Work, maximum

Consider a change of a system from state A to state B, From the first law 

As noted previously q and w vary according to the nature of the path between the two states— it is only their algebraic sum which is constant. It will now be shown that the second law places a restriction on the maximum amount of work which may be obtained. 

It has been shown already that if a system absorbs heat d from a heat reservoir at temperature the entropy change of the system is given by equation (M6)  

Let it be supposed that the heat bath is a large one. In this case IV remains constant and we obtain by integration of the above relation 

Now for passage between the assigned states A and B the right-hand side of this expression has a definite value since U and 8 are functions of state. It follows the the work —ti which is done by the system cannot be larger than a certain quantity, which may be denoted this is obtained in the reversible type of process, which corresponds to the equality sign in the above equation. If the process is not reversible it yields a smaller amount of work and there is a correspondingly smaller intake of heat, as follows also from equation (1 16). 

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Derive from Eq. XU-24 an expression for the maximum work of adhesion involving only and 7c. Calculate this maximum work for 7c = 22 dyn/cm and 0 = 0.030, as well as 7/. for this case, and the contact angle. 

There are several different fomis of work, all ultimately reducible to the basic definition of the infinitesimal work Dn =/d/ where /is the force acting to produce movement along the distance d/. Strictly speaking, both/ and d/ are vectors, so Dn is positive when the extension d/ of the system is in the same direction as the applied force if they are in opposite directions Dn is negative. Moreover, this definition assumes (as do all the equations that follow in this section) that there is a substantially equal and opposite force resisting the movement. Otiierwise the actual work done on the system or by the system on the surroundings will be less or even zero. As will be shown later, the maximum work is obtained when tlie process is essentially reversible . 

When the e.m.f. of a cell is measured by balancing it against an external voltage, so that no current flows, the maximum e.m.f. is obtained since the cell is at equilibrium. The maximum work obtainable from the cell is then nFE J, where n is the number of electrons transferred, F is the Faraday unit and E is the maximum cell e.m.f. We saw in Chapter 3 that the maximum amount of work obtainable from a reaction is given by the free energy change, i.e. - AG. Hence... 

The original pressure should not be more than 2,000 lb. per sq. in. if the maximum working pressure for the autoclave is 5,000 lb. The full operating pressure is not applied at the beginning because the pressure will rise as the bomb is heated thus at 256°, the pressure will be 1 - 8 times that at 20°. 

Exeigy, E, is the potential to do work. It is also sometimes called availabiUty or work potential. Thermodynamically, this is the maximum work a stream can deflver by coming into equiUbrium with its surroundings ... 

Potassium Heptafluorotantalate. Potassium heptafluoiotantalate [16924-00-8], K TaF, ciystallizes in colodess, rhombic needles. It hydroly2es in Foiling water containing no excess of hydrofluoric acid. The solubility of potassium heptafluorotantalate in hydrofluoric acid decreases from 60 g/100 mL at 100°C to 0.5 g/100 mL at room temperature. The different solubility characteristics of K TaF and K NbOF are the fundamental basis of the Matignac process (16). A phase diagram exists for the system K TaF —NaCl—NaF—KCl (68). Potassium heptafluorotantalate has an LD q value of 2500 mg/kg. The recommended TWA maximum work lace exposure for K TaF in air is 2.5 mg /m (fluoride base) (69). 

Joining material used in joints Working temperatures, < F Maximum working pressure, Ibf/in ... 

Heavy-duty (material 100 Ib/fF). For extremely heavy duty (150-200-Ib/ft material), the maximum working capacity with 20-hp motor is 35 fF. 

Fig. 5.4. The stability of complex systems is determined by changes in the free work Wf. Note the minus sign - systems try to move so that they produce the maximum work.

Analysis of this cycle indicates that an increase in inlet temperature to the turbine causes an increase in the cycle efficiency. The optimum pressure ratio for maximum efficiency varies with the turbine inlet temperature from an optimum of about 15.5 1 at a temperature of 1500°F (816°C) to about 43 1 at a temperature of about 2400 °F (1316 °C). The pressure ratio for maximum work, however, varies from about 11.5 1 to about 35 1 for the same respective temperatures. 

Dangerous goods only transported if the letter Y appears in appropriate columns of Approved Carriage list and Schedules 5 and 6 are complied with, and tank pressures do not exceed the maximum working pressure as per certifications. 

Table 3.6 gives commonly used maximum working stresses for various grades of cast irons up to 600°C. 

Tabic 3.6. Maximum Working Stresses for Various Grades of Cast Iron up to 600 C... 

By virtue of its chemical and thermal resistances, borosilicate glass has superior resistance to thermal stresses and shocks, and is used in the manufacture of a variety of items for process plants. Examples are pipe up to 60 cm in diameter and 300 cm long with wall tliicknesses of 2-10 mm, pipe fittings, valves, distillation column sections, spherical and cylindrical vessels up 400-liter capacity, centrifugal pumps with capacities up to 20,000 liters/hr, tubular heat exchangers with heat transfer areas up to 8 m, maximum working pressure up to 275 kN/m, and heat transfer coefficients of 270 kcal/hz/m C [48,49]. 

Consider first the steady flow of fluid through a control volume CV between prescribed stable states X and Y (Fig. 2.1) in the presence of an environment at ambient temperature Tj, (i.e. with reversible heat transfer to that environment only). The maximum work which is obtained in reversible flow between X and Y is given by... 

A corollary of this theorem is that the maximum work that can be extracted from fluid at prescribed state X is the exergy... 

Here Bq is the steady flow availability function at the so-called dead state, where the fluid is in equilibrium with the environment, at state (po> T )- The maximum work obtainable between states X and Y may then be written as... 

It is supposed here that the various reactants entering are separated at ( o. o) the various products discharged are similarly separated at (po.To). The maximum work may then be written as... 

Kotas [3] has drawn a distinction between the environmental state, called the dead state by Haywood [1], in which reactants and products (each at po. To) are in restricted thermal and mechanical equilibrium with the environment and the truly or completely dead state , in which they are also in chemical equilibrium, with partial pressures (/)j) the same as those of the atmosphere. Kotas defines the chemical exergy as the sum of the maximum work obtained from the reaction with components atpo. To, [—AGo], and work extraction and delivery terms. The delivery work term is Yk k kJo ln(fo/pt), where Pii is a partial pressure, and is positive. The extraction work is also Yk kRkTo n(po/Pk) but is negative. 

In general, we shall not subsequently consider these extraction and delivery work terms here, but use [ —AGq] as an approximation to the maximum work output obtainable from a chemical reaction, since the work extraction and delivery quantities are usually small. Their relative importance is discussed in detail by Horlock et al. [4]. 

Nominal Pipe Size in. Nominal Wall Thickness in. Maximum Working Pressure Grade B S = 20,000 P 9 Maximum Working Pressure Grade C S = 23,300 psig... 

Maximum working pressure has been rounded up to the next higher unit of 10 psig. No corrosion allowance is assumed same formula as ANSI B31.3... 

Excessive temperature can lead to premature failure of an item of equipment at pressures below its design maximum working pressure. Such a failure can create a leak, potentially leading to fire or explosion if gas is leaked or to oil pollution if oil is leaked. This type of failure should be gradual, with warning as it develops, and thus does not require as higli a degree of protection as those previously mentioned. 

Once the FMEA is completed, the specific system is analyzed to determine if all the devices are indeed needed. For example, if it is not possible for the process to overpressure the vessel, these devices are not required. If it is impossible to heat the vessel to a high enough level to effect its maximum working pressure, the TSH can be eliminated. 

If failure is initiated by an increase in internal pressure in combination with a malfunctioning of the pressure relief, the pressure at failure will equal the failure pressure of the vessel. This failure pressure is usually the maximum working pressure multiplied by a safety factor. For carbon-steel vessels, this safety factor can be taken as four. Mote precise calculations ate possible if the vessel s dimensions and material parameters ate known. 

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... 

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