Work of compression

The work destroyed in the single-stage compression is very much greater than the work 

If the compression is done in two stages, compressing first with a lighter mass to an intermediate volume and then with the heavier mass to the final volume, less work is destroyed the work destroyed is the area of the shaded rectangles in Fig. 7.5. 

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Compression. The work of compression is typically compared against the isentropic—adiabatic case. 

Calculation of Actual Work of Compression For simplicity, the work of compression is calciilated by the equation for an ideal gas in a three-stage reciprocating machine with complete intercoohng and with isentropic compression in each stage. The work so calculated is assumed to represent 80 percent of the actual work. The following equation may be found in any number of textbooks on thermodynamics ... 

Refrigerating capacity is the product of mass flow rate of refrigerant m and refrigerating effect R which is (for isobaric evaporation) R = hevaporator outlet evaporator mJef Powei P required foi the coiTipressiou, necessary for the motor selection, is the product of mass flow rate m and work of compression W. The latter is, for the isentropic compression, W = hjisehatge suction- Both of thoso chai acteristics could be calculated for the ideal (without losses) and for the ac tual compressor. ideaUy, the mass flow rate is equal to the product of the compressor displacement per unit time and the gas density p m = p. 

To reduce the work of compression in this cycle a two-stage or dualpressure process may be usedwhereby the pressure is reduced by two successive isenthalpic expansions. Since the isothermal work of compression is approximately proportional to the logarithm of the pressure ratio, and the Joule-Tnomson cooling is roughly proportional to... 

Coefficient of Performance. COP is the ratio of refrigerating effect to work of compression. The higher the value of COP, the higher the efficiency of the cycle. Referring to Figure 11-48A,... 

Work of Compression. This is the enthalpy of a lb of refrigerant at compressor discharge conditions minus the enthalpy of a lb of refrigerant at compressor suction conditions. 

Horsepower is the work done in a cylinder on the gas by the piston connected to the driver during the complete compression cycle. The theoretical horsepower is that required to isen-tropically (adiabatically) compress a gas through a specified pressure range. The indicated horsepower is the actual work of compression developed in the compressor cylinder(s) as determined from an indicator card. Brake horsepower (bhp) is the actual horsepower input at the crankshaft of the compressor drive. It does not include the losses in the driver itself, but is rather the actual net horsepower that the driver must deliver to the compressor crankshaft. 

Figure 12-20. Chart for solving theoretical work of compression or expansion. (Used by permission Edmister, W. C. Petroleum Refiner, V. 38, No. 5, 1959. Gulf Publishing Co. All rights reserved.)...

Cylinder heat is produced by the work of compression plus friction, which is caused by the action of the piston and piston rings on the cylinder wall and packing on the rod. The amount of heat generated can be considerable, particularly when moderate to high compression ratios are involved. This can result in undesirably high operating temperatures. 

Figure 2.7 Comparison of isothermal work of compression. Graph (b) represents the reversible process for which the work required for the compression is a minimum.

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. 

The total work of compression from a pressure P to a pressure Pi is found by integrating equation 8.27. For an ideal gas undergoing an isothermal compression ... 

If the gas deviates appreciably from the ideal gas laws over the range of conditions considered, the work of compression is most conveniently calculated from the change in the thermodynamic properties of the gas. 

The work of compression for an ideal gas per cycle under isothermal conditions ... 

In practice the cylinders are usually water-cooled. The work of compression is thereby reduced though the effect is usually small. The reduction in temperature does, however, improve the mechanical operation of the compressor and makes lubrication easier. 

The minimum work of compression in a compressor of n stages is therefore ... 

At the curved surface of the sphere, a force is acting that is directed toward the center of the sphere and tends to reduce its surface area. Hence, the gas pressure in the nucleus will be higher than the pressure Pq in the surrounding medium. An infinitely small displacement dr of tfie surface in the direction of the sphere s center is attended by a surface-area decrease dS = Snrdr) and a volume decrease dV (= dr). The work of compression of the nucleus is given by (Pnuci It... 

The intermediate pressure P2 can be chosen to minimize the overall work of compression. Thus ... 

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. 

Once it has been established that the components of a binary monolayer are to some degree miscible, the energetics of their interaction may be calculated directly from the 11/A isotherms of the mixture and its individual components. As proposed by Goodrich (1957), this technique employs the differences in the work of compression of the binary film and the work required to compress each of the films of the pure components to the same surface pressure. The result is the total free energy of mixing as expressed by the sum of the excess and ideal free energies of mixing in (14), where Nt... 

Table 11 Work of compression of the C-15 3,3, C-15 6,6, C-15 9,9, and C-15 12,12 ketodiacids on a pure water subphase at 25°C compressed at a rate of 19.24 A2/molecule per minute.

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