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 \(a \ll p V_m^2\). Refer to symbols below.

2. Inapplicable for high pressures.

Links:

1. Wikipedia.

pressure

pressure inside the system.

Symbol:

p

Latex:

\(p\)

Dimension:

pressure

molar_volume

volume of the system per amount_of_substance.

Symbol:

V_m

Latex:

\(V_{m}\)

Dimension:

volume/amount_of_substance

temperature

temperature of the system.

Symbol:

T

Latex:

\(T\)

Dimension:

temperature

attractive_forces_parameter

attractive_forces_parameter.

Symbol:

a

Latex:

\(a\)

Dimension:

pressure*volume**2/amount_of_substance**2

excluded_volume_parameter

excluded_volume_parameter.

Symbol:

b

Latex:

\(b\)

Dimension:

volume/amount_of_substance

law

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

Latex:

\[p \left(V_{m} - b\right) = R T \exp{\left(- \frac{a}{R T V_{m}} \right)}\]