January 1931
INDUSTRIAL AND ENGI,VEERING CHEMISTRY
equations may be worked out. The solution of different problems is then accomplished by merely making different substitutions in the general equation. Any single problem may be sol\-ed in much less time, as may be seen by comparing the follom-ing with the solution given by Olsen. The statement of conditions in Example I may be given as foll0n.s : PERCENTAGES OF:
Ivaste Sulfuric acid Nitric acid
ivS
Mix
-11
Then
1 1
hi hz
ni na
SI si
h3
113
sa
hi
n4
SI
++ +
POUNDSOF:
hilY
niW
hiS
1
35
,~. =
lOOO[OiO -0.60) +0.905(0.60 - 0.975) +0.325(0.975 -011
-
-"- 120 04
IA
~ 4 1 0 or 4 ~880.783 ~ = 1000[0 2023(0.60 0 ) 0 905i0.6012 -- 0 60) i0 . 2 2 5 ( 0 - 0.6012) I A - 12 804 - - 0 141"465 Or lOOO[O 2023iO 975 0 60) 0 0 225(0.6012 - 0 9 7 5 ) ]
-
+
+ +
-
.\- =
where, A = 0.2023(0.975 - 0 ) = -0.1410465
+ 0 + 0.905(0.6012 - 0.975)
SIW
haS
n d
naS
saS s3N
h4.bi
naM
s4.l.I
+ + +
hiW hzS h3N = h4X nlW nnS n3N = n4M SIW s ~ S SIN = s4M W + S+ N = M
That is: 850.783 Ibs. of waste 90.779 lbs. of sulfuric acid 5 8 . 4 3 8 lhs. of nitric acid
-___
1000 000 Ibs. of mixture
the quantities determined by the longer method
Byltlie use of determinants the general equations for S , W , and-l\- are:
Employment of general equations derived by the use of determinants will be found especially valuable where numerous problems are to be solved and where it would be advantageous to have them solved by routine men. Not only is the tediousness of stating the simultaneous equations eliminated, but the method is usable in the hands of those unfamiliar with algebraic operations save that of substitution as shown by actual tests with students. Literature Cited
In Example I, then: ni = 0 . 2 0 2 3 nl = 0 113 = 0 . 9 0 5 n 4 = 0.225
si =
0.6012 0.975
sz
=
53 SI
= 0 = 0.60
(1) Beaumont and Knudsen. ISD. EKG.CHEM.,21, 386 (1929). ( 2 ) Deatrick, J . Am. SOC.Apron., 2, 725 (1930). (3) Olsen, Van Nostrand's Chemical Annual, 6th issue, p. 815, 1926.
The Specific Heat of Liquid Diphenyl' Roy F. Newton, B. D. Kaura, and Thomas DeVries PURDUEUNIVERSITY, LAFAYETTE, IND.
HE recent commercial production of diphenyl and its use as a heattransfer medium have made desirable the determination of its yariouj physical constants. At the suggestion of the Indian Refining Company, the specific heat of liquid diphenyl has been determined in this laboratory.
T
The specific heat of diphenyl was first determined by a n electric heat input method and by the method of mixtures. Later, a s a check on these determinations, the specific heat was redetermined by another electric heat input method, and by correlating the rate of cooling of a container of diphenyl with the heat input necessary to maintain constant temperature. The results reported are believed to be accurate within 1 per cent.
First Electric Heat Method
The diphenyl sample was contained in a brass cylinder of about 200 cc. capacity, to which was screwed a cap carrying a thermocouple well, a stirrer, and a heating coil which extended in the form of a U nearly the entire length of the container. -1 thin copper cylinder, furnished with a uniformly n-ound heating coil, was placed around the diphenyl container with a clearance of about 0.5 cm. The surroundings of this apparatus were held a t constant temperature by means of a vapor jacket which consisted of two concentric cylinders brazed together in such a way that the vapor of a boiling liquid circulated between the cylinders and kept the inner one at a constant temperature, usually slightly 1
Received October 9, 1929 revised paper received July 14, 1930.
bzlow the boiling point of the liquid. Three coppercons t a n t a n thermocouples were used. One was in the well immersed in the diphenyl, the second was soldered to the outside of the brass container, and the third was soldered to the inside of the copper cylinder. The thermocouples were read potentiometrically with a precision of about 1 microvolt. The heat capacity of the container was determined by filling it with water and stirring until the temperature mas constant, at which time current from storage batteries was sent through the heating coil for a measured time, usually from 1 to 2 minutes. Throughout the heating, current measurements were made by determining the fall of potential between the terminals of a standard resistance in series with the heater. Current was supplied at the same time to the copper cylinder at such a rate that the temperatures of the copper cylinder and of the brass container remained equal. A few preliminary trials sufficed to show what current was needed in the copper cylinder heater, and usually the temperature of the water and of the brass container remained constant as soon as the stirring had removed the temperature gradients within the container. After completion of the run the resistance
I N D U S T R I A L A N D ENGINEERING CHEMISTRY
36
of the heater was determined. From the above data and the weight of the water the heat capacity of the container was calculated. The average value was equal within experimental error to the heat capacity obtained by multiplying the weight of the container by the specific heat of brass. The specific heat of diphenyl was then determined by filling the container with diphenyl, bringing the apparatus to constant temperature by circulating through the vapor jacket the vapors of water, xylene, or aniline and then supplying electric energy and taking observations as above. The shaft of the stirrer carried out an appreciable amount of D6
,
0.5
0.4.
I00
200
300
TEMPERATURE, DEGR€ES CENTIGRADE Figure I-Specific
H e a t of Liquid D i p h e n y l
heat, so that when steady conditions were reached the copper cylinder was at a higher temperature than the brass or diphenyl. During the runs it was necessary to raise the copper to a temperature such that, after the disappearance of the temperature gradients in the diphenyl, the thermocouple readings on the brass and in the diphenyl remained constant. Under these conditions the gain of heat from the copper equaled the loss through the shaft, and no correction for net gain or loss of heat was required. I n a few cases, where the heat applied to the copper cylinder was too much or too little, the temperature of the diphenyl slowly rose or slowly fell, and a small correction, calculated according to Newton's law of cooling, was applied. Method of Mixtures
A sealed container of diphenyl was heated to a definite temperature, then dropped into a large Dewar flask of water, and the temperature rise of the water was determined. The diphenyl container, which was made from thin brass tubing, was filled with about 50 grams of diphenyl, leaving only sufficient empty space for liquid expansion. The error due to vaporization into this space was calculated and found to be negligible. The diphenyl container was heated in the previously used vapor jacket for a t least 3 hours before being dropped. Independent experiments showed that the period of heating was considerably longer than necessary. A platinum platinum-rhodium thermocouple, insulated by a thin glass tube, was placed in contact with one side of the container. The Dewar vessel was immediately below the vapor jacket, and contained about 1800 grams of water, a stirrer, and a tenjunction copper-constantan thermoelement. The Dewar vessel was insulated from the vapor jacket by a lid consisting of two layers of transite and three layers of wood separated by air spaces. When the water in the Dewar vessel was heating or cooling slowly and uniformly, the insulating lid was removed, the container was dropped, and the lid was replaced. The temperature of the water was read at intervals until the water was again heating or cooling a t a small and uniform rate.
Vol. 23, No. 1
By applying Newton's law of cooling, the total rise in temperature was determined. The weight of water in the Dewar vessel was determined a t the end of each run. A single run furnished data for calculating the heat evolved on cooling the liquid diphenyl to its melting point, plus the heat of fusion, plus the heat evolved on cooling the solid to the temperature of the water in the Dewar. The difference between the heats evolved in runs a t two temperatures was used in each calculation of the specific heat of diphenyl. The diphenyl container was heated in the vapor jacket to the boiling points of water, xylene, aniline, diphenyl, and anthracene. The heat capacity of the diphenyl container was calculated from the specific heat of brass. The heat capacity of the Dewar vessel and its contents was determined by measuring the rise of temperature due to the addition of a known quantity of energy from an electric heating coil immersed in the vessel, and also by finding the rise in temperature due to dropping a brass container of water which had been heated to the boiling point of xylene. The platinum platinum-rhodium thermocouple was calibrated at the boiling points of water and of repurified naphthalene, and at the melting points of lead and zinc samples which had been obtained from the Bureau of Standards. The copper constantan thermocouple was compared with a Physikalisch-technische Reichsanstalt calibrated thermometer after checking its ice point and making the usual corrections. Specific Heat from Rate of Cooling
A special vacuum bottle was constructed with a long, narrow neck having a ground-glass joint a t the bottom of the neck, through which passed a stopper carrying the heating coil. The thermocouple was inserted through both inner and outer walls of the vacuum bottle. A small tube filled with charcoal was left on the apparatus after evacuating and sealing, which was immersed in liquid air during runs, to remove the last traces of air from the evacuated space. All but the charcoal tube was immersed in a thermostat maintained a t 25" C., and the diphenyl was constantly stirred during runs by rocking the whole apparatus, causing the air space in the diphenyl container to move back and forth. Preliminary experiments showed that such stirring removed all perceptible temperature gradients in a short time. The heat input necessary to maintain the diphenyl a t constant temperature was determined for several temperatures, and the rate of cooling with no heat input was determined over a wide range of temperatures. The heat input for steady temperature, in calories per second, divided by the rate of cooling at the same temperature, in degrees per second, gives the heat capacity of diphenyl and container. The heat capacity of the container was determined by making runs with water, and by other means, and was found to be equal to the expected heat capacitynamely, that of the Pyrex glass in contact with the diphenyl plus one half that of the connecting tubing. Second Electric Heat Input Method
The vacuum bottle was surrounded by a vapor jacket and agitated until the temperature was constant, when a measured quantity of electric energy was supplied. A minute or two after stopping the electric current the diphenyl began to cool slowly and uniformly. The corrected temperature rise was determined in accordance with Newton's law of cooling. Because of the good vacuum maintained by the charcoal cooled by liquid air, and because of the long narrow neck on the vacuum bottle, the correction for heat loss during the determination was comparatively small, from 4 to 10 per cent, During the heating period, which
INDUSTRIAL AND ENGINEERING CHEMISTRY
January, 1931
was usually about 10 minutes, current and potentia1 to the heater were alternately measured potentiometrically about once each minute. The heat capacities used were the same as those used in the rate-of-cooling method. Discussion The results of the four methods appear in Figure 1. While the individual determinations by any one method are not so concordant as might be desired, no one method is consistently at variance with the others, and all the values are satisfactorily represented by the straight line given in the figure, from which we obtain Specific heat .= 0.388 f 0.00057t where t is the temperatiire in degrees Centigrade.
37
The writers believe that this equation represents the specific heat of diphenyl from its melting point to 300" C . and perhaps higher, to within about 1 per cent. Although higher precision is desirable, the above figures are sufficiently accurate for most purposes, and the absence of any reliable figures in the literature to date justifies the publication of these results. Acknowledgment The authors take pleasure in expressing their indebtedness to the Indian Refining Company for the diphenyl used and for financial aid in the work. Appreciation is also expressed for the helpful suggestions made by F. X. Govers, of the Indian Refining Company.
The Specific Heat of Diphenyl' H. 0.Forrest, E. W. Brugmann, and L. W.T.Cummings RESEARCH LABORATORY OF APPLIED
HE increasing use of diphenyl as a heating
T
CHEMISTRY,
DEPARTMENT OF CHEMICAL ENGINEERING, MASSACHUSETTS INSTITUTE OF CAMBRIDGE,
The specific heat of diphenyl has been determined by two independent methods. A batch calorimeter was used in t h e range from 77.6' to 196.5' C., and a flow calorimeter from 147.7' to 347.0" C . The average deviation of t h e experimental points from t h e relation given is less than 2 per cent for both methods.
medium has required an accurate knowledge ofthe heat capacity of this material for the purpose of design of commercial equipment. The variation of the specific heat of the liquid is also necessary for the calculation of tables of thermodynamic properties of this material. Two methods have been used in measuring this property of liquid diphenyl. Experimental Methods BATCH CALORlMETER-The batch calorimeter used is shown in Figure 1. It consisted of a 1-auart (0.95-liter) Dewar flask surroinded by a heatinsulating jacket. The heat was supplied to the liquid by a coil of nichrome resistance wire wound in a Pyrex ring supported on the bottom of the flask. The energy supplied in this way was measured by an ammeter, voltmeter, and stop watch, all of which were calibrated. A motor-driven stirrer was used to mix the liquid thoroughly and maintain a uniform temperature throughout its mass. The temperature was measured a t the midpoint of the liquid with a thermometer graduated in tenths of a Centigrade degree. The flask was filled with a weighed amount of diphenyl such that a vapor space Figure 1 - Batch Calorime- of about 50 cc. was left above the ter liniiid. -~ --1--
The heat capacity of the apparatus was determined using isoamyl alcohol (Merck). The method was checked by determining the heat capacity of water and liquid naphthalene. The temperature of the liquid was measured at 1-minute 1
Received November 12, 1930.
MASS.
TECHNOLOGY,
intervals before, during, and after the h e a t i n g period. The temperature-time relation for a typical run isshown in Figure 2. D u r i n g the heating period the ammeter and voltmeter were read a t
intervals of 30 seconds. FLOW CALORIMETER-The apparatus used in connection with the flow calorimeter method is shown diagrammatically in Figure 3. It consists of a reservoir for liquid diphenyl immersed in a boiling-water bath, from which the diphenyl was displaced with nitrogen pressure greater than the vapor pressure of the diphenyl in any part of the system.
F RATURE-TIME R E L A T W R IFlC HEAT OF LIQUID DlPH
0
I
2
3
4
5
6
7
8
9
10
I1
12
13
14
IS
16
I7
TIME-UINUTES
From the reservoir the liquid flowed through an electrically heated preheater, which brought the liquid to the desired temperature level, and then into the flow calorimeter proper, which is shown in detail in Figure 4. The calorimeter was made of l/rinch (0.13-cm.) extra heavy iron pipe. The mixing chambers were filled with small coils of iron wire and closed on the ends by a metal disk with a '/isinch (1.6-mm.) hole in the center. The heating element was made by winding about 3 feet (0.9 meter) of No. 30 chrome1 wire on a Pyrex-glass worm. The electrical connection to the outside of the apparatus was made through one-piece spark plugs especially selected for
