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:
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:
- internal_energy¶
internal_energy
of the system.
- Symbol:
U
- Latex:
\(U\)
- Dimension:
energy
- temperature¶
temperature
of the system.
- Symbol:
T
- Latex:
\(T\)
- Dimension:
temperature
- Symbol:
S
- Latex:
\(S\)
- Dimension:
energy/temperature
- Symbol:
p
- Latex:
\(p\)
- Dimension:
pressure
- 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:
- \[U = T S - p V + \mu N\]