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

isochoric_molar_heat_capacity

Heat capacity at constant volume per unit amount of substance.

Symbol:

c_V(T)

Latex:

\(c_V(T)\)

temperature

temperature of the van der Waals fluid.

Symbol:

T

Latex:

\(T\)

Dimension:

temperature

attractive_forces_parameter

Parameter of the van der Waals equation denoting the magnitude of attractive forces between gas molecules.

Symbol:

a

molar_volume

Volume of the van der Waals fluid per unit amount of substance.

Symbol:

V_m

Latex:

\(V_m\)

law

u = Integral(c_V(T), T) - a / V_m

Latex:

\[u = \int c_V(T) \, dT - \frac{a}{V_m}\]