Irreversible processes work done

In a third experiment, the initial conditions of Vi, Pi for the ideal gas and its temperature, T are identical to those in the first two experiments. This time no heat is supplied (corresponding to an adiabatic process, q = 0) and a shutter is lowered in front of the moveable (frictionless) piston, after which the pressure on the piston is adjusted to, Pf, the same pressure that was experienced at the end of the two previous experiments. The air in the voidage between shutter and piston is now evacuated creating a vacuum, after which the shutter is withdrawn and the gas expands irreversibly. The work done is now ... 

This value represents the maximum work which could be done by performing the process in a reversible manner. On account of the irreversibility the work done in a real process is less. 

All processes that are not reversible are called irreversible processes. The following examples can illustrate the nature of the irreversible process. Work W is done on a system the work is wholly or partly transformed into heat by friction within the system - the process cannot be reversed, it is irreversible. A gas expands into a vacuum during the expansion, pressure and temperature vary from one location to another inside the gas and thus, the gas is not in equilibrium during the expansion - the process cannot be reversed it is irreversible. A system at low temperature absorbs heat from surroundings with a high temperature during the heat exchange, the system is not in thermodynamic equilibrium - the process cannot be reversed it is irreversible. 

Adamczyk (1976) is one of the few who tried to incorporate energy losses from the irreversible shock process into the calculation. He proposes to use the work done by gas volume in a process illustrated in Figure 6.12 and described below. 

That all actual processes are irreversible does not invalidate the results of thermodynamic reasoning with reversible processes, because the results refer to equilibrium states. This procedure is exactly analogous to the method of applying the principle of Virtual Work in analytical statics, where the conditions of equilibrium are derived from a relation between the elements of work done during virtual i.e., imaginary, displacements of the parts of the system, whereas such displacements are excluded by the condition of equilibrium of the system. 

Because A.Ssllll = —AS, AStor = 0. This value is in accord with the statement that the process is reversible, (b) For the irreversible process, AS is the same, at +7.6 J K 1. No work is done in free expansion (Section 6.3), and so w = 0. Because AU = 0, it follows that q = 0. Therefore, no heat is transferred into the surroundings, and their entropy is unchanged ASslirr = 0. The total change in entropy is therefore ASt()t = +7.6 J-K. The positive value is consistent with an irreversible expansion. 

When 3He is compressed, a mechanical work pdV is done. The ratio between the compression work and the cooling power is shown in Fig. 7.4. If some irreversible process takes place during the compression, the heating may exceed the cooling. In practice, this happens at 0.7-0.8mK. 

The key to this solution lies in the fact that the operation involved is an irreversible expansion. Taking Cv as constant between P i and T2, AU = — W = nCv(T2 — Pi) where n is the kmol of gas and T2 and Pi are the final and initial temperatures, then for a constant pressure process, the work done, assuming the ideal gas laws apply, is given by ... 

The varying P is substituted by nRT/V and the integration then performed over the changing volume. wrev is the work done by the gas in expanding reversibly from (Vf Pi) to (Vf, Pf). It can be equated to the area enclosed between the curve of P plotted versus V and the V axis (i.e. the abscissa) (see Frame 2). wKV is larger than the work done, Win, during the irreversible process of expansion and it also represents the maximum work obtainable from any expansion process which takes the gas from the state (Vi, Pi) to the state (Vf, Pf). 

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. 

We may also speak of the work done by the system being less than the work which the system could do by passing reversibly from 1 to 2. This loss of work is a measure of the irreversibility of the process. 

FIGURE 13.7 Work done by a system in reversible and irreversible expansions between the same initial and final states. The work performed is greater for the reversible process. 

In general, the work that can be obtained in an isothermal change is a maximum when the process is performed in a reversible manner. This is true, for example, in the production of electrical work by means of a voltaic cell. Cells of this type can be made to operate isothermally and reversibly by withdrawing current extremely slowly ( 331) the e.m.f. of a given cell then has virtually its maximum value. On the other hand, if large currents are taken from the cell, so that it functions in an irreversible manner, the E.M.F. is less. Since the electrical work done by the cell is equal to the product of the e.m.f. and the quantity of electricity passing, it is clear that the same extent of chemical reaction in the cell will yield more work in the reversible than in the irreversible operation. 

This maximum work is obtained if the process is sufficiently slow that there are no irreversibilities, for example, no resistive heating as a result of the current flow. This implies that the rate of reaction is very slow, and that the electrical potential produced is just balanced by an external potential so that the current flow is infinitesimal. This electrical potential produced by the cell (or of the balancing external potential) will.be referred-to as-the zero-current cell potential and designated by E. The work done by... 

---