Isotherms compression

Vapor-Compression Cycles The most widely used refrigeration principle is vapor compression. Isothermal processes are realized through isobaric evaporation and condensation in the tubes. Standard vapor compression refrigeration cycle (counterclockwise Ranldne cycle) is marked in Fig. ll-72<7) by I, 2, 3, 4. 

A quick method for sizing compressible isothermal flow is offered by the following method developed by Lapple. 

Transfer to the cold reservoir, and compress isothermally along DA till the initial state is reached. 

The membrane of the steam cylinder is now closed by the impervious shutter and the steam expanded (or compressed) isothermally and reversibly until it has the concentration E3 ... 

Example 8.2 Use Figure 8.9 to predict the phase changes that would occur when solid Sn at p = 0.1 MPa is compressed isothermally to p = 15 GPa at (a) 7 = 600 K (b) 7 = 550 K and (c) 7 = 250 K. Assume that the equilibrium phase changes occur rapidly enough to keep up with the change in pressure. 

Sf.I f-Tfst 4.4B In a petroleum refinery a 750.-L container containing ethylene gas at 1.00 bar was compressed isothermally to 5.00 bar. What was the final volume of the container ... 

Self-Test 4.8B A sample of dry air in the cylinder of a test engine at 80. cm3 and 1.00 atm is compressed isothermally to 3.20 atm by pushing a piston into the cylinder. What is the final volume of. the sample ... 

Self-Test 6.6A Suppose that 2.00 mol C02 at 2.00 atm and 300. K is compressed isothermally and reversibly to half its original volume before being used to produce soda water. Calculate w, q, and AU by treating the C02 as an ideal gas. 

Self-Test 7.3A Calculate the change in molar entropy of an ideal gas when it is compressed isothermally to one-third its initial volume. 

Salts of fatty acids are classic objects of LB technique. Being placed at the air/water interface, these molecules arrange themselves in such a way that its hydrophilic part (COOH) penetrates water due to its electrostatic interactions with water molecnles, which can be considered electric dipoles. The hydrophobic part (aliphatic chain) orients itself to air, because it cannot penetrate water for entropy reasons. Therefore, if a few molecnles of snch type were placed at the water surface, they would form a two-dimensional system at the air/water interface. A compression isotherm of the stearic acid monolayer is presented in Figure 1. This curve shows the dependence of surface pressure upon area per molecnle, obtained at constant temperature. Usually, this dependence is called a rr-A isotherm. 

The monolayer stability limit is defined as the maximum pressure attainable in a film spread from solution before the monolayer collapses (Gaines, 1966). This limit may in some cases correspond directly to the ESP, suggesting that the mechanism of film collapse is a return to the bulk crystalline state, or may be at surface pressures higher than the ESP if the film is metastable with respect to the bulk phase. In either case, the monolayer stability limit must be known before such properties as work of compression, isothermal compressibility, or monolayer viscosity can be determined. 

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. 

When spread from dilute hexane solution, acid-dependent enantiomeric discrimination was observed in the 11/A compression isotherms of the monolayer at 25°C (Fig. 12). It is interesting to note that at higher subphase acidities, both racemic and enantiomeric film systems become more highly expanded, and the surface pressures where enantiomeric discrimination commences occur at high (85-90 A2/molecule) average molecular areas. This may be taken as direct evidence of headgroup ionization effects. The surface... 

Figure 4 The path traversed in structural order-metric space as liquid water (SPC/E) is compressed isothermally at two different temperatures. Filled diamonds represent T = 260 K, and open triangles represent T = 400 K. The arrows indicate the direction of increasing density. A and C are states of maximum tetrahedral order at the respective temperatures, whereas B is a state of minimum translational order. Reprinted with permission from Ref. 29. 

Figure 13. Film hysteresis showing failure of film to expand reversibly along its compression isotherm. Recompression of such a film follows an isotherm with reduced surface area at each pressure. From Thompson (101).

Fig. 15. Compression isotherms (n vs. A) of dipaimitoyiphosphatidyichoiine (DPPC) measured at 25 °C in an atmosphere of N2 (dashed iine) and of N2 saturated with F-octyi bromide (soiid iine). insets Fiuorescence images of (a) the DPPC monoiayer compressed at 7t = 15 mN/m under N2, cieariy showing crystaiiine domains, and (b) the DPPC monoiayer in contact with F-octyi bromide, showing prevention of crystaiiization, even at high pressures (ti = 30 mN/m) [107],...

The remaining N — x molecules are compressed isothermally and reversibly from original volume V — xvl to a final volume V — givL. Thus the total volume remains constant. This work is approximately... 

Briggs results, as well as those of others, prove that the dotted line BC in Fig. 23 represents attainable physical conditions. Similarly the line FE is real, for it represents the condition of a vapor compressed isothermally beyond its vapor pressure (saturation pressure). Van der Waals equation8 and certain other equations of state have the mathematical form described by the line ABCDEFG. The portions BC and EF are called metastable. The question of importance in a discussion of boiling is does the portion CDE have any physical significance ... 

For the mixture of diamine (43) with diester (44) miscibility is necessary for a successful polycondensation. Miscibility was demonstrated by showing that the mixed monolayer obeyed Crisp s rule53 (see 4.2.1). For a 1 1 molar mixture of diamine (43) and diester (44) only a slight area change during monolayer polycondensation could be observed. The compression isotherm of the polymer film exhibits a diminished collapse area and pressure (Fig. 14). The structure of the final polymer is shown in Scheme 3. 

The quantity (HV2 — HV1) is the negative of the enthalpy change on compressing (isothermally) the vapor above the sea salt solution from pressure P2 to pressure P1 ... 

I. One mole of an ideal gas is compressed isothermally at 298K to twice its original pressure. Calculate the change in the Gibbs free energy. 

The third operation involves the gas at the third state C at temperature TL, which is compressed isothermally and reversibly to the fourth state D. Since the process is isothermal, AE = 0 and the work done on the system is given by ... 

One mole of an ideal gas, initially at 20°C and 1 bar, undergoes the following mechanically reversible changes. It is compressed isothermally to a point such that when it is heated at constant volume to 100 0 its final pressure is lObar. Calculate Q, W, AU, and AH for the process. Take... 

A particular quantity of an ideal gas [Cv = (5/2) R] undergoes the following mechanically reversible steps that together form a cycle. The gas, initially at 1 bar and 300 K, is compressed isothermally to 3 bar. It is then heated at constant P to a temperature of 900 K. Finally, it is cooled at constant volume to its initial state with the extraction of 1,300 J as heat. Determine Q and IV for each step of the cycle and for the complete cycle. 

One mole of an ideal gas is compressed isothermally but irreversibly at 400 K from 3 bar to 7 bar in a piston/cylinder device. The work required is 35 percent greater than the work of reversible, isothermal compression. The heat transferred from the gas during compression flows to a heat reservoir at 300 K. Calculate the entropy changes of the gas, the heat reservoir, and A5Iolal. 

Steam at 300(°F) and l(atm) is compressed isothermally in a mechanically reversible, nonflo process until it reaches a final state of saturated liquid. Determine Q and VP for the process. 

Clausius/Clapeyron equation, 182 Coefficient of performance, 275-279, 282-283 Combustion, standard heat of, 123 Compressibility, isothermal, 58-59, 171-172 Compressibility factor, 62-63, 176 generalized correlations for, 85-96 for mixtures, 471-472, 476-477 Compression, in flow processes, 234-241 Conservation of energy, 12-17, 212-217 (See also First law of thermodynamics) Consistency, of VLE data, 355-357 Continuity equation, 211 Control volume, 210-211, 548-550 Conversion factors, table of, 570 Corresponding states correlations, 87-92, 189-199, 334-343 theorem of, 86... 

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