Thermal Degradation of Wood and Cellulose

against the heating time for oven heating and heating beneath the surface of a molten metal. Good straight lines are obtained, except near the origin ...
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Thermal Degradation of Wood and Cellulose ALFRED J. STAhI3I Forest P r o d u c t s Laboratory, Forest Serrice, Lr. S. D e p a r t m e n t of Agriculture, M a d i s o n , Wis.

H

C;IT has two effects upon the properties of wood and cellulose-reversible (6,8, 24, 27, 29) and irreversihle. This report deals n ith t h e irreversilrle degradative changes caused by heat. CHEMIC4L CWAYGES

The literature is prolific on the changes t h a t accompany thermal degradation of cellulose. Viqcosity change8 (16,18, 63, e6) have been reported. Chemical interpretations have been made (Q-j, 7 , f3-15, 28). Goos (2)lists 213 compounds t h a t have been identified. Reduction in hl-groscopic and sn~elling characteristics have been reported (20, 22, 26). T h e specific chemical changes that occur during thermal degradation are still obscure. D a t a on decomposition products of Douglas fir san-dust and its components are given in Tables I and 11.

Table I.

Decomposition Products of Extracted Douglas Fir Sawdust

( H e a t e d in a s t r e a m of air a n d of nitrogen a t 3003 C. for 1.5 hours a t a t m o e p h e n c pressure) Decomposition P r o d u c t s n , % Weight" Noncon- Excess O\-W Heated Loss, densable rvight in 70 COZ HzO Tars 7-olatileb loss 2.3 L S.Dt Air 49.0 16.0 39.6 Nitrogen 47.0 7.8 31.1 5.2 2.9 0 a B a i r d o n weight of u n h e a t e d , oven-dry s a w d u s t . b Calc,ilated f r o m difference between original n-eight loss a n d x\-eiglit of other products. C Undeterminable, probably between 0.0 a n d 3.0. ~~

~~~~~

Table TI. Decomposition Products of Extracted Douglas Fir Sawdust and of Its Isolated Components ( H e a t e d in b o t h a n open s p t e m a t atinospher c presci re a n d In a olosed s y s t e m under t h e der eloped p r e m t r e a t 220" C 1 Materials and Heating Conditions Open system Sav.di:st a-Cellnlo-e He~nicell:tlose Lignin Cloqrd -3-itetn

a

Heating Time, Hours

TVeight Lo-d o give the order of magnitude of tiegrdation.

INDUSTRIAL AND ENGINEERING CHEMISTRY

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Vol. 48, No. 3

As these \\.eight losses are accompanied 111- a decrease in volume ( 2 0 ) ; t h e lose in specific gravity is too small t o use as a criterion of the degradation of old timbers due t o weight loss. Figure 5 is a plot 5itnilar t o that of Figure 4 for steamed wood. If the lines were extrapolated to room temperature, tliej- ~vould give ail espcctcd veight low of 5% if the wood m r e subjected to saturated Jvater vapor a t 20" C. for 1 year. This \vi11 be referred t o agxiii later. S o extended data on weight ioss for heating of cotton or paper pulp were found in the literature. D:rta are, however, available for strength loss caused by heating.

THERMAL DEGRADATION OF WOOD i s greater under these conditions

. . . closed system . . . presence of air . . . steaming conditions It is negligible under normal kilndrying conditions

KlYETICS O F STRENGTII LOSS

I

I

The calculated activation energy is about half of the value for t h e heating of wood under dry conditions. The log K value at 150" C. indicates t h a t t h e degradation is much faster under steaming t h a n under d r y heating conditions. Figure 4 gives t h e d a t a of Figures 1 and 2 plotted as the logarithm of the heating time against the heating temperature, extrapolated to room temperature. For each w i g h t loss, a good straight line is ohtained. These lines teiid t o coilverge a t t h e low temperature-long time e a d . This n-ould Ile cspected on t h e basis of t h e Arrhenius equation for a first-order re:iction rate, tlie temperature coefficient of t h e reaction rate t k n g inversply proportional to t h e absolute temperature. I t 100" C. t h e reaction rate for oven heating, as indicated 113' the Tveight loss, doublesfor each 10' C. increase in temperature. At 250" C . , it doubles for each 13" t o 1-1' C. rise in temperature. The ratio of temperatures is practically identic:d with the theoreticnl \-due. I s oven heating and heating beneath tlie surface of n molten metal give almost identical activation energies, their plots in Figure 4 should be parallel and identical hen t h e weight 10s.; due t o heating in an oven is 3.2 timer that for he:lting lrenmth t h e surface of a molten metal. The values plotted Inst ir-lien tlii. multiple \vas 3.3. From Figure 4 it is poi?ible to estimate the tic.gr;id;itio:i of nood in terms of iveight loss a t normal t e n q ~ e r n t u t ~ cover s liralonged periods of time. For esample, drj- \\-ood atol'ed for years a t 20" C. should lose 57, of its weight \vheri air c.ircul:rti= freely around it, but only 1 . 5 % if air circulation is esr~lnrle~l.

for the r a t e Similar lii~icticc:ilculatioiis can he made from of strength 10;s. \Then the logarithm of the residual strength is plotted against thc time, straight lines similar t o those of Figures 1 u ~ 1 t l 2 tire obtained hctivatio:l eiiergies for 110th ovi'n- :tnd steam-heated wootl were calculated from such plots t1ran.n from data of 3Iac1,cmi ( 9 , 1 1 ) for tlie residual modulus of rupture and the re*itlual work t o maximum load (area under the stre curves t o t h e point :it \\-hich ruptur(x occurs in moduius-of-ruy ture me:icurements.). Tahle I11 s1ion.s t h a t the Ltctivation energies so oI)t;iined agree very \vel1 with t h e corre3pontling values calculsted from t h e \\-eight 1 0 s T h e log fY values in Tahle 111 shnw th:i,t t h e rat? of Iws of niodiilw of rupture is ahout I O times thlit for t h e ivright lo.;s under lioth oven-heating and ptenniing conditionz. The rate of loss of ~vorlito maximum lo~tdi? still greater. Figures 1 a n t i 5 iilsu shmv t h e a!)pro\;imately tenfold gtwtter 105s i n Inotluliis of ruprui'c' t h m of \\.eight.

R

' weight LS. time of kigure 2. Logarithrn ~ i residual 16 inch heating of rotar>-cut SitLa sprilce Teneer thick, 5' inches loug, arid 1 inch w i d e (2Z) Open i\ niboli. O I P ~hr,ted Shadrd - \ m i d i , heated beneath surfare of molten metal

Figure 1.

Logarithm of residual weight u s . time of oven heating

0. 1 Arrrage of four Rpecimens each of southern pine, white

A

pine,

Douglas fir. and Sitka spruce 6 inches long i n fiher direction br 1 i n c h by- 1 inch (9-12) Rotary-cut Sitka spruce veneer ' / i s inch thick. 5:,'8 inches long, and 1 i n c h wide (21)

'Thc gr:rpli< she\\- t h a t a loss in modulus of rupture of orlly almut 107@ \rould lie expcctcd in 100 years at 20" C. ivlien air riTcu1:ites frc~e1~:iround the speviniens. Under t h e mnie ?ontlitionp, a l i w in work t o Initsirnun1 lo:d of about 407, ivould he cupccted. In the ?:we of limited access of xir> as would prevail foi, 1:rrgcr tin~l,ers,R 10.3 of only 37@in modulus of rupture and 12% in ~ v o r l to i maximum load ~vouldhe espected i n 100 yc'ar.*. t7ritler s:ituratecl atmoqjhere cnnditions, however, :I 10- of about -iOyoin niodulu. of rupture and 807, in v-ork t o m:i\;iiiium load v-oultl l w e\;;m:ted in 1 yrar nt 20" C. from a n extr:ipolation of the data of Figure 5. Extrqjolation of t h r logaritlinl of time-tem!)erature gI':iphs to room tcinperaturc giver re:rsi~iial~le \$-eight and strength loss values for dry wood (Figure 4). The values are excessively high, however, for steamed wood. It i i olrvious that suvh strength losses do not occur in t h e henrtn-oo(1 ( t h r dcntl p a r t ) of growing

INDUSTRIAL AND ENGINEERING CHEMISTRY

March 1356

415

Table 111. Activation Energies of Food and Cellulose Calculated f r o m Thermal Degradation Data Macerial Coniferous \vootl S o u t h e r n a n d white pine, S i t k a suruL'e a n d D o u g l a s fir sticks a n d S i t k a s p r u c e ycncci S i t k a spruce \-enerr S i t k a spruce sticks Llouglas fir sarrdiiat a-Ce!lulose froin Douglas fir Hemicellulose froin Douglas f i t Lignin froni Doiigias fir T i r e cord Cotton Kavm Papei

l00Vc rag 50% rag, 50'6 sulfite 30Ye r a g , 707, sulfite 100% yulfite Coniferous wood Sourliern a n d w h i t e pine. S i t k a s p r u c e , Douglas fir sticks S i t k a a p r u r e stick4

Heating C'oiiditiun

Property Lois .\Iensured

Ox-en Under iiioiten iiietal Oven Oven Oven Oven Oren Oren

ITeight \VeigIit Alodulus of r u p t u r e K o r k to mas. load Weight rTeiplit Weight ti-eight

Oven. 40Fe r e l a t i r e

Breakine s t r e n g t ! ~ Breaking s t r a n g t o

Iluinidlt)

Oren Oven Oren Oven

Folding Folding Folding I'olding

Temp.R:~nge,

Time Range

c.

120-1000 h r . tiO-lt,OO tir.

110 110

72-8(30 hr. 72-800 111. i2-EM0 h r . 72-8ii0 tir.

60

tin

ii0 ti0

K

Log

at

130' C.,

Hours

-3.9

93,5-250 I C 7 -300 102 -177 10% -177 110 -220 110 -220 110 -220 110 -220

1 hr.-2 4 yr. 1 niin.--C d a y s 1 lir.-188 d a y s 1 t ~ r , - 1 8 8d a y s Iti hr.-O4 days lti 1x-N days 7 lir.--64 days l i i iir.-04 days

endurance endurance endurance endurance

Activation Energy, Cal. /.\lolt*

-4.4

-2

Y -2 3 -4.0 -4.1 -3 4 -4.3

~I.N -ix

30,500 29.500

-2 3 -2.2

-120 -120 --120 -120

19,100 19,300 19,900 19,700

-1 2 -1.0 -0 8 0 -2

a1ii1

O w n . 95% absulute iiiimidity

FTeight Alodrilus of r u p t ) l r e rr0l.k t o I I I a Y . lodd

1-200 ill.. 1-32 h r . 1-32 lir.

121 -177 121 -177 121 -177

13,800 ifi.300 17,300

Breaking btrengtii Breakina strengtii

1 3-0 IF. 1 Iir.

-130

I03 -15Cl

13.300 ld,900

trees, Tr-here the moisture content may exceed the fiber saturation point for hundreds of years. Piling immersed in rvater has a h retained sufficieiit strength t o be serviceable for periods up t o 50 years. It thus appears unsafe to extrapolate the st,eaming d a t a to room temperature, as was done for heating under dry conditions. This is not surprising. as the concerit,ration of water vapor present drops off very rapidly with a decrease in temperature. Temperature \\-ould t h u s not orily affect the reaction rate in the normal \\-a?-, but also the Trapor concentration. T h e degradative effect due to kiln drying of softwoods can be estimated by considering the drying conditions t o be made up of a wet period a n d a dry period. Of course, in reality there is a gradual trariPition from one t o the other. For example, consider a kiln load of a softivood 1ie:ited for 2 dn t 160' F. ( 7 1 , l ' C.) and ,?I days a t 200" F. (93.3" C.) and the wood i3 verJwet lor oiil:- the fir>t 2 days. The loss in niodulus of rupture occurring during t h e 2 days while free moisture is still present would be only a h o u t 2.57, a n d t h e loss in work t o maximum load would be about 5%, even on the basis of the simple extrapolation of the d a t a of Figure 5 which has been shon-n t o give high values. T h e loss during t h e 5-day period wlipre the moisture content is lolv would be about 0.5% for t,he modulus of rupture and 2.0'3, for the work to maximum load. Hardlyoods (broad-leaf species) are dried at lon-er tempwatures but for longer periods of time to avoid mechanical degradatioii. A tj-pica1 long schedule niight be 5 days a t 130' F. (54.4"C.) for the first wet period and 20 d n ! ~;it 160" F. (71.1' C.)Cor the dry period. If for the nionient the thermul degr:idution of hardwoods is assuiiied t o be the s:riiic ;IF for soft\vood*, tl1e.i the 10s:. of modulus of rupture during the wet period uiidcr the most eevere direct extrapolntion conditions would be 2.5% :iiitl the loss in n-orli t o maximuni load n-ould be 5.0%. During the dry period the loss in modulus of rupture would be oiily 0.1% a n d i n the work to rnn\-iniiirn load, 0.47,. Hartln-ooils! hon-ever, pliol\- a greater thernial degradation t h a n softvoods, presumably because of the higher hemicellulose arid lorr-er lignin contents due to the fact that greater aniouiits of' 1. The values should not he more th:iii if tlic d u e s are doubled, t h e y would not I w scriouFlj- high. Cowad. Tripp, a n d Trinidad ( I ) give d a t a for the loss iii breaking sti,ength of lioth cotton and raj-on tire cord t h a t o c c u ~ upon ove:i heating a t 40% relative humidity. Table I11 shows t h a t the nctixxtion energies aiid the log K values are very similar. Wiegerinli ( 2 0 ) give3 d a t a for t h c thermal degradation of various yarns n-hcn heated a t high, low, a n d intermediate abso-

103

7

- 1 . 7.; -1.45

- 1 4,i

-1.20

lute humidities. He unfortunately carried the degradation sufficiently far t o calculate activation energies with a n y degree of a c c u r a c j ~only in the case oi heating a t high ahsolute humidities. V:ilues calculated from these d a t a for a ',purified" cotton and a viscose rayon are given in Talile 111. T h e vnlues are similar to those for rvood heated in steam, and the. log K values a t 150' C. are :iho in re:isonably good agreement with the values for wood dptrrrnincd from streiigth test d a t a .

ii

Figure 3. R 0.0 A 0

A,A

i

-&?J

Keciprocal of absolute temperature logarithm of h-

1's.

Slone of straipht line, of Fizures 1 and 2 mer unit of t i m e in hbur. I

Heated in oven IIeated heneath surface of mnlten metal (9-12) (21)

Rasch ( 1 7 ) give. d:tta for the lo;. i n fo1di:ig eiitlrir:iiicc, of paper made from lO07, rag a n d 1007, sulfite pulp :iiid Iiiixturw thereof n-hen heated in an oven for 72 hours :it four diifcrciit temperatures. -1ctivation energies v e r e cnlculnteti from 1ine:ii. 1)lots of the logarithm of t h e residud folding endurance plotted through the single time point and the origin. T h e values are given':in Table 111. .ictivation energies for the four papers are practically t h e same, but the log K values a t 150" C!. iricreaw i i i going from 100% rag paper to 100% sulfite piiper; intiic:iting t h i t the 5ulfite paper is about 12.5 tinies more seiiFitive t o heat dt~glntl;itionthan t h e paper made from rag ptock.

INDUSTRIAL AND ENGINEERING CHEMISTRY

416

Figure 4.

Logarith~nof heating time

LS.

Vol. 48, No. 3

temperature to attain various degrees of degradation of wood

Open s ~ n i h o l s , l i e a t i n n i ~ ~ o v e r ~ S h ~ d e ds ) m b o l s , heating bcncath surface of m o l t e n metal 0 Weiqht loss (Y-ZZ) A Weight losk ( 2 1 ) \Ioriulus of rupture 10.5 (9-12) 3.0parentheses. weight Iocs on oven h e a t i n g Dotlble parentheses, weight loss o n heating beneath surfare of mol t e n metal Single parentheses, modulus of r i i p t u r e loss on w e n heating

A,

times :I.- ~ L L S:IS T the wood jtaejf m ~ 1 Lu-cellulose isol:it*d from the I.'igwe 6 gives t h e d a t a of I1 h (171 p1ottc.d ns the log ot' titile wood. 1sol:itccl lignin, on t h e other hnnci, degrades only haif a8 rent l o w s in folding eliduraiice ngaiiist t h e temperature for d fnst as the ivuod. extrapolated to room temperature. Iiichter ( 1 9 ) determined t h e .\ctivatioi; eiicrgic~scnlculntecl froin n-eiglit Iov and strength loss iii folding enduiaiice of similar r a g paper a t 38" and 100 These values are also plottpd in Figure G . T h e ohserveti lo in folding endurance are very cloye to the v:ilues pretlictctl I,;e straight lines. It t h u s appe the 1o.s of folding entlnrarice with time nt m o m tci~ipcr:it w w -1 I.. Such it plot \rould iic needril for cnch ty1)c ( i f pul,itJ- of 1 ~ ~ 1 1 e r . In t h e case of this I):irticular p~%p('r.i t ~ o u l i ll i e r.xpcc,:c:cl to lose 24'3, of its folding endurance on storing n.ilh free nc. dry air a t 20" C. f o r 1.1J-ears. Degradation due t o stowge i n large roll.; sliould, of course, t i e appreciahly lew. COSCLUSIONS

Thermal degrsdntion of wood is greater i n the preeericc of air t h a n in its a l m n c e , because of oxidation b y atmoyiheric. o. It ie greaicr in a closed system, where acids formed bu in coiiceiitr:itio!i a n d hence can catalyze hydro t o a system :.:here the volatile products c:in esc enter. Thermal degradation for all t h e materials twteti iollo order renction. Thermal degradation is greater under steamiug than uiider dry heating eo!iditions. T h e activation energies for the tlegrarlation reactions arc about half as large as under dry heating co:iditions. T h e activatioii e,icrgies for t h e thermal degrad:ition of d r y wood are qimilar t o t h e values for t h e major cornpoileiits of wood. Hemicellulo~cfrom Dougla. fir, hon-ever, degrades :ihout four

;

-- ,=--PA--

;

"-)

Figure 5 . 1,ogarithnl of heating time in steam US. ternpeiature t o attain of \ nrious w*oocl degrees of degradation

0 C

Datn of \ I a c L e a n for 1054 of weight of softwood specimen8 .ilrnller t o thaw ' b f Figure 1 D a t a of R l a r L r u n for loss of modulus of rupture of Sltku spruce Eperirncnz birnilar to those of r l g u r e 1 ? o pTrcntllesec, r ~ i q h 1t 0 9 4

Parentheses. moduluq of rupture loss

March 1956

INDUSTRIAL AND ENGINEERING CHEMISTRY

417

loss d a t a are similar. Gnder both dry heating and steaniing conditions: the loss in modulu8 of rupture is shout 10 times t h e loss in weight, and the loss in work to masimum ioad is still greater. Plots of the logarithm of the heating time against the heating temperature t o attain different degrees of degradation under dry heating coiiditions when extrapolated t o room temperature give a n idea of the rate of natural degH€A TI/IG TEMPERATU,?€ {OC I radation of dry wood. OnljF i g u r e 6. L o g a r i t h m of heatiug time in o v e n c s . t e m p e r a t u r e to a t t a i n v a r i o u s losscs the work to maximum load in f o l d i n g e n d u r a n c e of 100% rag paper for softwoods is sufficiently 0 Data of Rasch affected t o be readily detected @ Data of Richter after 100 - e n r s ' storage a t room temperature under dry condihy 13. P.Walton, ~'01.I, Cheinic,:il C'aralog Co., S e w York. tion?. This extrapolation procedure cannot be applied to wood 1928. eyposed t o a moisture-saturated atmosphere. Pictet. -I., Sarasin. J..I l e l i , . Chinr. d c t a 1, 87 (1018). T h e t h e r i n d degradation of r o o d under normal liiln-drying Rice. E., J . SOC.Duers Colozcrists 65, 56 (1949). conditions is fortunately negligible. 11, R. €I., Lr. S.Bur. S'tandards J . Research 7 , 405 (1931 Rich, E. D., Pai-ier Trade J. 112 ( 6 ) , 35 (1941). Richter, G. .I ISD. ., Eiw. CHEM.26, I154 (1934). LITF;R 171.R E CITED S < ~ l i o r gR , . AI., Tarkow, H., Stamin, .\, J.. J . FoTest Produitc Conrn,-l. C. AI., T i i p p , T7. IT., Trinidad. 31.. Te+:z'Ze R e s e a x h Research Soc. 3 (a), 59 (1953). J . 21, 726. 841 (1951" Ftxiiiii, -1.J., Burr, €I. K . , Kline, .-I. .I.,I v n . EYG.C H E W Gms, -4.TT,, "Wood Chemistry," ed. by L.E. Kise and E. C. 38, 780 (1946). Jahn, vol. 11. pp. 345. S 3 0 . Reinhold, Ken- York, 1952. ~ T ~ i l l 1 1 1. , LJ., IIansen. L. A , , Ibid., 29, 831 (19371. EIawley, L. F., ITarris. E. E . , I z n . Esc. CHEM. 24, 573 S:nnim. .1.J., Harris, E. E., "Chemical Processi1.g of Wood," (1932). p . 346,Chein. Pub. Co.. S e w York, 1953. Hawley, L. F., Kiertelak, J., I t i d . , 23, 184 (1931). Stainm, A. J., J.ouphhorough, W. K., J . P h g s . Chern. 39, 121 Heuser, E., and Scherer, .1.,Brermsto$-Chem. 4, 97 (19231. (1934). Houtz, C. C., hIcLean. D. .I,, J . Piiys. Chem. 43, 309 Staudinger, II., Reinecke, F., Jlelliaiid Terctiiber. 20 ( 2 ) , 109 11 cl.?R\. \_._.,. (1939). IIurd, C. D., "Pyrolysis of Carbon Compounds." C'lieiiiical ?'arkow, H., Gtsmni, -1.J., J . Forest Products Research & r . Catalog Co.. S e w York. 1929. 3 ( 2 ) , 33 (1953). Kollmann, F., Forschungsheff 403B(ll). 1 (1940). Urquhart, A. R . , Williams, -4. 31.. J . T e z f i i e Inst. 15, T559 MacLean, J. D., Forest Product? Laboratory Rept. R1471 (1924). (1945). Venn, H. J. P.. I L i d . 15, T414 (1924). lIacLean, J. D., Proc. Am. Wood-Pveserwrs Assoc. 47, I55 Kiegerink, J . G., Tercfile Research J . 10, 357, 493 (1940). (19.51). Ibid., 49, 88 (19531

Ibid.,50 (1954). Mitchell, R. L., Seborg, R . AI.. Nillett, 31. A , , J. Forest Products Research SOC.3 (4), 38 (1953). Pictet, A,, "Cornprchensive S u r r e y of Starch Cheniistry," ed.

RCCEIT-ED for review June 10, 1956. .ICCEPTED October 17, 1 D 3 i . Division of Cellulose Chemistry, Syrnposiuni on Degradation of Cellulose a n d Cellulose Derivatives, 127th Meeting, ACY, Cincinnati, Ohio, 1IarrIt.Ipril 1955.

Correction I n the article entitled, "Densities of Ternary System Kitric Acid-Dinitrogen Tetroxide-Kater" [Robert W. Sprague and Ethel Ilaufman, ISD. ESG. CHEx 47,158 (1955)], the values of calculated density and error in Table I (page 180)for white acids correspond t o t h e following third-order expression for C Y : a =

1-0.23313

+ 2.94588 R

- 21.06723 R1

Table I . Error Table for C a l c u l a t e d V a l u e s of D e n s i t y a t 35" C. of White A c i d s , No D i n i t r o g e n T e t r o x i d e Density

76 H20

4

+ 78.76376 R 3 ]0

4 fj

Corrected Table I, corresponding to the second-order expression for c y , is presented herewith. Author's Note: T h e interpolation formula presented in the paper has been found awkward to use and, in addition, the interpolated value depends on the interval po - p1 chosen. X simpler method (and possibly a more accurate method) is to use a correction for t h e density calculated from the general equation in t h e region of interpolation (less than 4.57, ?rT20a); t h e correction is obtained by assuming the error to vary linearly along a line of constant water from zero a t 4.5y0Nz04 t o t h e value shon-n in Table I above a t 0% X204. For example, a t 35" C. for the composition ly0 hT2O,,15% H I O , 95% HSOa the calculated density

8 10

12 14 16 18 20

Calculated

Observed

Error

1 ,4830

1.4830 1.4729 1.4679 1.4641 1 4599

0.00 0.0035 0.0020 - 0.0008

1,4764 1.4699 1.4633 1.1668 1 ,4503 1.4437 1,4372 1.4306 1.4241 1,4175

1.4%2 1.4502 1.4480 1.4397 1,4337 1,426'8

-0,0031 -0.0049 -0.0065 -0.0078 -0.0091 - 0.0096

- 0.0093

~~~~~

is 1.4753; the error from the above Table I is 0.002; the correc45 - 1 tion is (-0.002) = -0,00155; then the corrected

(+)

density is 1.4738. ROBERTW.SPR.AGL-E