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Barometric Formula for Pressure

The barometric formula (also called the exponential atmosphere or isothermal atmosphere) is a formula used to model how the pressure of the air changes with altitude.

The pressure at altitude depends on the pressure at the surface and an exponential factor that decreases with altitude, gravitational acceleration and the molar mass of the atmosphere. The factor also declines more slowly with increased temperature.

Formula

QuantityVariable["p", "Pressure"] == E^((Quantity[-1, "MolarGasConstant"^(-1)]*QuantityVariable["g", "GravitationalAcceleration"]*QuantityVariable["h", "Height"]*QuantityVariable["M", "MolarMass"])/QuantityVariable["T", "Temperature"])*QuantityVariable[Subscript["p", "0"], "Pressure"]

symbol description physical quantity
p pressure "Pressure"
g gravitational acceleration "GravitationalAcceleration"
h height "Height"
M molar mass "MolarMass"
T temperature "Temperature"
p0 reference pressure "Pressure"

Forms

Examples

Get the resource:

In[1]:=
ResourceObject["Barometric Formula for Pressure"]
Out[1]=

Get the formula:

In[2]:=
FormulaData[ResourceObject["Barometric Formula for Pressure"]]
Out[2]=

Use some values:

In[3]:=
FormulaData[ ResourceObject[ "Barometric Formula for Pressure"], {QuantityVariable[ "T","Temperature"] -> Quantity[300, "Kelvins"], QuantityVariable["M","MolarMass"] -> Quantity[29, ("Grams")/("Moles")]}]
Out[3]=

Publisher Information