Maximum possible work

E. Ozone destroyer. Ozone is a powerful irritant. The maximum possible working concentration has been reported to be 0,15 to 1.0 part per million of air. It is necessary to destroy any excess ozone and to see that the exit tube from the above absorption assembly is connected to a good hood. It is safer to incorporate an ozone destroyer in the set-up. One such destroyer consists of two tall towers (30 in.) filled with broken glass moistened with 5% aqueous sodimn hydroxide and connected in series (Note 10). The room in which an ozonizer is used should be well ventilated. 

This equation, as illustrated in the (T, s) chart of Fig. 2.8 for an open circuit gas turbine, shows how the maximum possible work output from the ideal combustion process splits into the various terms on the right-hand side ... 

The rational efficiency may be defined as the ratio of the actual work output [Wcvlx to the maximum possible work output, approximately [—AGq],... 

With the two reservoirs at 7 and 7r, the maximum possible work is then... 

JO A portable power-supply system consists of a 30-liter bottle of compressed nitrogen, connected to a small adiabatic turbine. The bottle is initially charged to 13,800 kPa at 27°C and in operation drives the turbine continuously until the pressure drops to 700 kPa. The turbine exhausts at 101.33 kPa. Neglecting all heat transfer to the gas, calculate the maximum possible work that can be obtained during the process. Assume nitrogen an ideal gas for which CP = (7/2)R. 

Solution The procedure here is to calculate the maximum possible work Wideal which cap be obtained from 1 kg of steam in a flow process as it undergoes a change in state from saturated steam at 100°C to liquid water at 0°C. Now the problem reduces to the question of whether this amount of work is sufficient to operate a Carnot heat pump delivering 2,000 kJ as heat at 200°C and taking heat from the unlimited supply of cooling water at 0°C. 

The thermodynamic basis of the calculation of the maximum possible work potential or chemical exergy of reversible and irreversible chemical reactions is explained and discussed. Combustion is asserted to be fundamentally irreversible. It is a nonequilibrium uncontrollable chain reaction with hot branches, in a cool milieu, and a limited work output proportional to Carnot efficiency x calorific value (Barclay, 2002). 

For the maximum possible work, the calculation is similar, except that the maximum potential is used ... 

We can define this position of equilibrium in another way that will be useful in our study of thermodynamics. If we allow the mass Mj to fall through a distance dh it will do work M2gdh, by lifting M2 (where Mi < MJ. If we make M2 closer in magnitude to we shall get correspondingly more work, until at Mx == M2 an infinitesimal displacement will lead to work M1 g dh. This is the maximum work Mx can do, as it is now lifting an equal mass. When Mx = M2 the system is of course at equilibrium therefore we can define the equilibrium condition of the system as that for which a small displacement leads to the system doing the maximum possible work. 

Ft F2 + AF it will proceed at a discernible rate but do less than the maximum possible work. 

For an incompressible fluid (e.g., water), the common definition of the maximum possible work is the work that would be delivered if the fluid left the system with zero velocity and if the term in Bernoulli s equation were zero. For gases (e.g., steam), the common definition of maximum work is that work which would have been obtained for zero outlet velocity and isentropic operation. Although the forms of these maximum-work definitions are different, they can both be shown to be the same, because the term in Bernoulli s equation is related to the irreversible entropy increase. 

Case 2 If all off-day pairs are distinct, of the form (y, k) where j + k, then aU employees of type T3 and T4 in week i are associated with the same pair of off-days that they received in week (/ - 1). The type T4 are given both days off and the type T3 get the earliest day of the associated pair. The T2 employees get the remaining days of the T3 pairs. In this instance, the maximum possible work stretch wUl be five days. 

The solar to chemical energy eonversion efficiency ( soiar-to-chemicai) is defined as the portion of solar energy that is converted into the ehemical energy by the Gibbs free energy of the produets (i.e. maximum possible work that can be extracted from the products). 

For a given change of state the surroundings extract maximum possible work from the system if the process is carried out reversibly. 

T0 compute the maximum work, we need tw o other idealizations. A reversible work source can change volume or perform work of any other kind quasi-statically, and is enclosed in an impermeable adiabatic waU, so 6g = TdS = 0 and dU = S w. A reversible heat source can exchange heat quasi-statically, and is enclosed in a rigid wall that is impermeable to matter but not to heat flow, so = pdV = 0 and dU = 6q = TdS. A reversible process is different from a reversible heat or work source. A reversible heat source need not have AS = 0. A reversible process refers to changes in a whole system, in w-hich a collection of reversible heat plus work sources has AS = 0. The frictionless weights on pulleys and inclined planes of Newtonian mechanics are reversible w ork sources, for example. The maximum possible work is achieved w hen reversible processes are performed with reversible heat and work sources. 

To illustrate more clearly the difference between —AH and —AF, that is, between the heat liberated by a reaction and the maximum possible work which can be done by that reaction, we may consider molecules as containing two different types of energy. One is an ordered energy it unites the atoms to each other by primary or secondary valency bonds. It is this energy which can do work. The other is of a disordered nature (vibrational, rotational and translational). What primarily interests the biochemist is work, chemical or otherwise, obtainable from a reaction. If the reaction takes place with liberation of a great deal of useful energy, then work may be done. 

AF depends only on the products and reactants and not on the reaction pathway for example, AF of the oxidation of glucose is the same whether the sugar is burnt or metabolized in the body so long as the same initial and final conditions are obtained. No useful work is done in the first case and only heat is released, but AF of the reaction is the same, because it is equal to the maximum possible work and not to the actual work obtained. 

Heat and work are both commonly recorded as calories, but they are not equivalent forms of energy. Heat is a degraded form of energy work can be converted into an equal amount of heat, but heat cannot be converted to an equal amount of work. The heat that is released by a reaction at constant pressure is —AH, and this is not necessarily the same as the maximum possible work, — AF. As examples, a number of compounds including trichloroacetic acid and ammonium sulfate dissolve spontaneously in water (AF negative) but cool the solution therefore, at constant temperature heat would be absorbed, and AH is positive. AF and AH may differ by plus or minus several thousand calories, as in the case of glycolysis, wWe AF is —35,000 cal. and AH is —24,000 cal., one-third less. ... 

Actually, case (c) produces the maximum possible work. Any attempts to produce more work, by increasing further the external pressure, would lead to compression, i.e. the consumption of work. 

In discussing the concept of reversibility we concluded that a reversible operation yields the maximum possible work. Using an example of your own demonstrate that, when work is consumed, a reversible operation requires the minimum one. 

In comparing the quantity of work done in the two different expansions (Figs. 7-8 and 7-11), we found them to be different, thereby proving that work is not a state function. Additionally, the quantity of work performed is greater in the two-step expansion (Fig. 7-11) than in the single-step expansion (Fig. 7-8). We leave it to the interested student to demonstrate, through Feature Problem 125, that the maximum possible work is that done in a reversible expansion (Fig. 7-12). 

We know that ItUiirevI < Iw revl because a reversible process gives us the maximum possible work out from an expansion. If we now compare the previous two equations, we can see that ... 

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