INDUSTRIAL AND ENGINEERING CHEMISTRY
lune, 1944
at the extreme right which corresponds t o the gas in question. The intersection of this line with the CP/CVscale gives the desired value of t h e ratio. T o apply this method t o mixtures of gases, it is necessary t o use the correlation of critical temperature and pressure on the basis of molecular weight. From the compound scale a horizontal line is followed t o the critical conditions scale, and the critical pressure and temperature of a gas of this molecular weight are read from the right- and left-hand sides of the line, respectively. The reduced temperature and pressure are calculated and applied t o the T Rand P R scales t o locate a point on the reference line, a line is projected from this point t o the molecular weight scale on the extreme right, and the value of the ratio is read on the CP/CV scale as before. The use of this nomograph can be illustrated by the solution of the problem given by Edmister ( 3 ) . The value of y for propylene a t PR = 0.555 and T R = 0.95 is determined, as shown in the insert sketch of Figure I, t o be 1.53. This checks the value of 1.525 given by Edmister. (Here the point for propylene used does not correspond t o its molecular weight, as noted above.)
583
The previous formulas refer only t o perfect gases. For power requirements of actual gases, t h e isentropic work factor of York (6) must be included, together with the actual specific heat:
where M = molecular weight of gas C p = specific heat of gas, B.t.u./lb.
AHs = change in enthalpy along a n isentropic path The methods of calculating this factor were fully discussed by York (6) who recommended t h a t the calculation be based on the value of y a t t h e suction conditions of t h e compressor. The convenience in using the nomograph5 in evaluating t h e (2’2 - T1) term in Equation 4 is evident. APPLICATIONS
ADIABATIC EXPANSION AND COMPRESSION O F A PERFECT GAS
The ratio of specific heats obtained from Figure 1 is used t o calculate the outlet temperature for a n adiabatic expansion or compression of a perfect gas in t,he following relation: v - 1
where Tz = outlet temp. T I = inlet temp.
PZ = outlet pressure
PI = inlet pressure
A nomograph is constructed (Figure 2 ) from which the outlet temperature can be determined from the values of y , T I , and Pg/PL, the compression or expansion ratio. Figure 2 is the set square type, and either compression or expansion operations may be readily calculated with it. For compression, it is used by adjusting a right triangle so t h a t one leg passes through the proper values on both the y scale and on the compression ratio scale; the other leg passes through the desired value on the scale ’corresponding t o t h e temperature at lower pressure (inlet). The resultant outlet temperature is given by the intersection of the latter leg with the scale corresponding t o the temperature at higher pressure (outlet). For expansion calculations the lower calibrations on the horizontal scale giving the expansion ratio are used, the inlet temperature value is set on the temperature at higher pressure scale, and the exhaust temperature value is found on the temperature at lower pressure scale. The value of y used in Equation 2 is t h a t at the inlet conditions since, as previously mentioned, this equation requires a constant value of y. The theoretical power requirement in a single-stage adiabatic compression, based on perfect gas law relation, is:
where PI = pressure a t inlet, Ib./sq. in. Vi = volume of gas compressed, cu. ft./min. When the nomograph is used t o calculate the exhaust temperature, a more convenient form of Equation 3 is: h.p. = 0.007808 --?L (Tz 7-1
- Ti)
where h.p. = horsepower required per lb. mole/hr. of gas compressed
PROBLEM. A gas which consists substantially of a mixture of normal saturated hydrocarbons and has an average moIecular weight of 40 is t o be compressed adiabatically from 15 pounds per square inch absolute at 50” F. t o 100 pounds absolute. The outlet temperature and the theoretical horsepower required t o compress 300 moles (12,000 pounds) per hour of this gas is desired. Perfect gas laws will be assumed to hold for this case. This example is worked out according to the insert sketches i n Figures 1 and 2. For a gas of 40 molecular weight, P, = 639 and T o = 635” R. Thus a t inlet conditions, P R = 0.023 and T R = 0.804; and from Figure 1, y = 1.150. The compression ratio is 6.67 and, from Figure 2, the outlet temperature is found t o be 192 F. GENERAL. Figure 1 was constructed to determine y for hydrocarbons. For other gases or vapors, such as air and steam, when y is known (1, 4, Figure 2 may be used t o determine t h e outlet temperatures; the related methods of calculation described may be applied for the determination of tlhe theoretical power required. O
LITERATURE CITED
Dorsey, N. E., “Properties of Ordinary Water-Substance”, pp. 110,262,264, New York, Reinhold Pub. Corp., 1940. Edmister, W. C., IND.ENQ.CHIN.,30,352 (1938). Ibid., 32, 373 (1940). Ellenwood, F. O., Kulik, N., and Gay, N. R., Cornel1 Univ. Expt. Sta., Bull. 30, 9 (1942). Othmer, D. F., IND.ENQ.CHEM.,34, 1072 (1942). York, Robert, Jr., Ibid., 34,535 (1942). York, Robert, Jr., private communication, 1943.
Recovery of Sulfur from Sulfur Dioxide in-Waste Gases-Correction Attention has been called to a n error in our paper which AND ENGINEERING appeared in the April issue of INDUSTRIAL CHEMISTRY(pages 329 t o 332). Equilibrium constants K in Table 11, Equation 6, should read 0.1,0.4, and 0.7 for 150°, 200”, and 250’ C., respectively. On page 330, t h e last sentence of t h e second paragraph under “Thermodynamic Considerations” should read: “Inspection of the free energy values for reaction 6 seems to show t h a t diatomic sulfur is not seriously involved in t h e second step of the process.” T. F. DOUMANI, R. F. DEERY, AND W. E . BRADLEY UNIONOIL COXPLNY O F CALIFORNIA WILMINQTON, CALIF.
