Barometric formula

The barometric formula describes how gas pressure or density changes with altitude in a gravitational field. Its common isothermal form assumes constant temperature and an ideal gas in hydrostatic equilibrium.

Hydrostatic equilibrium: A state in which pressure gradients balance forces such as gravity, leaving a fluid at rest. The formula comes from applying this pressure-force balance to a gas column.
Pressure: Force exerted per unit area by a fluid or other material. The formula tracks pressure as the weight of overlying gas decreases with altitude.
Atmospheric pressure: The pressure exerted by the weight of a planet's atmosphere. The formula approximates its decrease with altitude under specified atmospheric conditions.
International Standard Atmosphere: A conventional atmospheric model specifying standard temperature, pressure, and density profiles with altitude. It uses layered temperature assumptions rather than one globally isothermal profile.
Ideal gas law: An equation relating the pressure, volume, temperature, and amount of an ideal gas. It connects density to pressure and temperature in the formula's usual derivation.
Density: Mass per unit volume of a substance. For an ideal gas at fixed temperature, density and pressure have the same altitude dependence.
Barometric altimeter: An instrument that estimates altitude from measured atmospheric pressure. It converts pressure changes into height using an assumed atmospheric profile.
Polytropic atmosphere: An atmospheric model in which pressure varies as a fixed power of density. Its temperature can vary with altitude, unlike the isothermal barometric model.
Scale height: The characteristic vertical distance over which an atmospheric quantity decreases by a factor of e in an exponential profile. It sets the altitude interval over which isothermal pressure falls by a factor of e.
Temperature: A physical quantity that determines the direction of heat flow and characterizes thermal state. The isothermal form treats temperature as constant throughout the vertical column.

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