Compression and Expansion

From the first law of thermodynamics, the internal work W needed for the compression of a gas can be calculated from the enthalpies and before and after the 

With the simplification of hydrogen as an ideal gas, we can substitute v from the ideal gas Eq. (1.4) and get  

In our case, the calculation gives Wi = 8220kjkg. In comparison tvith the tvork calculated above this is 6.2% less, which is because hydrogen deviates from ideal gas behavior in the pressure range under consideration. 

The compression of the gas in the tank to be filled also causes its temperature to rise. This effect even outweighs the Joule-Thomson effect. A simulation can be done based on the first law of thermodynamics. Regarding the reservoir and the tank as a closed adiabatic system, the internal energies of the two containers before and after 

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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. 

In the gas turbine (Brayton cycle), the compression and expansion processes are adiabatic and isentropic processes. Thus, for an isentropic adiabatic process 7 = where Cp and c are the specific heats of the gas at constant pressure and volume respectively and can be written as ... 

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... 

In the ultimate version of the reheated and intercooled reversible cycle [CICICIC- HTHTHT- XJr, both the compression and expansion are divided into a large number of small processes, and a heat exchanger is also used (Fig. 3.6). Then the efficiency approaches that of a Carnot cycle since all the heat is supplied at the maximum temperature Tr = T ax and all the heat is rejected at the minimum temperature = r,nin. 

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. 

Figures 12-37F and 12-37G use adiabatic compression and expansion (zero heat transfer). All heat added to the cycle comes from heating the engine exhaust by Heat rejected from the cycle, Qni> leaves through the aftercooler.

The main application for this cycle is the air-conditioning and pressurization of aircraft. The turbines used for compression and expansion turn at very high speeds to obtain the necessary pressure ratios and, consequently, are noisy. The COP is lower than with other systems [15]. 

Both the compression and expansion are isobaric processes hence, the total work is given by... 

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. 

Thus, theoretically, the clearance volume does not affect the work done per unit mass of gas, since Vi — V4 is the volume admitted per cycle. It does, however, influence the quantity of gas admitted and therefore the work done per cycle. In practice, however, compression and expansion are not reversible, and losses arise from the compression and expansion of the clearance gases. This effect is particularly serious at high compression ratios. 

FIGURE 9.13 Le Chatelier s principle predicts that, when a reaction at equilibrium is compressed, the number of molecules in the gas phase will tend to decrease. This diagram illustrates the effect of compression and expansion on the dissociation equilibrium ot a diatomic molecule. Note the increase in the relative concentration of diatomic molecules as the system is compressed and the decrease when the system expands. 

The compression and expansion of gases is covered more fully in Section 3.13. 

The economic operation of processes which involve the compression and expansion of large quantities of gases, such as ammonia synthesis, nitric acid production and air... 

The calculation of entropy is required for compression and expansion calculations. Isentropic compression and expansion is often used as a reference for real compression and expansion processes. The calculation of entropy might also be required in order to calculate other derived thermodynamic properties. Like enthalpy, entropy can also be calculated from a departure function ... 

Figure 24.26 Multistage compression and expansion with an economizer.

Complex refrigeration cycles can be built up in different ways. Figure 24.29 shows a cascade cycle with multistage compression and expansion of the high-temperature cycle. 

Kleppe, C.A. Chart for Compression and Expansion Temperatures, Chemical Engineering, Sept. 19, 1960, p. 213. 

Fig. 8 Representative compression and expansion 11/ 4 isotherms showing clockwise and counterclockwise hysteresis.

The few examples of deliberate investigation of dynamic processes as reflected by compression/expansion hysteresis have involved monolayers of fatty acids (Munden and Swarbrick, 1973 Munden et al., 1969), lecithins (Bienkowski and Skolnick, 1974 Cook and Webb, 1966), polymer films (Townsend and Buck, 1988) and monolayers of fatty acids and their sodium sulfate salts on aqueous subphases of alkanolamines (Rosano et al., 1971). A few of these studies determined the amount of hysteresis as a function of the rate of compression and expansion. However, no quantitative analysis of the results was attempted. Historically, dynamic surface tension has been used to study the dynamic response of lung phosphatidylcholine surfactant monolayers to a sinusoidal compression/expansion rate in order to mimic the mechanical contraction and expansion of the lungs. 

Unlike electron and scanning tunneling microscopy, the use of fluorescent dyes in monolayers at the air-water interface allows the use of contrast imaging to view the monolayer in situ during compression and expansion of the film. Under ideal circumstances, one may observe the changes in monolayer phase and the formation of specific aggregate domains as the film is compressed. This technique has been used to visualize phase changes in monolayers of chiral phospholipids (McConnell et al, 1984, 1986 Weis and McConnell, 1984 Keller et al., 1986 McConnell and Moy, 1988) and achiral fatty acids (Moore et al., 1986). 

In addition, it should be noted that none of the compression and expansion cycles for these films are coincident. The considerable hysteresis exhibited during the compression/expansion cycle is evidenced at every compression/expansion rate investigated, and is indicative of a stereoselective kinetic process that must occur upon film compression. Table 3 gives the monolayer stability limits of the amino acid methyl ester films as defined by... 

Compression and expansion rates of 7.1 A2/molecule/min. Values in units of A2/molecule. Standard deviations are at the 95% confidence level. 

Fig. 17 Surface pressure/area isotherms for the compression and expansion cycles of racemic (dashed line) and enantiomeric (solid line) stearoylserine (A), stearoyl-alanine (B), stearoyltryptophan (C), and stearoyltyrosine methyl esters (D) on a pure water subphase at 25°C carried out at a compression rate of 7.1 A2/molecule per minute. Arrows indicate the direction of compression and expansion.

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