingroup$ Indeed, formula is a bit messed-up, it should sound like : $$ P=P_{0}e^{-Mgz/R^{*}T} $$ where $M$ is an air molar mass and $R^{*}$ is a gas constant. $\endgroup$ Commented Mar 2, 2021 at 9:37