ANALYTICAL CHEMISTRY
1172
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p?&ehd of the yorkingeie$ode. 1
1
'The ripple voltage increases 1 ~ ~ '~ i, when the elecin the potential of r than bith small the total voltage in the cell. The rated csthode ray rent smaller than s than +0.02%), ,It (+0.1%), and
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f ~
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9%). ~
111
reuit a verv laree ply at the &azt :lased. The fixed t this momentary dieates the output same applies t o ndicates the elec.off switch for the n with shunts R-3
r wire adjusted to
time of assembly
, IND. & N e . CREM..
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1,
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ratio, but more than 25 volts have never been found necessary in any analytical applications of controlled potential electrolysis. The output supply is designed for s continuous maximum current of 5 amperes, but the components are all conservstively rated and currents up to 7 or 8 amperes can be drawn for short periods without damage. The inductance-capacitance filter comprising C-I, and C-2 must have an efficiency great enough to reduce the res1dua.i ripple
cl,
Graded Cathode
rmemmi C.O~TIOL. p. 0 , I I O I U I ~ U U L I ,WIUU, 4. F. Smith Chemio e l Co., 1948. (3) Hickling. A,. Trans. P o ~ s d a ySoc.. 38, 27 (1942). (4) Lingane, J. J., IND. END. CHEM..ANAL.Eo., 17, 332 (1945): ANAL.CEBM.,21. 497 (1949): Anel. Ghim. Ado, 2. 5 8 6 6 0 1 (1948): Pm&v SOC.Discussion, 1, 203 (1947). (5) Penther, C. J.. and Pompeo. D.J.. ANAL.CEEM..21, 178 (1949). R ~ c ~ i r February eo 1, 1950.
Machine Computation of Relation between Resistance and Temperature of a Resistance Thermometer DANIEL R. STULL ~oloChemical Company, Midland, M i e h .
M
ODERN scienc,
urru..vvb .nore conscious of the mle played by accurate physical data. In the design of process equipment and manufacturing apparatus, factors must be taken into consideration that received scant notice 20 years ago. These factors depend upon exact physical data for their elucidation. Exact physical data in many instances require the accurate measurement of temperature. Physical methods of analysis and testing depend heavily dso on accurate measurement of temperature. There are a number of accepted methods of accurate temperature measurement, hut the international teniperature s d e from -182.97' t o 630" C. is defined in terms of 8 standard platinum resistance thermometer ( 6 ) . Increased emphasis on accurate measurement of temperature mems increasing. use of platinum resistance thermometers. This excellent tool has been slow in gaining acceptance because of its high cost, fragility, size, chlibration, and the elaborate BCcompanying electrical measuring equipment. The measuring equipment has recently been automatized and made recording (7), and the work of Meyers (4) has brought the size down to where i t is comparable to an ordinary mercury thermometer. The tedium of the calibration was the motivating force for the Dresent effort.
THE EQUATIONS
I.Avlr
In the early days of resistance thermometry, Callendar ( 1 ) found that the formula relating the resistance to the temperature "89
where Rt is the resistance in ohms a t t o C., Ro and Rm axe the resistances at 0' and 100" C., and 6 is a constant determined from measurements of the resistance a t the boiling point of sulfur (444.60'
C.).
This equation served well from -40' C. upward, but below this temperature becomes increasingly in error as the temperature is lowered. In.1925, Van Dusen ( 8 )proposed an rtdditional term which compensates the discrepancy down to the oxygen point ( - 182.97' C.). The modified equation is:
V O L U M E 22, NO. 9, S E P T E M B E R 1 9 5 0
1173
Precision platinum resistance thermometry employs a four-constant equation
R l = Ro[l
+ At
f Bt* f C ( t
- 100)t3]
relating the resistance (in ohms) of the thermometer, Ri, to the temperatire, t o C. In use, the problem of finding the temperature for a measured value of the resistance is solved by constructing a table of resistances for even values of temperature. For a precision of 0.001' C., these temperature values should be a t about every degree for linear interpola-
tion in between. In this way, repetitive calculation demanding six-place accuracy arises. International Business machines have been employed in this computation. The information is supplied t o these machines in the form of punched cards, and t h e machines report the computation in punched form. The final step is the production of a printed record of the entire computation, including the answer. The time required for manual calculating machine operation is approximately decimated by the automatic machines operating with punched cards, while the fatigue of the operation is small by comparison.
where the symbols have t,he same meaning as in Equat:on 1 and p is a constant determined by calibration at the boiling point of oxygen (-182.97' C.). In 1948, the international temperature scale was defined (6) above 0' C. by Rt = Ro(1 At BtZ) (3)
+
+
where R I and Ro have the same meaning as before and A and B are the calibration constants. Below 0" C. a higher power term with a calibration constant, C, is added which holds down to - 182.97' C. and the equation becomes Rt = Ro [l f At Bt* c ( t - 100)PI (4)
+
+
Figure 1.
Specially Printed Card with Fields Delineated for This Computation
Figure 2.
Card Showing Computation Complete for One Temperature
In a recent publication Schwab and Smith ( 5 )have shown that Lquations 1 and 2 can be transformed into 3 and 4. UTILITY OF THESE EQUATIONS
i n use, the problem of finding the temperature associated with a measured resistance is a serious one, even after the coefficients of the equations are known. I t seems that the simplest solution to the problem is the computation of a table of values of Rr for even values of t . For 0.01" C. accuracy, the resistance must be known to the nearest 0.001 ohm, which necessitates 5-place accuracy in the computation. In such a table (to the nearest 0.001 ohm) AR for a 10.00" interval differs from it? neighbors by 0.002 to 0.003 ohm, so that linear interpolation o v a a 10" interval, does not introduce an error greater than about *0.02' C. Computation of the values of Rt a t values of t for 10" intervals from -200" to +500" C. requires about a 5- or &hour job with a manually operated calculating machine. When the resistance can be read to O.OOO1 ohm, linear interpolation over a 10" interval is not sufficiently accurate, so 6-place accuracy must be used, 0 and the table made for intervals of L o C. This 0 a enlarges the job of computing the table to 50 or 60 0 hours of work with a manually operated calculating 0 machine. Inasmuch as the only operations in0 volved are multiplication and summation and the 0 work is highly repetitive, automatic calculation is a not only indicated but highly desirable. a Having an installation of International Busia ness machines available, it was decided to apply a them to this problem. Eckert (2,9) has outlined a the functions and operating principles of the varia ous International Business machines, and refer0 ence should be made to his work if furt8herfamil0 iarity with these machines is desired.
.
a
APPLICATION OF MACHINE COMPUTATION TO THE PRESENT PROBLEM
Figure 1 shows a card specially printed for the calculations on the present problem.
a
Figure 3.
0 0
a 0 0 0
a 0 0 0
a a 0
a a a a
-. - "
a a
Section of Final Table Giving Values of Resistance for Each Degree and All of the Computation
ANALYTICAL CHEMISTRY
1174
L’arious “fields” are delineated and marked specifically. Columns 1 to 4 contain the value of t (the temperature): columns 5 to 10 the values of t 2 ; columns 11 to 18 the values of ( t - 100jt3; columns 19 to 24 the value of Ro,and so on. For automatic calculation, Formula 3 has been replaced by the equivalent formula:
Rt = Ro
’
+ Kt + Lt* + J1 ( t - 100)
t3
(5)
wliere K = Ro.4, L = ROB,and .1f = RcC. In this equation, the four constants K O ,K , L , and .If define the resistance of a given thermometer. Values of 1, t 2 , and ( t - l O O ) t 3 from - 2 0 0 ” to +500” C. weri: computed and punched into 700 cards in the first 18 columns. Each card represents one temperature value. Kest, the value of K O is “gang punched” (in each cnrd) by running the whole deck through th,e high speed reproducer. I n the same operation the information in columns 25 to 32 (number of the platinum resistance thermometer and the cards with negative temperatures) is alqo gang punched. After locking the value of li into a “multiplier,” and passing the deck through, the multiplier will punch product K t in rolumns 38 to 45, a t the rate of about 700 cards per hour. I n like manner, products Lt2 and ‘$1 ( t - 100)t3 are multiplied and punched in columns 46 to 62. lThe Droduct ,kl(t - 100)t3is reouired onlv on negative values of t. j The deck is now run again through the multiplier, which is now wired to add these products algebraically t o the IZO term and punch the Rt sum in columns 74 to 80. Figure 2 shows one of the
cards with the complete computation. The deck is now run through an “accounting machine,” which reads the information in the holes and makes a printcd record of all the information. Figure 3 shows a section of the final table giving the values of Rt for every degree, and all the computations in the event that checking is necessary. Thus in approsiniat,ely 4 Iiours’ machine time the entire computation of 700 temperatures is complet,e, and a printed record (triplicate if desired) of all the romputations is rendered. LITERATURE CITED
Callendar, H. L., Phil. Tmns. (London), 178, 160 (1887). (2) Eckert, W. J., J . Chem. Edz~cntion,24, 54-7 (1947). 131 Eckert, W. J., “Punched Card Methods in Scientific Computation,” Columbia University, New York. Thomas J. Watson Astronomical Computing Buieau, 1940. (4) Neyers, C. H., J . Rewarch .Tat[. Bur. Standards, 9, 807 (1932). (5) Schwab, F. R., and Smith, E. R., Ibtd., 34, 360 (1945). (6) Stimaon, H. F., Ibid., 42, 209 (1949). (7) Stull, D. R., Rev. Sci. Instruments, 16, 318 (1945). (8) Van Dusen, M. S...I. A m . Chem. Soc., 47, 326 (1925). (1)
RECEIVED April 13, 1950. Presented before the Division of Chemical Eduoation a t the 112th Meeting of the A v E R I c h s CHEMICAL SOCIETY, New York, N. Y.
Sampling Certain Atmospheric Contaminants by a Small Scale Venturi Scrubber P A U L L. MAGILL, M Y R A ROLSTON, J. A . MAcLEOD, AND R . D.-CADLE
Stanford Research Institute, Stanford, Calif.
A portable device for sampling air contaminants permits the scrubbing of large volumes of air by a small volume of liquid. This facilitates chemical analysis of the collected materials by making it possible to obtain relatively high concentrations of contaminants in the scrubbing liquid. The action of this portable field unit is based on the principle used in the Venturi scrubbers employed to remove fumes from industrial stack gases. Its efficiency for the collection of several gaseous and particulate air pollutants is discussed. These pollutants include ammonia, sulfur dioxide, sulfuric acid, and sodium chloride.
R
ECENT investigations of air pollution in metropolitan areas
have emphasized the need for a sampling device which makes it possible t o scrub large volumes of air with a small amount of scrubbing liquid. A device is also needed Yhich will sample these large volumes in a relatively short time. Most previous sampling instruments designed for the collection of air pollutants in a scrubbing liquid, such as impingers or bubbler trains (1, 8 ) , have the disadvantage of comparatively slow sampling rates or unduly large liquid volumes. Filtration techniques have been developed which are useful, and many advances have been made in this direction (10). However, filtering rates are usually slow and the neLassity for removing the filtered material from the filtering agent is often objectionable. The apparatus here described is a portable laboratory scale model of the Venturi scrubbers used for fume recovery in plant stack gases, and is based in principle on the industrial models described by Anthony (92). Essentially, it affords a means of injecting a scrubbing liquid into a rapidly moving stream of air a t a Venturi throat; the liquid stream is there reduced t o a fine spray with droplet acceleration, and subsequently the spray-gas mi\-ture is decelerated and separated. The efficient collection of particulate impurities probably is due chiefly to collision with water droplets and diffusion into the water ( 8 ) . Johnstone and Roberts
( 4 )have advanced a “diffusion theory” in which it is shown that aerosol particles of 0.1-micron diameter or less have sufficient Brownian movement to be considered aa acting like large gas molecules; thus the collection of such particles might be considered t o be analogous to gas absorption in liquid droplets. This type of scrubber has proved especially useful to this laboratory in sampling polluted city atmospheres, inasmuch as chemical analysis of trace substances is facilibted by their relatively high concentration in the scrubber liquid, as compared to other methods of sampling. It is valuable also because of its ability t o sample large volumes of air quickly during periods of peak contamination, which may be of short duration. I n addition to this application, the small Venturi-scrubber should also be usefu1,in industrial plants and other locations where it is desired to know the concentration of toxic substances in working areas. The use of this scrubber has been mentioned in several reports from this laboratory (6, 7,11). APPARATUS
Functional details of the mall scale Venturi scrubber used in this laboratory are diagrammed in Figure 1.
