Helmholtz free energy
The free energy ( in physics symbols in accordance with IUPAP, in chemistry, however, according to IUPAC also Helmholtz potential Helmholtz free energy or Helmholtz energy by Hermann von Helmholtz ) is the energy that is needed to generate a system that at defined temperature in thermal equilibrium with its surroundings. It is a thermodynamic potential, so that an extensive quantity of state, and is defined as:
With
- - Internal energy
- - Temperature
- - Entropy.
Thermodynamic relations
The free energy is obtained from the internal energy by a Legendre transform with respect to and:
With the natural variables
- Volume and
- Of particles.
The total differential ( characteristic function ) of the Helmholtz energy is:
With
- Pressure
- The chemical potential.
For isothermal processes () corresponds to the maximum work that can perform a system, the free energy change:
Only in the ( theoretical ) special case can be isothermal differences in the work - taking into account the first and second law of thermodynamics - calculate as such the internal energy or the enthalpy:
The free energy is linked through the following relationship with the canonical partition function:
With
- Boltzmann constant
Thermodynamics with electromagnetic fields
, Including electric and magnetic fields, the internal energy is given by:
With
- - Electric field strength
- - Polarization times volume
- - Magnetic field strength
- - Magnetization times volume
The free energy is now defined by:
The total differential is:
For constant volume, number of particles and electric field becomes: