Free energy differential¶
The fundamental thermodynamic relations are fundamental equations which demonstate how important thermodynamic quantities depend on variables that are measurable experimentally.
Notation:
\(d\) denotes an exact, path-independent differential.
Notes:
Temperature, volume, and particle count are so called natural variables of free energy as a thermodynamic potential.
For a system with more than one type of particles, the last term can be represented as a sum over all types of particles, i.e. \(\sum_i \mu_i \, d N_i\).
Conditions:
The system is in thermal equilibrium with its surroundings.
The system is composed of only one type of particles, i.e. the system is a pure substance.
Links:
- free_energy_change¶
Infinitesimal change in
helmholtz_free_energy
of the system.
- Symbol:
dF
- Latex:
\(dF\)
- Dimension:
energy
- Symbol:
S
- Latex:
\(S\)
- Dimension:
energy/temperature
- temperature_change¶
Infinitesimal change in
temperature
of the system.
- Symbol:
dT
- Latex:
\(dT\)
- Dimension:
temperature
- Symbol:
p
- Latex:
\(p\)
- Dimension:
pressure
- Symbol:
dV
- Latex:
\(dV\)
- Dimension:
volume
- chemical_potential¶
chemical_potential
of the system.
- Symbol:
mu
- Latex:
\(\mu\)
- Dimension:
energy
- particle_count_change¶
Infinitesimal change in the
particle_count
of the system.
- Symbol:
dN
- Latex:
\(dN\)
- Dimension:
dimensionless
- law¶
dF = -S * dT - p * dV + mu * dN
- Latex:
- \[dF = - S dT - p dV + \mu dN\]