Pressure of ideal gas from height and temperature

The barometric formula determines the dependence of the pressure or density of a gas on the height in the gravity field.

Notation:

1. \(g\) (g) is acceleration_due_to_gravity.

2. \(k_\text{B}\) (k_B) is boltzmann_constant.

Conditions:

1. The gas is ideal.

2. The gas is in a uniform gravity field.

Links:

1. Wikipedia.

final_pressure

pressure of the gas at final height.

Symbol:

p

Latex:

\(p\)

Dimension:

pressure

initial_pressure

pressure of the gas at initial height.

Symbol:

p_0

Latex:

\(p_{0}\)

Dimension:

pressure

molecular_mass

mass of a single gas molecule.

Symbol:

m

Latex:

\(m\)

Dimension:

mass

height_change

Change in height between initial_pressure and final_pressure.

Symbol:

Delta(h)

Latex:

\(\Delta h\)

Dimension:

length

temperature

temperature of the gas.

Symbol:

T

Latex:

\(T\)

Dimension:

temperature

law

p = p_0 * exp(-g * m * Delta(h) / (k_B * T))

Latex:

\[p = p_{0} \exp{\left(- \frac{g m \Delta h}{k_\text{B} T} \right)}\]