Isothermal change, free energy work function

Sd. Isothermal Changes in the Work Function and Free Energy.—For an isothermal change dT is zero, and hence, as noted above, equation (25.15) becomes... 

Derive expressions for (i) the free energy change, (ii) the work function change, accompan3ang the appreciable isothermal expansion of a van der WaalS gas. (Use the expression for V in terms of P derived in 21a.)... 

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. 

By arguments now familiar we have introduced a new function of state, G = E — TS + PV, the Gibbs (free) energy, involving the indicated combination of other functions of state. As is evident, changes in this quantity are tracked by the reversible performance of work at constant T and P other than mechanical. Moreover, if irreversible phenomena occur under isothermal-isobaric conditions in the absence of any work performance then... 

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 ... 

The work of adsorption is determined from Eq. (1) by using the Hnear section of the surface pressure curve as a function of the bulk concentration of the surfactant (the surface pressure does not exceed 3mN/M). The values obtained for the work of adsorption are usually compared with the values obtained for certain fractional surface coverages. Thus, it becomes possible to estimate the change in the free energy as a function of the molecular interaction in the monolayer. (The relation between the values of the work of adsorption determined from different isotherms is discussed in Refs. [37-39]). The adsorption entropy and enthalpy are determined from the temperature dependence of the work of adsorption [36-39]. 

---