IA'DUSTRIAL AND ENGINEERING CHEMISTRY
1246
Groups of such lamps can now profitably replace sun exposure of patent leather, making this process independent of the variations of the weather. Some mineral waters are about to be sterilized by exposure in thin films to this light. Accelerated tests are now made more rapidly than before because of the greater intensity of these long burning lamps. Sometimes a material catalyst will supplement the radiation, giving yields and products hitherto unknown, as demonstrated recently by Gardner in his researches on the solidifying of drying oils. Such researches now make possible a new
Vol. 22, No. 11
quick method of scrim oil manufacture. The dehydration of animal and vegetable food products in the presence of bright sunlight to prevent mold and bacteria growth is now commonly dependent on the weather. The artificial sunshine now makes possible continuous operation of this dehydration. A great number of reactions a t present known only as laboratory curiosities no doubt will eventually become industrial processes with this development of more powerful and convenient light sources.
Thermal Conductivity of Liquids' J. F. Downie SmithZ E S G I N E E R I I G SCHOOL, H A R V A R D U N I V E R S I T Y , C A M B R I D G E , XIASS
H E thermal c o n d u c tivity of liquids is a subject on which virtually no theoretical work has been done. Weber (3) derived an empirical expression for thermal conductivity,
The thermal conductivities of several liquids, many of which are new, are tabulated. A general equation is proposed for the thermal conductivity of all non-metallic liquids at 30" C. and atmospheric pressure. This equation is: kzO.12 - - - 8.1 X 10+ (pCXM'!6)1'15
Lees used a modification of his method for solid nonc o n d u c t o r s . A correction has to be made for the heat conducted through the walls of the containing vessel. p CQ.4 Goldschmitt used a modiUnfortunately, this equation does not give the temf i c a t i o n of t h e h o t - w i r e perature coefficient. method of S c h e i e r m a c h e r . k = 0.00359 Cp ?! x 3 A graph is included which may be used instead of the The liquid is contained in a where m = molecularweight of equation to determine conductivities. small-diameter tube with the liquid heated wire in the center. C = specific heat p = specific gravity Callendar measured the heat carried away by a current of liquid flowing through an electrically heated tube. This equation is satisfactory for some liquids, but for others Bridgman used two concentric cylinders with the liquid it does not give accurate results. For water the agreement contained between them, heated a t the center of the apparatus with observation is closer than 5 per cent. For some liquids by an electrically heated high-resistance wire. the agreement is not so close. It is this last method which was used by the author in his Bridgman (1) suggests as a formula for the approximate determinations. Indeed, the copper-cylinder assembly which determination of thermal conductivity of electrically non- was made by Bridgman in 1923 was kindly loaned by him to conducting liquids the author. This saved considerable time, for great skill was required in the fashioning of this very delicate piece of equip k = 2ao/d2 ment. where a = gas constant = 2.02 X D = velocity of sound in liquid d = mean distance of separation of centers of molecules, Apparatus assuming an arrangement which is cubical on the . average, and calculating d by the formula d = Two copper cylinders, A and B , Figure 1, are assembled ( M / p ) 1 I 3 where , M is the absolute weight in grams concentrically. The outside diameter of the inner cylinder, of one molecule of liquid A , is "8 inch (9.5 mm.) and the inside diameter of the outer rllthough this formula is interesting from a theoretical cylinder is 13/32 inch (10.3 mm.), so that there is an annular standpoint, it does not help much if we need an accurate space 1/e4 inch (0.4 mm.) wide between the two cylinders. value for thermal conductivity, for in some cases the values This annular space contains the liquid to be tested. Heat is supplied to the inner cylinder, A , by passing a current of obtained are more than 30 per cent off. These two formulas seem to be the only ones for the deter- electricity through a high-resistance wire, H , in the center of the cylinder. A number of flat copper strips, C, ensure good mination of thermal conductivity of liquids in general. Experimentally not much work has been done in this field thermal contact between cylinder B and the thick cylinder, either. A few of the investigators are Milner and Chattock, X . The heat from the wire H passes radially through cylH. F. Weber, Jakob, Chree, Wachmuth, Lees, R. Weber, Gold- inder A , the annular layer of liquid D, cylinder B , the copper strips C, the steel cylinder, XI and out to the oil bath, which schmitt, Graetz, Winkelman, Callendar, and Bridgman R. Weber supplied heat to the top of a column of liquid from is stirred rapidly and kept a t a fairly constant temperature by a vessel kept a t a certain temperature by oil which was elec- thermostatic control. The temperature difference of the cylinders A and B is trically heated, while the bottom of the column was cooled by a horizontal copper plate standing in ice. The tempera- determined by three thermocouples T (only one shown). It is ture difference was taken a t two points 1 cm. apart by copper- assumed that the temperature of the copper cylinder A at constantan thermocouples. The heating from the top was the diameter of the inner thermocouple junction ring is the same as that a t the inner face of the liquid; and that the done to avoid convection currents. temperature of the other cylinder, B , a t the diameter of the 1 Received August 8, 1930. outer thermocouple junction ring is the same 8s that at the 2 National Research Fellow, Harvard University Engineering School.
T
I N D USTRIBL AND ENGi 'NEERINC CHEMISTRY
November, 1930
outer face of the liquid. This is a very close approximation, owing to the very high thermal conductivity of the copper relative to the liquid. The thermocouples were made of copper-constantan and were of such a length that when they were inserted in the cylinders the junctions came half-way down the cylinder. This avoided end effects as far as possible. T h e t h e r m o s/c.mo.%icouples were made of three pieces of wire, the central part being constantan and the others copper. T h e y were butt silver soldered together, and twclve c o a t s of i n s u l a t i n g enamel were baked on at 210" C. in an electric furnace. The wire was 0.006 inch (0.1524 mm.) in diameter. The three thermoconples at 120-degree i n t e r v a l s were connected in parallel so that a mean temperaturc could he obtained, since the resistances of the three were nearly alike. *i_ R.iul~uru iru Thefirst heatingwire *-*""-c--was made of chromel, a b-. high-resistance a l l o y . Figure l-Copper Cylinder Assembly and was0.005inc. (0.127 Three-Hole PIUS mm.) in diameter and was double silk covered. Five coats of insulating enamel were baked on at 210" C. in an electric furnace. This wire, however, gave trouble by breaking away from the soft solder which fastened i t in place, so finally manganin wire was used. The same procedure was employed with this wire as with the chrome1 and it gave no trouble. A thin strip of copper connected the wire to the copper lead, J . The strip was insulated from the cylinder A by means of a thin mica washer. This copper strip and the two thermocouple connections were soldered to three No. 18gage copper wires which passed through glass tubes to tho instruments. Leakage of oil into t,he system was prevented by the rubber washers Tli. The brass tube F was used for filling and for taking care of the thermal expansion and evaporation of the liquid under test. All joints here were soft soldered. The apparatus was filled under vacuum. The heating current entered through the wire J , passed in succession through H , through a German silver strip a t the top to B, then to F, and out to the return lead. This heating current could he reversed in direction. The couDer .. cvlinder assemblv is shown in Fignres 2 and 3. To measure the heat inuut to the heatinmvire a uotentiometer and milliammeter were used. The milliammeter determined the current flowing and the potentiometer gave the voltage drop from the junction of M and J to the cylinder F. It was assumed that this voltage drop was equal to the voltage drop across the high-resistance wire. A simple calculation will show that the error in this assumption is less than 0.1 per cent. The circuit for measuring the heating current consisted merely of the heating wire, a variable resistance, a milliammeter, and a storage battery in series. The milliammeter had a guaranteed accuracy of 0.25 per cent of full range value at any point on the scale, and had two ranges, from 0 to 500 milliamperes and from 0 to 100 milliamperes.
-
lYW".*
1247
To measure the voltagc drop across the heating wire II Leeds and Northrnp type K potentiometer was used. To determine the e. m. f . of the thermocouples the following scheme was suggested hy Im Behr, of the keds and Northrup Company, and it was incorporated in the set-up shown in Figure 4. A 2-volt storage battery supplies current to a resistance R. Tappcd across this resistance are two wires, UT,and W?. This circuit is completed by resistances of 9999 ohms and 1ohm in series. The total voltage drop across the 10,000ohms is given by a millivoltmeter with a guaranteed accuracy of 0.25 per cent of the full range value at any point on t.he scale. This voltage, divided by 10,000 gives the voltage drop across the 1-ohm coil. Across the extremities of this standard coil are tapped two wires, L, and L$,which form part of a circuit including a galvanometer, high protective resistance, key, reversing switch, and thermocouples. By suitably varying R until the galvanometer shows no deflection when the key is pressed, the e. m. f. of the thermocouples, multiplied by 10,000, can he read directly on the millivol& meter, which has two ranges, from 0 to 500 and from 0 to 100 millivolts. There are reversing svitches in each circuit to allow for changing the direction of flow of current, and thus balancing thermal effects. The l n h m resistance was made of manganin and checked to considerably better than 0.1 per cent against a standard resistance. In order to avoid thermal effects around this resistance, it was placed in a wooden box and completely covered np, the cracks being filled with beeswax. The two resistances and rcv e r s i n g switch for millivoltmeter xerc t h e n placed in a larger wooden liox with a hinged glass top, to prevent tliermal cffects ( h e to air currents in blhe room. T h e constantteniperature hatli ( F i g u r e 5) w a s heated hy gas unt,il the temperature of t.hc oil was nearly t h a t a t which the test was to be made. The gas was then turned off and the r e m a i n d e r of the h e a t i n g was done by electricity. At 30" C. the electrical heater was merely a 150-watt lamp, but at 75" and 100" C. a 660-watt heater had t o be used. This hid1 c u r r e n t prohibitled the Figure 2 -Copper Cylinder Assembly of an open mercury xelay o%ng to thld danger of fire from the large spark and also to corrosion of the mercury. The very small current necessary to prevent sparking at the thermostat control, which was of the ordinary mercury-in-glass type, would not actuate the armature of the main relay, so that the current was built up from 0.02 ampere in the thermostat circuit to about 0.1 ampere in the secondary circuit of an intermediate relay, which in turn was the primary circuit of a contactor fully submerged in transformer oil. This con-
1248
INDUSTRIAL AND ENCIZVEERINCCHEMISTRY
tactor was of the normally closed type, and actuated the 660-watt heater. Method ofTesting
The oil in the constant-temperature bath was brought up to the temperature a t which the test was to be made. The annular space between the copper cylinders was filled with the liquid whose conductivity was to be determined. This had to be done under >'acuum. The thermoeouples and heating wire were soldered tothewiresinthe thrcc-hole plug. This equipment was placed in the large steal cylinder and the nut on the three-hole plug screwed rip tightly against the rubber washers. The whole thing was then immersed in tlie eoostant-temperature bat,h and connections to tlie e l e c t r i c a l circ u i t s were m a d e . Figure 3--Copper Cylinder Assembly After eqoilillrium had Showing Thermocouples b e e n r e a c h e d . the heating currcnt was turned on. The heating current was usually in t.he region of 200 to 450 millianiperes. Wheii equilibrium had again been reached, positive and negative values of thermocouple e. m. E. and potential drop through the heating wire were taken for both positive and negative directions of the heating current. I n general, a total of twelve readings was taken for thermocouple e. m. f. (six positive and six negative, or three positive and three negative for the positive direction of the heating current and t.he same for tlie negative direction). Six readings of current and six of potential drop through the heating wire were taken generally. The niagnitirde of T*LS*OC(I"PLCI tho thermocouple e. m. f. was about 22 microvolts, g i v i n g a temperature difference between the copper cylinders around 0.55"C. This small temperature difference, as pointed out by Rridgnan, helps to keep down convect.ion currents. An arithmetic mean of each s e t of readings was taken for t,he 5io-r B*rrss final substitution i n the Figure 4-Set-Up for Measurine Thermocouple 8. M. F. formula ~~~
(e,- e,) was obtained from the calibration curve for the thermocouples. This calibration was performed on contiguous lengths of wire cut from the same spools from which the thermocouples were made. Corrections
The corrections for this equipment were easily obtainable. The only one which it was considered necessary to include in
Vol. 22, No. 11
the calculations was the change of thermoelectric power of the couples with temperature. According to the calibration curve, it appears that dE/dT is a linear function of the temperature, and is represented by the formula: dE/dT = (39.43 - 0.07341) X 10-6vvoltpei " C. where t = temperature, in C .
Thus dE/dT at 30" C. = 41.63 x 10-6; a t 75' C. 44.94 X 1 0 ~ . - 6 ;and at 100" C. 46.77 X 10-6 volt per degree. The change in resistance of the heating wire with temperatures does not appear as a correction term, for the voltage drop across tlie heating wire and the current flowing through it arc measured at eaeli t.emperature. Thus the change in resistance with temperature is automatically taken care of in the readings. There is a very slight leakage of heat across the air from the inner to the outer copper cylinder. This was assumed to be negligible. Another correction w-hich should be applied was pointed out by Bridgman-that is, the effect of heat transfer by radiation thronglii the liquid froin one cylinder to the other. Assuming that the walls radiate as a black body, and considering that the radiation from each wall is like that from an infinite plane, J3ridgman calculated that the ratio of the heat radiated per unit time from unit area of the inner wall to the heat conducted from one wall to the other through the liquid is less than 2 per cent for the case of methanol. IIe points out that the error is probably much smaller tlian this, and owing to the uncertainty he applied no correction. I n this paper no correction i s made, for the same reason. There is a small leakage of heat from inner to outer cylinders through the German silver at tlie two ends. This German silver was 0.002 inch (0.0508 mm.) thick, and on account of it.s poor thermal conductivity the heat leak was small. It %'as further reduced by increasing the inside diameter of the outer cylinder for a short distance a t each end. This reduced the heat transfer through the liquid at these paink. By so choosing the dimensions of the apparatus one effect could be made to compensate tlie other for the mean of tho liquids used. Since the thermal conductivities Bridgman obtained and those obtained by the author are of the same general order, the same construction could be used. Variations Due to Temperature
The results are tabulated as thermal conductivities at 30" and 75' C. for standardizing liquids and a t 30", 75", and 100" C. for the oils. Owing to the low boiling point of ethyl
alcohol, this substance was not tested at 75" C. At 30" C. readings were always steady, but as the temperature was raised they began to devidte slightly from the mean reading for the particular direction of the heating current. It seems probable that this is due to the decreased viscosity a t the higher temperatures, causing an increased tendency to have convection currents in the liquid film, small though it is. Furthermore, at 30" C. it was easy to regulate the teniperatiire of the oil batli to 0.1' C., but at 75" and 100" C. this was not obtainable owing to the lag in time necessary to affect the mercury in the Pyrex thermostat. This variation affects the readings slight.ly, and i t was noticed that the readings taken while the bath was heating were different from those made while it was cooling. The effect was small, however, and the mean cannot he far wrong. Results As stated before, this copper-cylinder assembly was used by Rridgman in his investigations of thermal conductivity in 1923. Unfortunately, however, he had no note of the accurat,e dimensions of the two radii of the liquid cylinder, so
INDUSTRIAL A N D ENGINEERING CHEMISTRY
Sovemher, 1930
that i t was impossible for the present writer to determine ahsolute thermal conductivities. Nevertheless, if it can he assumed that the thermal conductivity of some substance is so accurately determined that it can be used for calibration of the equipment, then absolute values for other liquids can he determined. The liquids used for calibration were tolu-
Figure S ~ C ~ n s f ~ n f - T e mBath, ~ e ~ Showing ~ f ~ ~ eThermostats. Relays, Efc.
enc, ethyl alcohol, isoamyl alcohol, and distilled water. It can be seen from Table I that the closeness of the agreement with other observers warrant~sthe use of this method of get,ting absolute values. wld8, Comparison of Results Iff. and Aufhor ~. T~~YM CONDUCTIVITY, AL k (C.G S . Uhms) smith
0
Bthyl alcohol, absolute Ethyl rlcohol, 99.8% Ethyl alcohol, 95% Distilled water niuene
Isoamyl slcohol Rabbeth spindle oil"
30 30
30
75 30 75 30
76 30 75 30 75
." .. a
Goldschmitt
c.
100
VeloFile B (ancient saniplel~
Bridgman
0.~0430 0.~0436 0.040435 0.000460 0.04144 0.W144 0.00157 0.00148 0.00164 o . 0 ~ 0 ~ 6 70.00~1864 0.000333 0.00033S 0.000339 0.Ol1030" 0.000364 0.000338 0.000348 0 . 000341 0.00033s 0.000333 0.000341 0.000338 0.000381 0.000337 0.000336 0.000329 0.000316 0.000312 0.000809
1249
The first assumution. of course. is not justified. and is merely made to show the effect of an impuriiy such as water. I n zeneral. however. it is exuected that the effect of imnurities in fiquids will not be so gre& as in the case of water and alcohol, because the conductivity of water is exceptionally high. Bridgman went to extremes in obtaining pure liquids. The liquids used here, however, for calibration purposes, were distilled water, 99.8 per cent pure ethyl alcohol, and toluene and isoamyl alcohol of unknown purity. Since the last two liquids were merely used as additional check points, and water and ethyl alcohol were taken as standard, the purity of the t.oluene and isoamyl alcohol is not highly important. Nevertheless, the results obtained for these two substances are quite close to those obtained by others. These liquids were all run twice, to sce if the results were reprodneihle; and it v a s found that they were. The one exception was water a t 75" C. At this point the thermal rondnctivity varied from 0.00148 to 0.00154, with several values in between, for water was run six times on account of several minor trouhles developing in the equipment when water was used. (At 30" C. the variation was small.) After all t.he trooblcs were eliminated, the value obtained was 0.001'18, and this is the value which has been written down for 7 5 O C., althongh it is realized that it may be low. The difficultyin testing water lay in the fact that, for the set-up used, 0.1 microvolt error in thermocouple e.m.f. made a difference of 1 per cent in thermal condnctivityfor water. This was not so for other liquids of lower conductiviby where thc temperature difference of the thermocouple junctions would hc greater. It shonld be pointed out. that a difference of 0.0003 inch in the size of the outside diameter of the liquid cylinder (provided that the inner diameter reniains constant) makes a difference of 1.0 per cent in thermal conductivity. 'It, seems probable. therefore. that t,licre mav be a considerable error in values if we do not know the exact sizes. Since, however, the azreement with other observers for the standardizinp liquids is very good when i t is assumed that the radii of the liquid cylinder arc accuratelv 13/82 and inch (10.3 and 9.5 mm.), i o correction factor Gas applied.
.
llydioczrhon oils.
An absolute check was not obtained, however, probably owing to impurities in tho liquids. This can very readily be shown hy the results of two tests on ethyl alcohol of different purities. I n one test ethyl alcohol of better than 95 per cent purity was used and the thermal conductivity was determined. I n the other test the conductivitv of ethvl alcohol Figure 6-1natrumenf Layout of better than 99.8 per cent was determined. The difference between the two conductivities at tho same tnnnerature (and If we assume that the 0.2 per cent impurity in the ethyl at atmospheric pressure) was found to be &bo& 6 per cent. alcohol tested was water, then for 100 per cent ethyl alcohol If it is assumed that water is the impurity and that the water the thermal conductivity would he 0.000433, which agrees and alcohol act in solution, so far as thermal conductivity is very well a i t h the results of Bridgman and with Goldschmitt. concerned, just as they do when separate, then by ratio of The conductivity of liquids increases with pressure by about thermal conductivities it can be shown that the purity of the 2 per cent per 100 atmapheres at 30" and 75" C., according alcohol in the first case was 97 per cent, which is probably to Bridgman. This is so small that it can be neglected for not far wrong. ordinary calculations involving modcrate pressures.
I N D U S T R I A L Ah'D ENGINEERING CHEMISTRY
1250
Last year a preliminary attempt to determine thermal conductivities was made using the same copper cylinder assembly, but with a different method of measuring the heating current and the thermocouple e. m. f . The deflection of a galvanometer mirror was used to determine the e. m. f . and the deflection was calibrated by noting the movement given to it by a Weston acid cell, which was, in turn, calibrated against
VOl. 22, No. 11
Critical Tables as 0.000316, which would bear out the belief of a positive temperature coefficient. Proposed Empirical E q u a t i o n
The theoretical equation of Bridgman is the only equation of its type which the author knows. Weber's empirical formula is perhaps the best empirical equation yet obtained. Equations for liquids of a particular type have been used, such as that published by the Bureau of Standards (/ti for petroleum oils. This equation is: 0.813 k = __ [l
- 0.0003(t - 32)] d thermal conductivity of oil in B. t. u. per hour per sq. f t . per inch per O F. d = specific gravity of liquid :t 6Oo/6O0F. t = temperature of liquid in F.
where k
=
The Bureau of Standards estimates that this equation has an estimated accuracy of 10 per cent. For red oil, for example, this equation gives about 0.000370 a t 30" C., whereas the observed value was 0.000337. KOequation thus far has been able to predict conductivities with any degree of satisfaction. The author therefore attempted to determine an empirical equation for all non-metallic liquids, and one has been found which satisfies every liquid for which complete information could be obtained-in all fifteen liquids of widely varying characteristics. This equation was first obtained in the form: k = Ap
Figure 7-General Equation 1 for Thermal Conductivity of Liquids a t 30 C. a n d Atmospheric Pressure
a Weston standard cell. The resistance of the heating wire. however, was not obtained in place, but was determined separately. Also the temperature coefficient of the wire was not determined, but mas taken from a handbook for the particular material used. The agreement with Bridgman, however, was very close. The results are given in Table 11. Table 11-Thermal Conductivities of Liquids by Old Method. parison w i t h Results of Bridgman TBMPERA-
MATERIAL
TURE
c. Isopropyl alcohol Toluene n-Hexane
30 60 30 60 30 60
I 1
Isoamyl alcohol Ethyl alcohol Benzene
a
30 30 60
fi-Cymene
30
n-Octane
60 30
60
!
z1.16C0.4
( p ~ ~ l / % ) l ~ t i l
-
(1)
where k = thermal conductivity a t 30" C. in gram-calories per see. per sq. cm. per C. per cm. p = specific gravity of liquid relative to water a t 30" C. 2 = viscosity of liquid in centipoises C = specific heat of liquid J4 = molecular weight of liquid
A11 values are to be obtained at 30" C.
Com-
THERMAL CONDUCTIVITY, k
Smith
0.000377 0.000371 0.000352 0.000348 0.000328 0.000325 0.000354 0.000352 0.000433 0.000367 0.000363 0.000322 0.000325 0.000347 0.000338
Bridgman
0.000367 (0.000364)a 0.000364 (0,000347) 0.000364 (0.000350) 0.000430
Values in parentheses were obtained by interpolation.
It will be noticed that p-cymene has a positive temperature coefficient. So far as the author knows, water is the only other liquid now determined which shows this characteristic. When this positive coefficient for p-cymene was obtained, the author thought that he had made a mistake, so he made another run on a fresh sample of liquid. The second result checked the first quite well. Later it was noticed that the value of p-cymene a t 12" C. was given in the International
Figure 8-General Equation 2 for Thermal Conductivity of Liquids a t 3OOC. a n d Atmospheric Pressure
k (m)
pCM'
'6
If we plot against ( 7 on log-log ) paper we get a remarkably straight line. (Figure 7) However, it may be objected that the viscosity varies so much that it is the predominating factor on each side. This is true for the whole length of the line, but is not so if we exclude the
Sorember, 1930
I X D U X T R I A L A N D ENGINEERING CHEMISTRY
two high-viscosity oils, since all the factors in the equation then vary through about the same ratio. I n this restricted length the straight line represents the points quite well. It would be better, however, to avoid this difficulty by eliminating viscosity from one side of the equation. Then kzo"2 we can plot lo') against ( p C N 1 ' 6 ) . I t can be pc0.4 seen that we again have a straight line with a slope in this case of 1.15 and a constant of 8.1. (Figure 8)
(
assume that the thermal conductivity obtained from the graph is correct, then, working backwards, the specific heat would be 0.487, or 5.7 per cent higher than used. If the equation of Fortsch and Whitman gave a value of specific heat which was too low for Rabbeth spindle oil and too high for red oil, then the points obtained by using correct specific heats would be closer to the straight line for thermal conductivity than those shown. Even a little error in specific heat here would be of considerable help. on Liquids Used t o Get General E q u a t i o n
Table 111-Information
Water Methanol Ethyl alcohol Benzene Carbon disulfide Toluene Acetone n-Octane n-Heptane n-Hexane n-Pentane o-Xylene m-Xylene Red oil Rabbeth spindle oil
Figure 9-Graph f o r D e t e r m i n a t i o n of T h e r m a l Conductivities of Liquids a t 30' C. a n d Atmospheric Pressure
Therefore our equation can be taken as:
1251
1 26
2 6.5
I . 185 0.963 1.096 1.220 1.122 1.41
2.55 1.90 2.27 2.64 2.34 3.11
i ,260
2.70 2.98 3.35 2.08 2.29 0.1965 0.622
-2 47 ..
1 17.5
1 353 1.473 1 032 1,105 0,1583 0,408
14.06 7.19 6.77 5.62 4.73 5.63 6.15 5.98 5.68 5.60 5.49 5.82 5.63 9.85 7.58
0.780 0.746 1,120
1.016
_____
Also there may be an error in the observed value of thermal conductivity for these oils; but they were both run twice and checked to 0.33 per cent. It is realized, however, that there is a much greater probability that the thermal conductivity equation is not so exact as we should like to see it. Kevertheless, the close agreement with observation for all the liquids tested gives it some degree of importance. The properties of the two hydrocarbon oilq at 30" C'. are given in Table IT. Table IV-Properties
of Red Oil a n d R a b b e t h Spindle Oil
MOLECV-
SpECIpIC
This is the proposed general equation for thermal conductivity of non-metallic liquids a t 30 O C. and atmospheric pressure. If it is preferred, the graph may be used instead of the equation,3 and to avoid confusion one is redrawn without points. (Figure 9) The equation may also be written in the form:
1.613 0.865 0.882 0.744 0.625 0.741 0,800 0.783 0.753 0.734 0.706
LIQVID HEAT
CoSITY
SPE- THERMAL CONLAR CIFIC DUCTIVITY, k AT WEIGHTGRAVITY 30' C.
Gram-cal.1sec.l
CP.
sq. cm./' C./cm
Red oil Rabbeth spindle oil
0.437 0.460
283 15
418 303
0 94 0.852
0.000337 0.000341
Acknowledgment The specific heats of the two oils were not actually measured, but were obtained from the formula of Fortsch and Whitman ( 2 ) ,so perhaps this may account for the error shown. The molecular weights of the oils were determined by H. 0. Forrest and L. W. Cummings of Massachusetts Institute of Technology, using diphenyl as a solvent. The molecular weight of Rabbeth spindle oil was checked to 0.33 per cent using d-camphor as a solvent. It can be seen from the graph that, outside of the two oils, there is in only one case an error of 4.5 per cent; and in no other case is there an error greater than 3.5 per cent. For red oil the error is about 6 per cent and for Rabbeth spindle oil it is nearly 9 per cent. However, as has already been pointed out, the specific heats of the oils were not determined in the laboratory. For Rabbeth spindle oil the specific heat a t 30" C. was calculated to be 0.460. Now in the equation for thermal conductivity specific heat enters to the 155th power. If we a The required information o n most of the liquids used in plotting the graphs can be obtained from the International Critical Tables, Smithsonian Physical Tables, Handbook of Chemistry and Physics by Hodgman and Lange, and the Mechanical Engineers' Handbook by Marks.
The author is much indebted to P. W. Bridgnian, of Harvard University, for the use of his copper-cylinder assembly, and for several valuable suggestions given during the progress of t.he work. Acknowledgment is also due to C. H. Berry, of Harvard Engineering School, for numerous ideas which have been used and for practical assistance. Literature Cited (1) Bridgman, P V O LA. m . .Acad. A r f s Sci., 59, 7 (1923). ( 2 ) Fortsch and Whitman, IND.ENG.CHEM.,18, 796 (1926) (3) Weber, ll'ied. A n n . , 10, 101, 304, 472 (1880).
Improvement in Road-Making Refinery experts in Canada have produced a non-volatile liquid asphalt suitable for low-cost secondary roads. This asphalt is now being used, notably in the prairie provinces, for the construction of waterproof roads of .good riding quality. The cost works out a t $3000-4000 per mile instead of $20,000-25,000 for asphaltic macadam or concrete. The new method of secondary road construction, known as the mix-in-place method, using liquid asphalt and gravel, not only is adapted to roads lacking a good binder, but can be applied to road beds having a compacted crust of gravel and clay.
