Isothermal compression-expansion

In contrast to isentropy, the process of isothermal compression-expansion, which is accompanied by heat release or heat absorption, is represented by an exergy vector with the slope of < 1 in the regimes of heat absorption and heat release as shown in Fig. 11.10(a). 

Two other important quantities are the isobaric expansivity ( coefficient of themial expansion ) and the isothermal compressibility k, defined as... 

Figure 4.14 Behavior of thermodynamic variables at Tg for a second-order phase transition (a) volume and fb) coefficient of thermal expansion a and isothermal compressibility p.

By an assortment of thermodynamic manipulations, the quantities dn/dp and [N (d G/dp )o] can be eliminated from Eq. (10.48) and replaced by the measurable quantities a, /3, and dn/dT the coefficients of thermal expansion, isothermal compressibility, and the temperature coefficient of refractive index, respectively. With these substitutions, Eq. (10.48) becomes... 

Other Refrigeration Methods. Cryocoolers provide low temperature refrigeration on a smaller scale by a variety of thermodynamic cycles. The Stirling cycle foUows a path of isothermal compression, heat transfer to a regenerator matrix at constant volume, isothermal expansion with heat transfer from the external load at the refrigerator temperature, and finally heat transfer to the fluid from the regenerator at constant volume. 

The Intercooled Regenerative Reheat Cycle The Carnot cycle is the optimum cycle between two temperatures, and all cycles try to approach this optimum. Maximum thermal efficiency is achieved by approaching the isothermal compression and expansion of the Carnot cycle or by intercoohng in compression and reheating in the expansion process. The intercooled regenerative reheat cycle approaches this optimum cycle in a practical fashion. This cycle achieves the maximum efficiency and work output of any of the cycles described to this point. With the insertion of an intercooler in the compressor, the pressure ratio for maximum efficiency moves to a much higher ratio, as indicated in Fig. 29-36. 

The modulus indicates that heat is absorbed (+), during die isodrermal expansion, but released (—) during die isothermal compression. In the adiabatic processes no heat is supplied or removed from die working gas, and so... 

The experiments result in an explicit measure of the change in the shock-wave compressibility which occurs at 2.5 GPa. For the small compressions involved (2% at 2.5 GPa), the shock-wave compression is adiabatic to a very close approximation. Thus, the isothermal compressibility Akj- can be computed from the thermodynamic relation between adiabatic and isothermal compressibilities. Furthermore, from the pressure and temperature of the transition, the coefficient dO/dP can be computed. The evaluation of both Akj-and dO/dP allow the change in thermal expansion and specific heat to be computed from Eq. (5.8) and (5.9), and a complete description of the properties of the transition is then obtained. 

A wide variety of physical properties are important in the evaluation of ionic liquids (ILs) for potential use in industrial processes. These include pure component properties such as density, isothermal compressibility, volume expansivity, viscosity, heat capacity, and thermal conductivity. However, a wide variety of mixture properties are also important, the most vital of these being the phase behavior of ionic liquids with other compounds. Knowledge of the phase behavior of ionic liquids with gases, liquids, and solids is necessary to assess the feasibility of their use for reactions, separations, and materials processing. Even from the limited data currently available, it is clear that the cation, the substituents on the cation, and the anion can be chosen to enhance or suppress the solubility of ionic liquids in other compounds and the solubility of other compounds in the ionic liquids. For instance, an increase in allcyl chain length decreases the mutual solubility with water, but some anions ([BFJ , for example) can increase mutual solubility with water (compared to [PFg] , for instance) [1-3]. While many mixture properties and many types of phase behavior are important, we focus here on the solubility of gases in room temperature IFs. 

The entropy change accompanying the isothermal compression or expansion of an ideal gas can be expressed in terms of its initial and final pressures. To do so, we use the ideal gas law—specifically, Boyle s law—to express the ratio of volumes in Eq. 3 in terms of the ratio of the initial and final pressures. Because pressure is inversely proportional to volume (Boyle s law), we know that at constant temperature V2/Vj = E /E2 where l is the initial pressure and P2 is the final pressure. Therefore,... 

FIG. 17 H-A isotherms for C60 on a pure aqueous subphase at 21°C (a) Monolayer prepared by spreading 50 p.L of a 0.1 mM solution in benzene (b) monolayer prepared by spreading 200 p,L and (c) a compression-expansion cycle of a monolayer prepared by spreading 100 p,L of a 0.5 mM solution. (Reproduced with permission from Ref. 232. Copyright 1993 American Chemical Society.)... 

The dynamic surface tension of a monolayer may be defined as the response of a film in an initial state of static quasi-equilibrium to a sudden change in surface area. If the area of the film-covered interface is altered at a rapid rate, the monolayer may not readjust to its original conformation quickly enough to maintain the quasi-equilibrium surface pressure. It is for this reason that properly reported II/A isotherms for most monolayers are repeated at several compression/expansion rates. The reasons for this lag in equilibration time are complex combinations of shear and dilational viscosities, elasticity, and isothermal compressibility (Manheimer and Schechter, 1970 Margoni, 1871 Lucassen-Reynders et al., 1974). Furthermore, consideration of dynamic surface tension in insoluble monolayers assumes that the monolayer is indeed insoluble and stable throughout the perturbation if not, a myriad of contributions from monolayer collapse to monomer dissolution may complicate the situation further. Although theoretical models of dynamic surface tension effects have been presented, there have been very few attempts at experimental investigation of these time-dependent phenomena in spread monolayer films. 

The difference between the static or equilibrium and dynamic surface tension is often observed in the compression/expansion hysteresis present in most monolayer Yl/A isotherms (Fig. 8). In such cases, the compression isotherm is not coincident with the expansion one. For an insoluble monolayer, hysteresis may result from very rapid compression, collapse of the film to a surfactant bulk phase during compression, or compression of the film through a first or second order monolayer phase transition. In addition, any combination of these effects may be responsible for the observed hysteresis. Perhaps understandably, there has been no firm quantitative model for time-dependent relaxation effects in monolayers. However, if the basic monolayer properties such as ESP, stability limit, and composition are known, a qualitative description of the dynamic surface tension, or hysteresis, may be obtained. 

The Yl/A isotherms of the racemic and enantiomeric forms of DPPC are identical within experimental error under every condition of temperature, humidity, and rate of compression that we have tested. For example, the temperature dependence of the compression/expansion curves for DPPC monolayers spread on pure water are identical for both the racemic mixture and the d- and L-isomers (Fig. 13). Furthermore, the equilibrium spreading pressures of this surfactant are independent of stereochemistry in the same broad temperature range, indicating that both enantiomeric and racemic films of DPPC are at the same energetic state when in equilibrium with their bulk crystals. 

Shorter chain analogs of DPPC were also investigated in order to determine if the lack of stereo-differentiation in monolayer properties could be due to DPPC s higher gel point or complicating steric effects. Figure 15 shows the compression/expansion isotherms of DPPC as compared with racemic and enantiomeric dimyristoylphosphatidyl choline (DMPC) and dilauroyl phosphatidyl choline (DLPC). Again no stereodifferentiation in monolayer properties was observed as reflected by 11/A isotherms or dynamic surface tension. 

Figure 17 shows the 11/A isotherms of racemic and enantiomeric films of the methyl esters of 7V-stearoyl-serine, -alanine, -tryptophan, and -tyrosine on clean water at 25°C. Although there appears to be little difference between the racemic and enantiomeric forms of the alanine surfactants, the N-stearoyl-tyrosine, -serine, and -tryptophan surfactants show clear enantiomeric discrimination in their WjA curves. This chiral molecular recognition is first evidenced in the lift-off areas of the curves for the racemic versus enantiomeric forms of the films (Table 2). As discussed previously, the lift-off area is the average molecular area at which a surface pressure above 0.1 dyn cm -1 is first registered. The packing order differences in these films, and hence their stereochemical differentiation, are apparently maintained throughout the compression/expansion cycles. 

Fig. 19 Surface pressure/area isotherms for the compression/expansion cycle of enantiomeric (dashed line) and racemic (solid line) SSME monolayers on pure water subphase at (a) 20°C, (b) 25°C, (c) 30°C and (d) 40°C. The compression rate is 29.8 A2/ molecule/min. Reprinted with permission from Harvey et al., 1989. Copyright 1989 American Chemical Society.

When spread from a benzene/hexane solution on to a slightly acidic water subphase, spread films of racemic and enantiomeric STy exhibit nearly the same IT/A isotherms (Fig. 22) and surface shear viscosities (Harvey et al., 1990). The shapes of these isotherms and the apparently small differences between the compression/expansion characteristics of these fluid homochiral and heterochiral monolayers is conserved throughout the... 

Enantiomeric discrimination and its relation to film component reorganization upon compression can also be observed in dynamic surface tension hysteresis loops. Figure 26 shows the WjA isotherms generated upon five successive compression/expansion cycles (from II = 0 to lOdyncm-1) of racemic and enantiomeric films containing 17 mole percent palmitic acid. The hysteresis loops, obtained on the apparatus described in Section 2 (p. 63), show that the first compression/expansion cycle of the racemic system is repeated in each successive cycle. Upon expansion of the film from the maximum surface pressure back to Odyncm-1, the racemic film returns to its original state without detectable reorganization of the components. However, the... 

Fig. 32 Surface pressure/area isotherms for the compression/expansion cycles of diastereomeric monolayers of (R or S)-iV-(a-methylbenzyl)stearamides mixed 1 1 with (R or S )-stearoylalanine methyl esters on a pure water subphase at 35°C. Dashed lines denote heterochiral pairs (R S or R S) and solid lines denote homochiral pairs (R R or S S ).

Fig. 38 Surface pressure/area isotherms for the compression/expansion cycles of meso- (dashed line) and ( )-(solid line) azobis-[6-(6-cyanododecanoic acid)] on a pH 3 subphase at 22°C. Compressed at a rate of 15.5 A2/molecule per minute. Reprinted with permission from Porter et al., 1986a. Copyright 1986 American Chemical Society.

Hysteresis was generally observed in the compression-expansion cycles of the force-area isotherms, indicating that the timescale for relaxation of the fully compressed film back to its expanded state was slower than the movement of the barrier of the Langmuir trough. Our studies, like many others, imply that monolayers are metastable and that reversible thermodynamics can only be applied to their analysis with caution. 

The reader interested in the liquefaction technologies can see, for example, ref. [14,15], We will only remind that in most cases, the gas cooling is obtained by the Joule-Thomson process an isothermal compression of the gas is followed by an expansion. This procedure leads to a cooling only if the starting temperatures are lower than the inversion temperature 7] = 6.75 TCI (for a Van der Waals gas), where TCI is the critical temperature. 

Typical values of the isobaric expansivity and the isothermal compressibility are given in Table 1.2. The difference between the heat capacities at constant volume and constant pressure is generally negligible for solids at low temperatures where the thermal expansivity becomes very small, but the difference increases with temperature see for example the data for AI2O3 in Figure 1.2. 

Table 1.2 The isobaric expansivity and isothermal compressibility of selected compounds at 300 K.

In order to calculate the dilational contribution exactly a considerable quantity of data is needed. The temperature dependence of the volume, the iso-baric expansivity and the isothermal compressibility is seldom available from 0 K to elevated temperatures and approximate equations are needed. The Nernst-Lindeman relationship [7] is one alternative. In this approximation cP,m -Cv,m is given by... 

The effect of a change in volume on the entropy is given by the ratio of the iso-baric expansivity and isothermal compressibility of a compound ... 

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