Work-function, Helmholtz Free Energy

A = work function (Helmholtz free energy), Btu/lb or Btu C = heat capacity, Btu/lb °R Cp = heat capacity at constant pressure = heat capacity at constant volume F= (Gibbs) free energy, Btu/lb or Btu g = acceleration due to gravity = 32.174 ft/s ... 

A= Work function, Helmholtz Free Energy °C = Degrees Centigrade (temperature)... 

In the past, A has been known by a number of names work function, maximum work function, Helmholtz function, Helmholtz free energy, and simply free energy. The lUPAC agreement is to use the symbol A and call it the Helmholtz energy. 

Work function or maximum work (Helmholtz free energy)... 

We first calculate the potential energy ((/, kJ/mol) and vibrational Helmholtz free energy (A vib, kJ/mol) for the unit cell at fixed temperature (T, K) and lattice constants (a, m) using the full quantum mechanical partition function. These two terms, in conjunction with a work term in the presence of an applied stress, provides the the Gibbs free energy (G, kJ/mol). 

Note that the roman capital A represents chemical allinity. while the italic capital, 4 symbolizes the Helmholtz free energy (also called work function), It follows that the condition for chemical equilibrium is... 

F and G are naturally taken as functions of X, ..., T and of Pi,, P i, T, respectively. At times one speaks of F as llie Helmholtz free energy and of G as the Gibbs free energy. In an isothermal reversible transition, the amount W of work done by a system is equal not to the decrease of its energy U but to the decrease —A F of its (Helmholtz) free energy. In die presence of internal sources of irreversibility... 

Gibbs used ifr for this function G. N. Lewis called it the work function, with the symbol A and in many European countries it was called the Helmholtz free energy, with the symbol F. By international agreement the accepted name is the Helmholtz energy and the symbol is A. 

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. 

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... 

Here we have introduced a new convenient function of state F = E - TS which is termed the Helmholtz free energy (function). If no work is performed,... 

For constant volume process, the similar property, which is a measure of feasibility of processes, is the Work Function or the Helmholtz Free Energy, A, which is mathematically defined as... 

The thermodynamic work function is the Helmholtz free energy, A, where... 

In the above we have invented a new function of state, A = E — TS, involving state functions that had been previously introduced. A is called the Helmholtz (free) energy function. The right-hand side follows from Eq. (1.12.7d). As is seen, changes in A are tracked by the reversible performance of work at constant T. If no work is involved, but irreversible (and therefore, uncontrollable) processes are allowed to occur at constant temperature, we find from the above that... 

Gibbs free energy is a potential for reversible work in constant T-P processes, and always decreases in spontaneous processes. By comparison with (5.26) it is clear that G is a measure of the net work or non-PAV work. This function therefore contrasts with the Helmholtz work function, which measures total work, including mechanical PY work. The Gibbs free energy is a particularly useful measure of the electrical or chemical work attainable from a process and is used a great deal with chemical systems where PY work is often unimportant. 

In order to express Eq. (6-7) in a more concise fashion, it is useful to define an extensive function of state. A, the work function or Helmholtz free energy. The Helmholtz free energy is defined by the relation... 

The difference U - TS = F characterizes extensive property, which is called isochrone-isothermal potential. This concept was introduced in 1882 by Herman Ludwig Ferdinand von Helmholtz (1821-1894). As heat TS is considered associated energy, he called it free energy. Often this potential is called Helmholtz free energy. Therefore, under isochrone-iso-thermal conditions maximum useful work is the function of free energy, or Helmholtz energy, change ... 

---