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

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:

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