Molar internal energy

If the equation of state is known, the internal energy of a substance can be found as a function of volume at constant temperature.

Conditions:

1. The fluid is homogeneous and in a single phase state.

Links:

1. Wikipedia.

molar_internal_energy

internal_energy of the van der Waals fluid per unit amount_of_substance.

Symbol:

u_m

Latex:

\(u_\text{m}\)

Dimension:

energy/amount_of_substance

temperature

temperature of the van der Waals fluid.

Symbol:

T

Latex:

\(T\)

Dimension:

temperature

isochoric_molar_heat_capacity

molar_heat_capacity at constant volume as a function of temperature.

Symbol:

c_Vm(T)

Latex:

\(c_{V, \text{m}}{\left(T \right)}\)

Dimension:

energy/(amount_of_substance*temperature)

attractive_forces_parameter

attractive_forces_parameter.

Symbol:

a

Latex:

\(a\)

Dimension:

pressure*volume**2/amount_of_substance**2

molar_volume

molar_volume.

Symbol:

v_m

Latex:

\(v_\text{m}\)

Dimension:

volume/amount_of_substance

law

u_m = Integral(c_Vm(T), T) - a / v_m

Latex:

\[u_\text{m} = \int c_{V, \text{m}}{\left(T \right)}\, dT - \frac{a}{v_\text{m}}\]