Heat bath

A warm bath is the idealized notion of a system environment that provides a constant temperature. For this purpose, an exchange of heat between system and environment must be ensured. This is also called thermal coupling.

In reality, a heat bath is basically only approximately feasible, to the environment must be much larger than the system itself In addition, a link must be established by an appropriate choice of the materials of the system walls: metal, for example, is a good conductor of heat.

In practice, the chemistry, biochemistry and biophysics, it is assumed that the constant temperature is given naturally by the surrounding medium, usually the room temperature through the atmosphere or the temperature of the living cell by an aqueous solution.

Thermodynamics

In the theory of thermodynamics to provide a constant temperature plays an extremely important role:

• One couples (constant volume and particle ) thermally, so the system is to describe to the heat bath by the canonical ensemble with the associated Boltzmann statistics a closed system. The thermodynamic potential, which is minimized, in this case, the free energy.
• If you couple a closed system that can change its volume (pressure and particle number constant), thermally to the heat bath, as the belonging to this preparation thermodynamic potential is the Gibbs free energy.
• If you couple a system that can exchange particles with its surroundings (volume and chemical potential constant) is thermally coupled to the heat bath, so is the associated with this preparation thermodynamic potential is the grand potential.

Statistical Physics

The statistical physics provides the following requirements for a heat bath:

• The system is prepared mikrokanonisch ( meaning it is the definition of temperature as ab initio predictable heat bath - characteristic )
• The heating bath is infinitely large ( much greater than the system, which is coupled to the heat bath ), so that the delivery of a finite amount of energy does not change the temperature of the heating bath
• The leading term of the entropy in the limit of large particle numbers is extensively ( reason alone, the system must be very large, for small systems, the entropy does not need to be extensively namely )
• The energy spectrum of the system is open at the top (otherwise would be negative temperatures are possible )
• The entropy grows with increasing energy to ( so that the temperature increases with increasing energy)

The partial derivatives of the extensive entropy with respect to its three variables extensive natural energy, volume and number of particles results in three intensive variables which are characteristic of the heat bath, ie temperature, pressure and chemical potential: