Dieterici equation

Dieterici equation is another type of semi-empirical equations approximating real gases along with the more well-known van der Waals equation of state.

Notation:

  1. \(R\) (R) is molar_gas_constant.

Notes:

  1. Like the van der Waals equation of state, the Dieterici equation is semi-empirical.

  2. It approximates moderate pressures of real gases much better than the van der Waals equation within the conditions stated below.

  3. Can be converted to the van der Waals equation under an additional limit \(a \ll R T V_m\)

Conditions:

  1. Only applicable in the limits \(b \ll V_m\) and \(a \ll p V_m^2\).

  2. Inapplicable for high pressures.

Links:

  1. Wikipedia.

pressure

Pressure inside the system.

Symbol:

p

molar_volume

Volume of the system per amount of substance.

Symbol:

V_m

Latex:

\(V_m\)

temperature

temperature of the system.

Symbol:

T

Latex:

\(T\)

Dimension:

temperature

attractive_forces_parameter

Parameter specific to each individual substance, usually attributed to the magnitude of attractive forces between particles of the system.

Symbol:

a

excluded_volume_parameter

Parameter specific to each individual substance, usually attributed to the amount of excluded molar volume due to a finite size of particles.

Symbol:

b

law

p * (V_m - b) = R * T * exp(-1 * a / (R * T * V_m))

Latex:
\[p \left( V_m - b \right) = R T \exp \left( - \frac{a}{R T V_m} \right)\]