August 1949
INDUSTRIAL AND ENGINEERING CHEMISTRY
1749
outer coating is designed t o have greater mechanical strength after burning, so t h a t it will not be so easily blown away by the -_ wind stream. There appear t o be no systematic differences in the results obtained with L 700 the several plasticizers investigated. Afterglow, although a significant property in the still-air burning tests because of reignition, was not important in either the laboratory moving-air or wind-tunnel burning test. However, in the mind-tunnel tests large sections of the aluminized coating on a panel, doped with cellulose acetate butyrate containing aluminum pigment, were ignited I A I I 2 110 15 20 and blown away as a shower of burning O f 1 1 T I M E IN SECONDS particles downstream. This could conceivably constitute a reignition hazard. LTOTAL D E S T R u C T IO N E F F E C T I V E DELAY T I M E ( E O T I Since coating systcms examined in the INITIAL FAILURE IN OUTER COATING wind-tunnel tests were selected from those MAY OCCUR ANYWHERE IN T H I S R A N D E showing up best in the laboratory tests, the differences in fire-retardant effectiveness TO = T E M P E R A T U R E AT OUTER PANEL SURFACE LFIRE H I T S PANEL 7 ; = T E M P E R A T U R E AT I N N E R PANEL SURFACE among the svstems is relatively small. HonTeier, there is no doubt that these coatFigure 6. Typical Time-Temperature Record of a Test Panel during Windings are substantially superior in f i e reTunnel Burning Test tardancy t o a cellulose acetate butyrate system alone. Their superiority over cellulose nitrate systems is marked. Under the conditions of fire, the cellulose acetate butyrate melted before i t ignited. The coating melted also with chlorinated ACKNOWLEDGMENT neoprene systems 5 and 6. The authors wish t o acknowledge the assistance given by P. An almost universal property of the fie-retardant systems was Dier and J. W. McElwain of the National Bureau of Standards the development of blisters by the generation of gases incident t o and the staff of the Fire Test Unit of the Civil Aeronautics Adthe pyrolysis of the fire-retardant materials. The only exception ministration Experimental Station in supplying some of the data was system 11 which did not exhibit the blisters characteristic reported here. of the other systems but seemed t o be one big bubble; zinc borate was the pigment used in this system, which showed the best fireLITERATURE CITED retardant properties of any tested. From the point of view of (1) Kline, G. M., J. Research Natl. Bur. Standards, 14,575 (1935). keeping the coating in place for as long a period as possible, the (2) Ramsbottom, J. E., “Fire Proofing of Fabrics,” p. 24, London, formation of small blisters is better t h p the formation of one His Majesty’s Stationery Office, 1947. (3) Reinhart, F. W., and Kline, G. M., IND. ENG.CHEM.,32, 186 large bubble, which might easily be blown loose by the wind (1940). stream. During the progress of the tests, it became apparent that a n RECEIVED J u n i 16, 1948. Presented before the Division of Paint, Varnish, important limiting factor in protection was the brittleness of the and Plastics Chemistry a t the 113th Meeting of the AMERICAN CEEMICAL burnt out,er coating. Some improvement can be expected if the Chicago, Ill. SOCIETY, F L A M E S H U T OFF A F T E R FABRIC DESTRUCTION
1000
1
-1
Correction Factor for Latent Heat Method f o r Obtaining Haggenmacher Correction Factor without Use of Critical Values R . R. DREISBACH T h e Dow Chemical C o m p a n y , Midland, Mich.
A method has been developed for calculating the Haggenmacher correction factor for latent heats by means of a modified Antoine equation for vapor densities and the law of rectilinear diameters for liquid densities. This method eliminates the necessity of having critical values, and uses instead the boiling point and liquid density. AGGENMACHER (3, 4, 6, 6) has developed a number of formulas from an equation of state for saturated liquids and the Clapeyron-Clausius equation by means of which the latent
heat of vaporization and external work of vaporization can be accurately calculated. The three Haggenmacher equations pertinent to this article are:
RT
AH -AA
=
T,“P
R T a dp ~MP d l d l
= P(V,
-
Vl) =
-
F :-d
1 - TZP __ p,T3
(2) (3)
INDUSTRIAL AND ENGINEERING CHEMISTRY
1750
specific volume of saturated vapor, g./ml. specific,volume of liquid, g./mi. gas constant = 62,3iO ml.-mm./ C. in Equation 1 1.987 cal.-molc/' C. in Equation 2 abtolute temperatuw,
K.
molecular weight saturation pressure,
TABLE
I.
C'O\Il'.kRIsOV
OF
H CALCULATED
tenipernt,ure,
€+I!
ta ne
c.
2.5 30 35.34
Hexant,
25
60 6fi.88
Ileptarie
'30
98
Renzerie
20 40
K.
critical pressure, mm. rate of change of vapor Cblorobcnsonc ~ r e s s u r e with teniperature, mm./' C. latent heat, cal./g. external work of vaporization, m - - l- .- / - ,e . 0
,
T3P ~~~~
1
-
pjj3
,
i
I
9 WITH DETERMIXED T'AL7-F\TALT'ES AN
T%
1'
512.12 614.59 756.52 152.73 572.52 715.62 590.4 750.53
.lllll.
O
B Y b;QCAl'ION
4XD EIAGGENMACHER C.4LCULATED
rn 111
critical
Vol. 41, No. 8
known tis t,he Haggenniacher cor-
rection factor, and d l be represented hereafter by ._
2.4
i,:
H*:
60 80 131 7
'rABLX
75.753 182.93 390.95 757..59 760.0
g'I
AZ, Eq. 7 1.50 0.03241, 0.95662 1 . 6 2 0,04548 0.55093 1 . 6 4 0.03865 0.94408 dt/dp
1-
483.05 407.18 335.15 1383.9 400.71 325.05 364.32 290.83 3078.2 1350.7 663.96 357.70 284.00
1.5 1.60 1.62 1.60 1.62 1.1 1.2 1.2 1.23 1.02
0.16186 0,05261 0.04411 0,05508 0.04563 0,27731 0,13402 0,07079 0,04266 0.04802
11. I~.irraUSED I N
Pentane 6.82858 1050 4 1,17621 981.1 0,64601 -0.000902
liexane 0.93882 1212.5 1 31889 1137.3 0,67764 -0.000884
0.97823 0.94747 0,94031 0.54723 0,93939 1.0016 0.58709 0.97385 0.55754 0.95886
C.4LCULA'I'IXG
I-lcytane 7.04427 1367.4 1.43069 1283.9 0 70063 -0.000832
AH, Detd. 86.80 85.8 85.38 85.9 80.4 81.85 77.8 74.0 103.82 100.71 97.84 94.16 75.9
AH,
Eq. 9 87.14 86.11 84.98 86.12 80.52 79.43 76.19 75.12 104.15 100.47 97.26 94.03 75.99
J'",
'c71,
AND
Benzene 7,01523 1291.4 1,34130 1207.4 0.90043 -0.001054
Haggeliinache!.
87.12 86.13 84.95 87.43 81.46 80.20
77.12 75.75 104.5 100.8 97.26 93.58
dt/dp Chlorobenileiie
7.18492 1 5 % .8 1,57147 1455.8 1.1274 -0.00108
Ab.
Because the value of the expression is dependent on accurate critical data, its useiuliiess is somewhat restricted by the meagerness or lack of accurate critical data. Then too, it is rather cumbersome to calculate the expression. Dreisbach and Spencer (1, 8 ) gave formulas for calculat>ingd t l d p from the boiling point of a compound at two pressures 01' one boiling point if the Cox chart family to which t,he compound belongs is known, and for calculating vapor and liquid densities accurately to well above one atmosphere when the boiling point, molecular weight,, and liquid density X I Y known at two temperatures. These three equations are: dt =
&I
B 2.3026 P ( A - 10gioP)'
log,,cl, = ii" -
viliere
i ~ h e m t sif 1.0 is t,alren as tlic volunic: of liquid, the error is riegiigible. Table I compares the accuracy of this method with that using critical values. Data for latent heat and Haggenmacher's values :ire taken from the lit'erature (3). The compounds used are list,ed by Drcisbach and Spencer (2),as well as the values of A , B, .4*, H", a , and b, and also the vapor and liquid densities where the temperatures are applicable (Table 11). -411alternate equat,ion for latent heat can \re developed frc~riit h e h - o Dreisbach and Spencer arricles ( I , 2 ) : (8)
B*
t + 230
et2
=
2.3026 X 1.987
=
4.57527 (9:
-4, B = constarits of Antoine equation A4*, B* = constants of modified Antoine equ'ation for vapor density constant = intercept of sum of densill- linc :tt 0 " c. b = constant = slope of sum of density line d , = densities of liquid and vapor, respectivrlj, a
dl,
=
Since we are iiow able to calculate the vapor and liquid densities accurately, we have the liquid and vapor volumes which are the reciprocals of the densities. Rearranging Equation 1 givcs
by iiieans of which we can obtain AZ, since the values of all tlw expressions on the right-hand side are known. The temperature, t , corresponding to any pressure, p , or vice versa, is obtained from the Antoine equation, and V , and V I from Equations 5 and 6; hence the values of the critical constants are not necessary. The value of 4 2 from this expression is more accurate since it has none of the errors arising from the deviation from the ideal gas laws but is based on experimental data. At the boiling point Vi varies from approximately 1.2 t o 1.5 nil. per gram for hydrocarbons, depending on the compound; if this value is taken as 1.2, tlierc would be a maximum error of 1.5-1.2/300 or O.l%, sincc V , varies from approximately 300 t o 350 ml.per gram. When the temperature approaches 0' C., V Iis a little more than 1.0 ml. per gram, but V , is around 10,OOO mi. per gram in most cases; therefore, neglecting the liquid density introduces an error of about 0.0170,
~ ~ I i e rBe = constant of Aritoine equation 41 = molecular weight
This gives a slightly different method of evaluating A 2 if t h e value of latent heat is known at temperature t . Equation 9 s h o w that for any Cox chart family a table of numerical values can be set up for, say, every 10" C. and for any pressures desired which will give the uncorrected value of latent heat in calories per inole; when this value is niult'iplied by correction factor AZ, the correct value is obtained. Table I s h o w that the Haggenmacher factor, AZ, as given i i i his work is in close agreement with the value obtained by €!!quation 7 as evidenced by the slight difference in the resulting latent heat values. Equation 3 can be used with the same value of 42 for calculating the work performed in vaporization, and will check the values given by Haggenmacher with the saint accuracy as do the latent heat values shown in Table I. LITERATURE CITED
(1) Dreisbach, R. R.,and Spencer, It. S., IND. ENG.CHEM.,41, I T ( i (1949). (2) I b i d . , 41, 1363 (1949). (3) Haggenmacher, J. E., Ibid.,40,436 (1948). J. Am. Chem. SOC.,66,313 (1944); 68,1123 (4) Haggenmacher, J. E., (1948). (5) Ibid., 68,1633 (1946);Phys. Reu., 69,242 (1946). (6) Haggenmacher, J. E.,J . Am. Chem. Soc.. 69,707 (1947). RECDIVED August 19. 1948.
