Internal energy formula

The formula of the internal energy differential can be integrated using the Euler’s theorem on homogeneous functions to get the following expression.

Notes:

1. This formula works for a single-component system. For a multi-component system replace the product of chemical potential and particle count with a sum over each type of components.

Links:

1. Wikipedia.

internal_energy

internal_energy of the system.

Symbol:

U

Latex:

\(U\)

Dimension:

energy

temperature

temperature of the system.

Symbol:

T

Latex:

\(T\)

Dimension:

temperature

entropy

entropy of the system.

Symbol:

S

Latex:

\(S\)

Dimension:

energy/temperature

pressure

pressure in the system.

Symbol:

p

Latex:

\(p\)

Dimension:

pressure

volume

volume of the system.

Symbol:

V

Latex:

\(V\)

Dimension:

volume

chemical_potential

chemical_potential of the system.

Symbol:

mu

Latex:

\(\mu\)

Dimension:

energy

particle_count

particle_count of the system.

Symbol:

N

Latex:

\(N\)

Dimension:

dimensionless

law

U = T * S - p * V + mu * N

Latex:

\[U = T S - p V + \mu N\]