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INDUSTRIAL A N D ENGINEERING CHEMISTRY
intersect PR and PL a t corresponding values for the same value of TR. TRcan be determined since Tc is known; and since the value of P a t one temperature is known, and the value of PR may be obtained immediately for that point, the value of the critical pressure may be determined from the equation Pc = P / P , either from the nomogram or arithmetically. If the vapor pressures are known a t two points of temperature and the critical temperature is also known, the critical pressure and any other value of temperature and pressure may be determined. This solution uses Figure 3 in a cut-and-try calculation, which is simpler in use than the following description: Two points are obtained on the A scale of Figure 3 corresponding to values for water a t the two given temperatures. It is then desired to find the focal point on the diagonal scale which is characteristic for this compound. This cannot be done directly; but consideration of another property of the chart allows it t o be done indirectly. The critical pressure which is also to be obtained will be represented by some unknown point on scale I or 11; and this point must be assumed as a start in the cut-and-try calculation. The known two values of vapor pressure of the compound are indicated on scale IV or V, and are connected by lines with the assumed critical pressure point on scale I or 11, which lines are continued to intersect scale VI in two points. Each of these
Vol. 34, No. 9
points has t o be connected by a line drawn through the corresponding one of the first mentioned two points on the A scale. These lines should intersect at a common point on the diagonal scale, which point represents the ratio of the reduced latent heat of the compound t o that of water. If these two lines do not intersect a t a common point on the diagonal, the value of the critical pressure which mas assumed is incorrect, a new value is assumed, and the geometric construction is repeated. Two or three trials will usually give the desired value of the critical pressure and the focal point on the diagonal. The focal point, of course, fixes all points of vapor pressure, which may then be determined as indicated above. Furthermore, it may be noted that the latent heat of the compound may also be obtained a t any temperature.
Acknowledgment The painstaking assistance of Frederick G. SaTYyer and of Robert F. Morley in the calculations and preparation of graphs is gratefully acknowledged.
Literature Cited (1) Osboine, N. S.,and Meyera, C. H., J . Research .VatZ. Bur. Standards, 13, 1-20 (1934) (Research Paper 1391). ( 2 ) Othmer, D. F., IXD. EXG.CHEM..32, 841 (1940).
Absorption of Liquids by Coal Application of Radiographic Methods to the Problem GEORGE W. LAND Battelle Memorial Institute, Columbus, Ohio
T
HE reduction of the dust from coal by the application of liquids such as water, calcium chloride solutions, or oil depends on the maintenance of a film of the liquid on the coal that will stick the smaller t o the larger pieces or will agglomerate the small particles into larger pieces which will not be carried in air currents. Various investigators (1, 4, 6) have found that even such liquids as petroleum oils, which do not evaporate a t ordinary temperatures, disappear rapidly from the surfaces of some coals and leave the coal as dusty as before treatment. This disappearance has been attributed to absorption of the liquid into the cracks and pores of the coal substance. Of the various coals of the United States studied by Pilcher and Sherman (I),the lower rank coals of Indiana and Illinois were found to be the most absorptive for oil. I n further research on this problem for Bituminous Coal Research, Inc., aimed a t finding the most suitable and economical materials and methods for the treatment of such coals, use has been made of radiographic methods to determine the relative rate of absorption of coals of various ranks and of the banded constituents of the coals. The method used was similar to that employed by Beeching (2) who made radiographs of English and Scottish coals before and after immersion in solutions of lead acetate and lead nitrate in water. Because the lead salts are more absorbent to x-rays
than the coal material, their presence when absorbed in the coal is plainly shown on the film. Beeching’s pictures shon-ed that the lead solutions penetrated not only the cracks of the coal, but also the general body of the coal where no cracks were evident. He concluded that this second type of penetration niust be into the pore space of the coal. Using a formula in which he related viscosity, surface tension, and specific gravity of the solutions to the height of capillary rise of the liquid into a partially submerged piece of coal in a given time, he calculated that the mean diameter of pores was of the order of 50 X 10-7 cm. This value is of the same order as that determined for bituminous coals by the moisture equilibration method and Anderson’s formula, used by Rees, Land, and Reed ( 5 ) .
Experimental Procedure Because of the desire to relate absorption directly to the use of oil, a 20 per cent by volume solution of tetraethyllead in 200-viscosity oil was first tried. Radiographs of Illinois No. 6 and Pocahontas coals before and after immersion in this solution showed some evidence of penetration of the oil and lead solution, but the x-ray absorption of tetraethyllead was not great enough t o cause as high a degree of darkening of the
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INDUSTRIAL AND ENGINEERING CHEMISTRY
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*
Before Immersion
After irnrnermon
Pocahontas
Illinois No. 6
FIGURE1. NATURAL-SIZESPECIMENSOF COAL PHOTOGRAPHED BY NORMAL LIGHT Bedding planes parallel t o film
Bedding planes perpendiouiar t o film
RADIOGRAPHS, OF POCAHONTAS KO. 3 COAL BEFORE IMMERSION IN LEADACETATESOLUTION
FIGURE2.
AND AFTER
Before Irnrnersion
After
imrnersion
-Bedding planes parallel t o film
FIGURE3.
Bedding planes perpendioular t o film
RADIOGRAPHS OF ILLINOIS No. 6 COAL BEFORE AFTER IMMERSION IN LEADACETATE SOLUTION
AND
The radiographic examination of coal before and after immersion in solutions of lead salts has proved a useful method for estimating the order of absorption of liquids by the coal substance. Photographs show clearly the greater absorption of the lower rank Illinois No. 6 coal than of the high rank Pocahontas No. 3 coal. Of the banded ingredients of the Illinois No. 6 coal, the fusain is shown to absorb the solutions most rapidly and completely; vitrain absorbs much less than fusain but more than clarain and durain. Of the various sizes of coal treated to allay dust, that for residential stokers is most universally treated. The preparation of this coal by double screening with removal of the finer sizes, as those below 10 mesh or inch, is common. This is done not only to improve the appearance but also the performance, as McCabe (3) showed that screening removes much of the more friable vitrain which also leads to excessive coke formation in the fuel bed. The very friable fusain is also removed by double screening. The evidence presented that fusain and vitrain are the constituents which absorb most liquid shows that their removal will lead to more economical and more permanently effective dustless treatment.
’/,
Durain
Clarain Vitrain Fusain SPECIMENS OF BANDEDCONSTITUENTS O F ILLINOIS NO. 6 COAL PHOTOGRAPHED WITH NORMALLIGHT
FIGURE4.
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INDUSTRIAL AND ENGINEERING CHEMISTRY Before
After 1 minute
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lumps of coal were among those used in making the radiographs. Figure 2 shows Pocahontas No. 3 coal before and after immersion in the lead acetate solution. The evidences of penetration of the solution are clearly visible. Cracks which show only faintly before immersion are much darker in the pictures after immersion. I n addition, many dark lines, which are cracks that absorbed lead acetate, show in the “after” pictures where none were visible in the “before” pictures. A certain amount of general darkening can also be seen in the after pictures. This is taken as evidence of the absorption of the lead salt into the pores of the coal. Figure 3 shows similar pictures of Illinois KO. 6 coal. There is the same absorption in cracks as with the Pocahontas, but the Illinois coal shows much more general darkening than the Pocahontas. This is evidence of the greater porosity of the Illinois coal. A b s o r p t i o n by Banded Ingredients of Illinois No. 6 Coal
After 2 minutes
After 5 minutes
FIGURE 5. RADIOGRAPHS OF FUSAIN BEFORE A N D AFTER PARTIAL IMMERSION I N LEADACETATESOLUTtON
film as is desirable. Because of this and also because tetraethyllead in the concentrations used is highly toxic, a water solution of lead acetate was used for further investigations. A 30 per cent by weight solution of lead acetate was found to have a much greater absorbing power for x-ray than the equivalent tetraethyllead solution. Radiographs of Illinois No. 6 and Pocahontas coal were made with this lead acetate solution, before and after immersion. Radiographs were also made of durain, clarain, vitrain, and fusain from Illinois No. 6 col~lbefore and after partial immersion for various lengths of time. Radiographic expowres were made at 40 kilovolts and 5 milliamperes, with a distance from target to film of 39 inches. The time of exposure was 25 seconds per inch of sample thickness. The solutions were held at 100” F. All sperimens except the Pocahontas and the first Illinois No. 6 coal were immersed to a depth indicated on the pictures by the black pointer. These two samples were immersed completely. Priiits in any set were exposed for the same length of time and given the same development. R e l a t i v e Absorption of Pocahontas and Illinois No. 6 Coal Figure 1 shows pieces of Pocahontas and of Illinois No. 6 coal by normal lighting. These
Figure 4 is a normal photograph of some of the pieces of the banded ingredients of Illinois No. 6 coal used to make the radiographs. Figures 5, 6, 7 , and 8 are radiographs of the bands before and after partial immersion in lead acetate (down to the black pointer) for the times indicated. I n all of these pictures the lefthand exposure was made with bedding planes parallel to the film, the right-hand with bedding planes perpendicular to the film.
Before
After 30 minutes
After 10 minutes
After 60 minutes
FIGURE6. RADIOGRAPHS OF VITRAIN BEFORE AND AFTER IMMERSION IN LEADACETATESOLUTION
PARTIAL
After 10 minutes
Before
FIGURE 7.
After 30 minutes RADIOGRAPHS O F IMMERSION I N
After 60 minutes
DURAINBEFORE AND AFTER LEADACETATESOLUTION
PARTIAL
After 10 minutes
Before
After 60 minutes BEFORE AND AFTER PARTIAL IMMERSION I N LEADACETATE SOLUTION
FIGURE9. RADIOGRAPHS O F i L L I N o I s No. 6 BEFORE PARTIAL IMMERSION IN LEADACETATESOLUTION Water Solution 20-sea. viscosity
-
35-sec. viscosity
Glucose Solutions390-see. viscosity 2950-seo. viscosity
After 30 minutes
FIGURE8. RADIOGRAPHS OF
CLARAIN
FIGURE10. RADIOGRAPHS OF
ILLINOIS N O .
6
C O A L AFTER
H HOUR PARTIAL IMMERSION IN LEADACETATE SOLUTION
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Figure 5 shows fusain. After only 1 minute of immersion the piece absorbed a large quantity of lead acetate and was almost completely saturated at the end of 5 minutes. Figure 6 shows the absorption of vitrain. Some penetration into cracks can be seen after 10 minutes. After 30 and 60 minutes more penetration into cracks is evident as well as a great deal of general darkening. For durain (Figure 7) there is some absorption in cracks but the larger part is in the pores. Certain streaks or layers through the durain seem to be more absorptive than others. I n the radiographs of the piece with the bedding plane parallel to the film, a certain amount of darkening is apparent near the bottom. The radiographs of the durain with planes perpendicular to the film show that this darkening is due to absorption by a section on the right-hand side, which has taken up considerably more than the rest of the piece. Clarain (Figure 8) shows this same type of absorption; that is, certain streaks through the clarain are more absorptive than the rest.
Effect of Viscosity on -4bsorption To obtain evidence of the effect of viscosity of solutions on absorption, four 30 per cent lead acetate solutions were made in which the viscosity was varied by adding glucose. The water solution has a viscosity of approximately 20 Saybolt Universal seconds a t 100" F. The solutions with added glu-
Water Solution [ 20-sec. viscosity
-
35-seo. viscosity
Glucose Solutions 300-see. viscosity 2950-sec. viscosity
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cose had viscosities of 35, 390, and 2950 Saybolt Universal seconds. Figure 9 shows the four pieces of coal used in this study before immersion in the solutions. Figures 10, 11, and 12 show the same specimens after I , 4, and 21 hours of partial immersion. I n each of these figures the top pictures were made with the bedding planes of the coal parallel to the film, the bottom set with the planes perpendicular to the film. These pictures show that the water solution penetrated the coal more rapidly and more completely than the more viscous solutions. The 35-viscosity solution shows as much penetration into cracks as the water solution but not so much into the general body of the pieces. The 390-viscosity solution shows very little penetration above the level of immersion. The 2950-viscosity solution s h o w no penetration above the immersion level after 21 hours.
Literature Cited Ambrose, H. A., and Gaspari, J. R., Power, 81, 378 (1937). Beeching, R., J . Inst. Fuel, 11, 240; 12, 35 (1938). McCabe, L. C., Mech. Eng., 60, 217-21 (1938). Piloher, J. M., and Sherman, R. 9., Bituminous Coal Research, Ino., Tech. R e p t . 6 , 19 (1939). Rees, 0. W., Land, G. W., and Reed, F. H., IND.ENG.CHEY., 33, 416-19 (1941). Wilkins, E. T., J . Inst. Fuel, 10,213 (1937). PRESENTED before t h e Division of Gas a n d Fuel Chemistry a t the 103rd Meeting of the AMERICAN CHEMICAL SOCIETY,Memphis, Tenn.
Water Solution 20-eec. viscosity
Glucose Solutions 35-sec. viscosity 390-see. viscosity 2950-sec. viscosity
I
. .
FIGURE 11. RADIOGRAPHS OF ILLINOIS KO. 6 COALAFTER 4 - H o u ~PARTIAL IMMERSION IN LEADACETATE SOLUTION
FIGURE12. RADIOGRAPHS OF ILLINOIS No. 6 COALAFTER 2l-HOUR
PARTIAL IMMERSION IN LE.4D
ACETATESOLUTION
