Irreversible compression

According to Eq. (20) the compression of isotropic solid polymers having positive thermal expansivity must be accompanied by the internal energy inversion. AU inversion at compression has been estimated71 to occur at strains 5-15%. At compression, irreversible plastic deformations occur which prevents a correct experimental determination of AU. With inversion parameters, AU for isotropic poly-... 

Assume that 1.00 mol of an ideal gas is initially confined in a cylinder with a volume of 22.4 L at a temperature of 273.15 K. The external pressure is increased to 1.50 x 10 Pa and the gas is compressed irreversibly and isothermally untU P = 1.50 x 10 Pa. Find the largest and smallest values that w might have. 

Lets review the mechanical process from which we learned about reversibOity and irreversibOity. In Section 2.3, we considered a piston-cylinder assembly that underwent an isothermal expansion/compression, as shown in Figure 3.2u. When we remove the 1020-kg block, as depicted on the left, the piston expands irreversibly. Likewise, when we replace the block on the piston, it compresses irreversibly. In this case, the driving force for change is a pressure difference. The processes are illustrated on the Pv curve at the bottom. Notice that the irreversible processes have a definite directionality. The arrows that describe the expansion process do not overlap with those that describe the compression process. As we saw, the work needed to compress the assembly was greater than the work obtained from expanding it and is represented by a very different directional process (with different arrows and different shaded area on the Pv curve). The irreversible expansion and compression processes are distinct and different. 

There appear to be two stages in the collapse of emulsions flocculation, in which some clustering of emulsion droplets takes place, and coalescence, in which the number of distinct droplets decreases (see Refs. 31-33). Coalescence rates very likely depend primarily on the film-film surface chemical repulsion and on the degree of irreversibility of film desorption, as discussed. However, if emulsions are centrifuged, a compressed polyhedral structure similar to that of foams results [32-34]—see Section XIV-8—and coalescence may now take on mechanisms more related to those operative in the thinning of foams. 

It suffices to carry out one such experiment, such as the expansion or compression of a gas, to establish that there are states inaccessible by adiabatic reversible paths, indeed even by any adiabatic irreversible path. For example, if one takes one mole of N2 gas in a volume of 24 litres at a pressure of 1.00 atm (i.e. at 25 °C), there is no combination of adiabatic reversible paths that can bring the system to a final state with the same volume and a different temperature. A higher temperature (on the ideal-gas scale Oj ) can be reached by an adiabatic irreversible path, e.g. by doing electrical work on the system, but a state with the same volume and a lower temperature Oj is inaccessible by any adiabatic path. 

Under compression or shear most polymers show qualitatively similar behaviour. However, under the application of tensile stress, two different defonnation processes after the yield point are known. Ductile polymers elongate in an irreversible process similar to flow, while brittle systems whiten due the fonnation of microvoids. These voids rapidly grow and lead to sample failure [50, 51]- The reason for these conspicuously different defonnation mechanisms are thought to be related to the local dynamics of the polymer chains and to the entanglement network density. 

In the case of most nonporous minerals at sufficiently low-shock stresses, two shock fronts form. The first wave is the elastic shock, a finite-amplitude essentially elastic wave as indicated in Fig. 4.11. The amplitude of this shock is often called the Hugoniot elastic limit Phel- This would correspond to state 1 of Fig. 4.10(a). The Hugoniot elastic limit is defined as the maximum stress sustainable by a solid in one-dimensional shock compression without irreversible deformation taking place at the shock front. The particle velocity associated with a Hugoniot elastic limit shock is often measured by observing the free-surface velocity profile as, for example, in Fig. 4.16. In the case of a polycrystalline and/or isotropic material at shock stresses at or below HEL> the lateral compressive stress in a plane perpendicular to the shock front... 

Polytropic. Sometimes the compression process has certain associated irreversibilities. The actual operation is therefore approaching adiabatic, but not quite. This "approximately adiabatic" operation is called polytropic. 

Solid substances are forced into unusual and distinctive conditions when subjected to powerful releases of energy such that their inertial properties result in the propagation of high pressure mechanical waves within the solid body. The very high stress, microsecond-duration, conditions irreversibly force materials into states not fully encountered in any other excitation. It is the study of solids under this unique compression-and-release process that provides the scientific and technological interest in shock-compression science. 

Numerous resistance measurements have been carried out under high-pressure shock compression [79D01]. Most of the work has been motivated by the desire to develop stress gauges to measure pressures in shock-compressed materials. Other measurements were undertaken to determine critical pressures to induce phase transformations. Although most of the work is not carried out in sufficient detail to relate resistance observations to defect characterizations, excess resistance at given shock pressures is observed in every case compared to comparably loaded static pressure observations. The presence of residual resistance for times after the loading is removed provides explicit evidence for irreversible changes in resistance due to defects. 

A third objective is similarly obvious. If compression and expansion processes can attain more isentropic conditions, then the cycle widening due to irreversibility is decreased, cr moves nearer to unity and the thermal efficiency increases (for a given t). Cycle modifications or innovations are mainly aimed at increasing (by increasing or decreasing a)-... 

We next consider the application of the exergy flux equation to a closed cycle plant based on the Joule-Brayton (JB) cycle (see Fig. 1.4), but with irreversible compression and expansion processes—an irreversible Joule-Brayton (IJB) cycle. The T,.s diagram is as shown in Fig. 2.6. 

For an irreversible Carnot type cycle (ICAR) with all heat supplied at the top temperature and all heat rejected at the lowest temperature (Tmax = rmi, = To, / UT = 0, icAR=l). but with irreversible compression and expansion (rxicAR = < 1). Eqs. (2.33) and (1.17) yield... 

Consider again the simplest case of compressor delivery air (mass flow i/>, at T ), mixed at constant pressure with unit mass flow of combustion products (at Tf) to give mass flow (1 + i/>) at Ts (see the T, s diagram of Fig. 4.5). The compression and expansion processes are now irreversible. 

For two step cooling, now with irreversible compression and expansion, Fig. 4.7 shows that the turbine entry temperature is reduced from Ti. to by mixing with the cooling air i/ H taken from the compressor exit, at state 2, pressure p2, temperature T2 (Fig. 4.7a). After expansion to temperature Tg, the turbine gas flow (1 + lp ) is mixed with compressor air at state 7 (mass flow i/h.) at temperature Tg. This gas is then expanded to temperature T g. 

Figure 15.5 shows the ideal open cycle for the gas turbine that is based on the Brayton Cycle. By assuming that the chemical energy released on combustion is equivalent to a transfer of heat at constant pressure to a working fluid of constant specific heat, this simplified approach allows the actual process to be compared with the ideal, and is represented in Figure 15.5 by a broken line. The processes for compression 1-2 and expansion 3-4 are irreversible adiabatic and differ, as shown from the ideal isentropic processes between the same pressures P and P2 -... 

If the system is not isolated, its entropy may either increase or decrease. Thus, if a mass of gas is compressed in a cylinder impervious to heat, its entropy increases, but if heat is allowed to pass out into a medium, the entropy of the gas may decrease. By including the"gas and medium in a larger isolated system, we can apply (10) of 45, and hence show Jhat the medium gains more entropy than the gas loses. An extended assimilation of this kind shows that, if every body affected in a change is taken into account, the entropy of the whole must increase by reason of irreversible changes occurring in it. This is evidently what Clausius (1854) had in mind in the formulation of his famous aphorism The entropy of the universe strives towards a maximum. The word universe is to be understood in the sense of an ultimately isolated system. 

Microindentation hardness normally is measured by static penetration of the specimen with a standard indenter at a known force. After loading with a sharp indenter a residual surface impression is left on the flat test specimen. An adequate measure of the material hardness may be computed by dividing the peak contact load, P, by the projected area of impression1. The hardness, so defined, may be considered as an indicator of the irreversible deformation processes which characterize the material. The strain boundaries for plastic deformation, below the indenter are sensibly dependent, as we shall show below, on microstructural factors (crystal size and perfection, degree of crystallinity, etc). Indentation during a hardness test deforms only a small volumen element of the specimen (V 1011 nm3) (non destructive test). The rest acts as a constraint. Thus the contact stress between the indenter and the specimen is much greater than the compressive yield stress of the specimen (a factor of 3 higher). 

For an irreversible process it may not be possible to express the relation between pressure and volume as a continuous mathematical function though, by choosing a suitable value for the constant k, an equation of the form Pv = constant may be used over a limited range of conditions. Equation 2.73 may then be used for the evaluation of / 2 v dP. It may be noted that, for an irreversible process, k will have different values for compression and expansion under otherwise similar conditions. Thus, for the irreversible adiabatic compression of a gas, k will be greater than y, and for the corresponding expansion k will be less than y. This means that more energy has to be put into an irreversible compression than will be received back when the gas expands to its original condition. 

The work done in a reversible compression will be considered first because this refers to the ideal condition for which the work of compression is a minimum a reversible compression would have to be carried out at an infinitesimal rate and therefore is not relevant in practice. The actual work done will be greater than that calculated, not only because of irreversibility, but also because of frictional loss and leakage in the compressor. These two factors are difficult to separate and will therefore be allowed for in the overall efficiency of the machine. 

In practice, there will be irreversibilities (inefficiencies) associated with the compression and the additional energy needed will appear as heat, giving rise to an outlet temperature higher than Tn as given by equation 8.31. 

As an alternative to seals, irreversible bonding can be applied, e.g. by laser welding the surface of a microstructured stack [29, 30] or by diffusion bonding via vacuum compression of a microstructured stack [18, 37-39], For better handling and fluid interconnection, diffusion-bonded stacks may be surrounded by a shell [18, 37-39], Diffusion-bonded stacks typically are more compact. In addition, this interconnection technique is principally amenable to small-series production. Accordingly, it is seen as a proper way to realize future commercial, off-the-shelf micro reactors,... 

Flux Decline Plugging, Fouling, Polarization Membranes operated in NFF mode tend to show a steady flux decline while those operated in TFF mode tend to show a more stable flux after a short initial decline. Irreversible flux decline can occur by membrane compression or retentate channel spacers blinding off the membrane. Flux decline by fouling mechanisms (molecular adsorption, precipitation on the membrane surface, entrapment within the membrane structure) are amenable to chemical cleaning between batches. Flux decline amenable to mechanical disturbance (such as TFF operation) includes the formation of a secondary structure on the membrane surface such as a static cake or a fluid region of high component concentration called a polarization layer. 

Evans RW, Attard GA. 1993. The redox behavior of compressed bismuth overlayers irreversibly adsorbed on Pt(lll). J Electroanal Chem 345 337-350. 

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