The Barometric Formula
Note that the model calculation assumes a uniform temperature, and is therefore not a realistic model of the atmosphere. The temperature tends to decrease with height, so the model calculation will overestimate the pressure at a given height.

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The Barometric Formula
The development of the barometric formula makes use of a number of concepts from kinetic theory, such as the ideal gas law and the associated molecular constants. In the exponential, the two terms have the units of energy. The numerator mgh is gravitational potential energy and the term kT is thermal energy. 
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The Barometric Formula

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The Barometric Formula

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Atmospheric Pressure, Selected HeightsCompared to the standard Atmospheric pressure at sea level, 760 mmHg = 760 torr, the pressure at some heights above the earth are:
These pressures are considerably below those predicted by the barometric formula, which can be used to calculate variations in barometric pressure with height near the earth. (The predicted pressures above used temperature 300K and pressure 760 mmHg.) Though the pressure decreases rapidly, even at 200 km (124 mi) there is enough residual atmospheric pressure to gradually slow a satellite, limiting its lifetime. 
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Constituents of the AirThe constituents of dry air can be expressed as volume percentages, which will translate to the partial pressures out of the total atmospheric pressure Since a mole of any ideal gas occupies the same volume, it follows that the volume percentage is also the percentage by number. The average molecular mass can then be found by weighting the masses by their volume percentages above.

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