Isothermal reversible work

The figure usually given for reversible work of separation is for an isothermal process. Because some of the actual processes under consideration are by no means isothermal, one is left in some doubt as to whether the comparison between the actual work requirement and the isothermal reversible work is a legitimate one. Therefore in... 

Considering the first equality, Is measurable. It Is the Isothermal reversible work required to extract ions from phase a for electrons In a metal It represents the electronic work function. For metals, a, can also be obtained from thermo-emission or the photo-electric effect. Sometimes a is called the real (Gibbs) energy of hydration of ion i. The logic behind this last definition stems from the second equality In [3.9.61. The standard molar Gibbs energy of solvation of an Ion [1.5.3.11 equals when Is referred to the gas... 

Interfacial Tension. As already seen, interfacial tension is of fundamental importance in determining the capillary forces acting on trapped oil within porous media. Interfacial tension arises from an imbalance in the forces of attraction between molecules in the bulk phase and molecules at the interface. It can be defined as the isothermal reversible work of formation of unit area of interface in a system of constant composition (7). 

The next step is to find the Helmholtz energy of the layer as a whole. Generally, for a bulk phase the total Helmholtz energy F is obtained as the Isothermal reversible work JpdV, which can be computed if p(V), that is, the equation of state, is known. 

These expressions define the Isothermal reversible work done on the system after the enlargement the resulting Helmholtz or Gibbs energy resides in the interface. The definition y = (3U/9A)gy, is also operational, but virtually impracticable how can one enlarge an interface iso-entropically ... 

The arrows in figs. 5.8b and c Indicate the adhesion and immersion process, respectively. The corresponding work w of adhesion is the isothermal reversible work needed to create one unit area of SG interface, plus one unit area of LG interface under the simultaneous annihilation of 1 unit are of SL interface. 

For further thermod)mamic elaboration it is useful also to bring the work of cohesion into the picture. Generally speaking, upon spreading, as in fig. 5.8a, the internal cohesion of the liquid has to be overcome in order to achieve adhesion between liquid and solid. Figure 5.9 Indicates how the work of cohesion is defined. An infinitely long column of unit cross-section is cut into two halves and is the isothermal reversible work required to achieve that. Only for liquids or c... 

Show that for a van der Waals gas, the isothermal, reversible work of expansion for 1 mole is given by... 

The isothermal reversible work of deformation w per unit volume of an elastomer is given by the statistical theory of elastomer deformation as... 

Consider the work w that must be done to break a colunm of material of cross-section a and separate the two parts to infinity under reversible, isothermal conditions the work done is then the increase in the Helmholtz function of the material resulting from the separation. Initially, all the molecules in the neighbourhood of the plane along which the separation is going to take place are bulk molecules. Separation, however, changes the environment of these molecules and they become surface molecules with quite different energies. This increase in energy, measured by the isothermal, reversible work of separation, arises from the difference in the intermolecular forces experienced by molecules in the... 

Based on isothermal reversible work done in transferring one mole of ions of the solute 2 from infinity in vacuum) to a given part in the interfacial region which has a non-zero average charge and where the electrostatic potential is I, it is possible to define the so-called electrochemical potential of component 2 [70]... 

Consider a single homogeneous phase of one eomponent of unehang-ing eomposition. If it undergoes an isothermal reversible ehange and does work, then from the first law of thermodynamies ... 

The combination of properties U - TS occurs so frequently in thermodynamic analysis that it is given a special name and symbol, namely A, the work fimction or maximum luork (because it represents the maximum work per unit mass, obtainable during any isothermal reversible change in any given system). Therefore, it is seen that... 

Theorem.—The work done in any isothermal reversible cyclic process is zero (J. Moutier, 1875). 

If a gas obeys Boyle s law the diminution of potential on isothermal reversible expansion is equal to the diminution of free energy, and both are equal to the maximum work. 

If a relationship is known between the pressure and volume of the fluid, the work can be calculated. For example, if the fluid is the ideal gas, then pV = nRT and equation (2.14) for the isothermal reversible expansion of ideal gas becomes... 

Thus, in an isothermal reversible process, dA equals the reversible work. Note that <5vr in equation (3.92) is the total work. It includes pressure-volume work and any other forms, if present."1... 

Path A is an isothermal, reversible expansion. Path B has two steps. In the first step, the gas is cooled at constant volume to 1.19 atm. In the second step, the gas is heated and allowed to expand against a constant external pressure of 1.19 atm until the final volume is 7.39 L. Calculate the work for each path. 

STRATEGY Because entropy is a state function, the change in entropy of the system is the same regardless of the path between the two states, so we can use Eq. 3 to calculate AS for both part (a) and part (b). For the entropy of the surroundings, we need to find the heat transferred to the surroundings. In each case, we can combine the fact that AU = 0 for an isothermal expansion of an ideal gas with AU = w + q and conclude that q = —tv. We then use Eq. 4 in Chapter 6 to calculate the work done in an isothermal, reversible expansion of an ideal gas and Eq. 9 in this chapter to find the total entropy. The changes that we calculate are summarized in Fig. 7.21. 

As depicted in Fig. 5, both the protein molecule and the sorbent surface are electrically charged. In an aqueous environment, they are surrounded by counterions, which, together with the surface charge, form the so-called electrical double layer. The Gibbs energy of an electrical double layer, may be calculated as the isothermal, isobaric reversible work required to invoke the charge distribution in the double layer... 

By modifying the procedure described above to explode a wire in the water sphere while the system was under compression, they did attain explosions. Measuring the rebound of the cylinder and the loss of aluminum, they could estimate the work produced by the event. Assuming the maximum energy transfer to the water would occur by constant volume heating to the aluminum temperature, foUowed by an isothermal, reversible expansion, they estimated an efficiency of about 25%. Clearly the exploding wire led to an immediate and effective dispersal of the water. 

Let T represent the tension of a wire of length L, A represent its cross-sectional area, and Y represent the isothermal Young s modulus (L/A)(dT/dL)T- For a wire, A and Y are essentially constant as the tension is increased, and L changes very little with changing tension. (See Exercises 2.8 and 2.10.) Show that the work for an isothermal reversible increase in tension of a wire is... 

Isothermal. The procedure used to calculate the work and energy quantities in an isothermal reversible expansion of a real gas is similar to that used for the ideal gas. 

Derive an explicit equation for the reversible work of an isothermal expansion for each of the following cases ... 

Thus, the reversible work is a limiting maximum value for the magnimde of work obtainable in an isothermal change, with the equality applying to the limit when the process becomes reversible. 

A hypothetical cycle for achieving reversible work, typically consisting of a sequence of operations (1) isothermal expansion of an ideal gas at a temperature T2 (2) adiabatic expansion from T2 to Ti (3) isothermal compression at temperature Ti and (4) adiabatic compression from Ti to T2. This cycle represents the action of an ideal heat engine, one exhibiting maximum thermal efficiency. Inferences drawn from thermodynamic consideration of Carnot cycles have advanced our understanding about the thermodynamics of chemical systems. See Carnot s Theorem Efficiency Thermodynamics... 

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... 

The work done by any system on its surroundings during expansion against a constant pressure is calculated from Eq. 9 for an isothermal, reversible expansion of an ideal gas, the work is calculated from Eq. 12 or 13. A reversible process is a process that can be reversed by an infinitesimal change in a variable. 

It may be of interest to show how the reversible work for any percentage yield can be calculated by another equation which does not involve a graphical integration. Designating the feed, concentrated brine, and fresh water streams as 1, 2, and 3, respectively, we can write for an isothermal, reversible process... 

The Gibbs free energy change during a reaction is a measure of the reversible work (other than pressure-volume work) that can be obtained from the process at constant T and p. Since cellular processes are isothermal and isobaric, free energies are the quantities of choice in studying metabolic processes with respect to their ability to carry out the work of cells. 

---