Isothermic processes Helmholtz energy

Helmholtz energy (sometimes also called Helmholtz free energy, or Helmholtz function) is the thermodynamic state function equal to the maximum possible nonexpansion work output, which can be done by a closed system in an isothermal isochoric process (T = const, V = const). In terms of the -> internal energy and -> entropy... 

There are other forms of the Gibbs-Helmholtz equation which are more frequently employed these deal with changes in the free energy, heat content, etc., accompanying an appreciable process. The process may be chemical or physical in nature the only restriction is that it takes place in a closed system, i.e., one of constant mass, which is in equilibrium with the external pressure. For the initial and final states, indicated by the subscripts 1 and 2, respectively, of an isothermal process, equation (25.8) becomes... 

One should not conclude from Eq 4.2-7 that the reversible work for any process is equal to the change in Helmholtz energy, since this result was derived only for an isothermal, constant-volume process. The value of VK , and the thermodynamic functions to which it is related, depends on the constraints placed on the system during the change of state (see Problem 4.3). For example, consider a process occurring in a closed system at fi.xed temperature and pressure. Here we have... 

Since a reversible change provides the maximum (minimum) amount of work for a given expansion (compression), the change in Helmholtz energy provides a bound on the work associated with an isothermal process. 

For isothermal processes on closed systems, the reversible work is given by the change in Helmholtz energy, as already noted in (3.2.15). 

The Helmholtz free energy (or Helmholtz fimctlon),f, is defined by f/-7S, where f/is the "internal energy. For a reversible isothermal process, AFrepresents the useful work available. 

It is convenient to use as thermodynamic variables temperature T and density p = N/V N is the number of particles and V is volume. Further on, we shall restrict to isothermal processes, while density will be allowed to change in space. In this variables, the Helmholtz free energy is expressed as F = N f p, T), and pressure p and chemical potential p are defined as... 

The energy change for any equimolar process occurring at constant temperature is a work process. If the isothermal, equimolar process is carried out reversibly at constant pressure, the work is Gibbs free energy. If the isothermal process is carried out reversibly at constant volume, the work is Helmholtz free energy. 

T, U, H, S denoting thermodynamic temperature, internal energy, enthalpy and entropy, respectively). Work in an isothermal process under constant volume equals the Helmholtz energy change ... 

Equation (1.77) implies that the maximum work done by the system under isothermal conditions can be carried out by the change of Helmholtz free energy. The state function A is known as the work function. The Helmholtz free energy is not useful for most chemical and biological processes since these processes occur at constant pressure rather than at constant volume. 

For a system at constant temperature, this tells us that the work done is less than or equal to the decrease in the Helmholtz free energy. The Helmholtz free energy then measures the maximum work which can be done bv the system in an isothermal change For a process at constant temperature, in which at the same time no mechanical work is done, the right side of Eq. (3.5) is zero, and wo see that in such a process the Helmholtz free energy is constant for a reversible process, but decreases for an irreversible process. The Helmholtz free energy will decrease until the system reaches an equilibrium state, when it will have reached the minimum value consistent with the temperature and with the fact that no external work can be done. 

Equivalently (Figure 2.2), dS nw = 0 at equilibrium. The Gibbs function thus expresses the second law as dG < 0 for all possible processes in constant-temperature, constant-pressure systems. (Similarly, the Helmholtz free energy function. A, expresses the second law for isochoric, isothermal systems as dA < 0 for all possible processes.)... 

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