Robert A. Nelson Byram Hills High School Armonk. NY 10504
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On Finding a Middle Ground for SI
As a teacher of physics I read with interest the article by A. \P. ad am sot^ (11expressing the views a f n chemist toward S1
units. I would like to attempt to sort the logic from the emotion and offer a reasoned reply. The fundamental problem seems to be bow to make accepted convention as nearly as possible consistent with accepted practice. Chemists like their grams, liters, calories, moles, and millimeters of mercury. What would be the best compromise on units to cause the least amount of commotion? ... . AdamsoncriticizesSI for rhnosing the kilogmm as the base unit tor mais. But in advocatinr the CGS units he would have us choose the centimeter as thchase unit for length! Whatever choice we make we are bound to run into some exceptions to the rule in nomenclature ber;luse of historical precedent. The SI base units have been chwen so as to give the derived units a convenient size without the need for numerical factors. The unit of force, the newton, is defined by the relation N = kgm/s2. The unit of energy, the joule, is defined by the relation J = N.m. The newton and the joule have sizes which are convenient for most laboratorv measurements. Although the liter (L) is not an official SI unit, it is accepted as a unit of conveniencefor use with SI. The orieinal definition of the liter in 1795 was the volume of 1000 cm3-exactly. It was not until 1901 that the definition was changed to he the volume of 1 kg of water a t the temperature of its maximum densitv - (4OC). . .. even thoueh a senarate unit for volume was conceptually unnecessary. This was to allow chemists to conmare liauid densities directlv with water with greater preckon than they could compnie densities from the measured mass and volume. Subsequent measurements estahlished that the new liter was 0.028 cmVarger than the old definition as a result of a very small discrepancy in the construction of the. nlatinum cvlinder which served as the l e d representation of the kilugrnm I~eginningin 1799 (fhii was replaced hy a new platinum-iridium rylinder in 1889J.However, in 1964 the liter once again was defined as IUOO cm:'. It would be oreferable toexnress all values of enerev in joules. In partirular, the joule should he used to measure heat energy instend of the calorie. 'l'hus in effect the specific heat of water, which varies acrnrding to the rempernture, would be ahout 4190 J, rkrK). i.e.. 4.19 .J/re.'CJ. llnwever. if this were considered to h i a n intolerable nknherto use in practice the calorie mivht he acceptable as a unit of convenience fix limited use, like the physicists'electron volt. To make thedefinition clear it would he necessary to specify the inrervnl over which the temperature of one gram of water is increased hy one degree Celsius. The interval often cited is from 14.5 to 15.5OC. Alternatively, the calorie may he drfined as an exact multiple of the ioule. The thermovhemical calorie, dvfined as 4.184 .J exactl;, has been used by the National Bureau of Standards since 1948. For historical reasons the conversion factor hetween the calorie and the ioule has been called the "mechanical equivalent of heat." The nascal (Pa = N/m2) should not be difficult to acceot as a unk of In fact, the standard atmosphere (101.3i5 kPa), the millibar (0.1 kPa), the millimeter of mercury, and the torr are all defined in terms of the pascal. Mercurv barometers could easilv he calibrated in kilooascals. ~ f t e ;all, who actually holdsa meter stick up to ;barometer when measuring pressure? Certainly it is absurd to calibrate an aneroid barometer in millimeters of mercury. ~~~
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The SI unit pascal clearly distinguishes the unit of' pressure from thr unit ofhwgth, just 3s the newon clrarly distinguishes the unit of force from the unit of mass. In order to avoid a n association with length, many scientists prefer to use the t&r instead of the millimeter of mercury. However, even though these two units are nominally equivalent and are used synonomouslv in the literature.. thev. are not identical. The m"illimeter of mercury (mmHg) is defined as the pressure of a column ofmercurv 1mm hieh a t 0°C. havine an assumed densitv of 13.5951 e;cm3. at a standard location where the gravitati"nal field is 680.665 c m 1 s ~ 2 iThus . a presiure e x ~ r e w din mmHa onlv represents the height of airctirrou~ mercury column, &t the true height as 06servedon a harometer. In practice the readine of amercurv barometer must be wrrectedcn OOC,not only ~o.acrounrfor ihrrmd expansion of the scale, but also t~ecausethat is the temperatureut whirh the density of mercury has its nominal Galue. Additional corrections for local gravity are usually neglected. In principle the pressure of a standard mercury column 760 mm high would he very nearly 101 325.014 Pa. The rounded figure 101 325 Pa was adopted by the Tenth General Conference of Weights and Measures in 1954 as the definition of one standard atmosohere of nressure (3).Subseouentlv. the torr was defined by the ~ r i t i sstand&; i lnstitutik in i958 as exactly 11760atm. Therefore, the mmHg and the torr differ by about (0.014/101325) X 100%,or about one part in 7 million (4). One of the functions of SI is to eliminate such ambieuities. I do not understand why Adamson makes suchgn issue over the units of electricity and magnetism when there are so many other valid concerns that he might have discussed in the same space. The questions he raises were resolved after more than a-half cc:ntu& 01' debate. An excellent historical account has been riven by Silshee ( 5 ) .The final decision toadopt a fourdime&ional~system of electrical units based on the meter, kilogram, second, and ampere was reached by consensus of the International Committee of Weights and Measures, the International Electrotechnical Commission, and other scientific organizations during the 1930's. After a delay caused by World War I1 the MKSA system was put into effect on Januarv 1.1948. 'I'he nmccpt of "rationalization" was intn~duced hy Heaviside ( 6 )almost one hundred years am! Heaviside chose units such that the factors 2x and 471 were present in the equations of electrodynamics for only those cases possessing circular or spherical symmetry, where they belong, and were absent for cases possessing plane or rectangular symmetry, where they do not belong. If one's only point of contact with the theory of electricity and magnetism is Coulomb's law, then i t might be difficult to understand why the coefficient should he expressed lI(4n~o). However, whv doesn't Adamson write the law in the form given in most elkmentary physics books, namely F = kqq'Ir2, and avoid the need to discuss 4 x and ro altogether! The value of k is very simple to remember: it is 9 X lo9 N.m21C2; its order of magnitude is 10'0. Would he have us chanee the unit of mass iust to set the coefficient in Newton's law of gravitation F = Gmm'lr2 equal to one? One point on which I completely agree with Adamson concerns the status of the mole as a base unit. As he says, the mole is a particular mode of counting, like the dozen, just as the radian is a particular mode of subdividing a circle. The concept of the mole arises because of the existence of a dual system of measuring mass: a set of relatiue masses on the
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Volume 56, Number 10. October 1979 / 661
atomic scale, based on the mass of a carhon-12 atom, and a set of chemists and physicists and would seem to satisfy the criof absolute masses on the laboratory scale, hased on the proterion of makine" accented convention consistent with nctotype kilogram. Astronomers have yet a third set of relative cepted practice. masses on the astrophysical scale, hased on the mass of the Finallv. I think we should remember the difference between sun. If the atomic mass unit and the solar mass unit were a unit and a standard. A unit is a numher ratio which is used known in terms of the kilogram with sufficient nrecision, onlv as a basis of comnarison between nhvsical auantities of the one unit of mass would benecessary or indeeddesirable. ~ u t same kind. It is an intrinsically ahs&ct concept. A standard is an artifact or reproducible phenomenon which is used as the like liauid densities between 1901 and 1964, atomic masses physical embodiment of the unit. Since 1795, for example, we and askonomical masses can he compared k i t h each other with greater preciiiim than rhcy can he rumpartd with the consider the unit of length, the meter. to have remained inplatinum-iridium cylinder which now defines the kilogram. variant but the standard used to represent it has changed as The con\.emiun factor hetween atomic m a s units and grams techniques for measuring length precisely have changed. (or kilograms) i given by Avogndru's number. One gram is Originally, the meter was defined as the length of one ten equal roan ,\vogudro numher ofatomic mass u n i k T h i s is like millionth of the earth's quadrant, but the standard used to the conversion~factorbetween the calorie and the joule: a represent it was a certain platinum bar whose length was one calorie is a "mechanical equivalent" of joules. Any measuremeter between its ends. In 1889 the meter was defined as the ment of Avoeadro's number is eauivalent to an absolute distance between two lines engraved on a new bar of platimensurtmtm o i the mass of a partirulnr atom in grams. num-iridium, which also sewed as the standard, and reference S m e d a v it will be r~mwihletodefuwthe kiloaram in trrmsof to the earth was abandoned. In 1960 the standard became the the mass of a parti&u atom directly. This might he done by wavelength of a certatn emission spectrum line of krypton-& counting the numher of atoms in a nreciselv known volume tmitted hv a disrharre tul)c under snecified condirions. The of a perfert crystal hy X-ray diffraction techniques. At present unit is n& as A d a i s o n asserts, gi;en by one single wavesuft'iriently perfect crystals do not exist, hut it i;conreival)le length. Recently a measurement of the speed of light was that they k y be grown in the "weightless" environment of obtained (299 792 458.7 f 1.1 m/s), by measurement of the orbiting space laboratories. When this day comes, the value wavelength and frequency of a laser, in which the principal of Avogadro's number will he given by definition and will not source of error was the realization of the krypton wavelength itself. I t has therefore been proposed that this measurement he subject to further experimental revision. should he taken as the basis of a new definition of the meter, I h a w two rerummrndations for the reclassification of the in which the speed of light would he assigned the value 299 792 mule: F~rst.the molc should be clasiil~edas a su~nlementary 458 m/s by definition (8, 9). The meter would thus be the unit. The ~ ; ~ ~ l e m e n units t a r ~form a special c&gory which distance traveled by light in a vacuum in 3.335 640 952 ns. The ~ r e s e n t l vcontains onlv two geometrical units, radian and definition would me& that our present cesium-133 frequency steradian. Like the radian, the mole is dimensionless. The standard of time would also become a secondary standard of mole also exhibits a pronertv characteristic of supplementary length! l'hat wmld make theorists very happi because ac(7).For exam& physicists units in that it is often cording to Finitein's theory of relativity space and time are usually express the unit of torque as N.m, hut the unit is aspects of the snmr four-dimensional manifold. n r o.~ e r~ l vexnressed ~ . N d r a d . Similarlv. .. chemists often m o t e Whether we teach physics or chemistry, we teachers have Awgadro'h numher as 11 pure n~untwr,hut in fact it curries the much ill crmnmm. Our srwi:ialtv fields meet at manv common unit mol-1. (:hemists also often cite "rram-atomic wirht"in points. It is very much in our best interests to come to some g, when actually it carries the unit g/mol. kind of mutual accord on our choice of units, if onlv to avoid Second, the fundamental size should he the kilomole, deconfusion among our students. Some hending on both sides fined as the number of elementary entities equal to the will be necessary. numher of atoms in 12 kiloerams of carbon-12. This choice would consistent with the rhoice uf the kilugram as a base Literature Cited unit. It would makr the am11a coherent SI derived unit.since I amu is dimensionally and numerically equivalent to 1 gtmol, (11 Adsmson,A. W.. J. CHEM. EDUC..55.634 (1978). (21 "Handbook &Chemistry and Physics? 42nd Ed., Chemical Rubber Publishing Comor 1 kghmol. The unlt oiconcentriltion preferred by chemists, p8ny.Cleueland. 1960.p. 3167. the mol L, wo~lldalso he a wherent derived unit, sinre I molll. (31 Page. C. H., and Vignureu., P. (Editoml, "The hternational System ofunits (SIl,"3rd Ed.(Nat Bw.Stand. (~.S.l.Spec.Publ.3301. uS.Govl. Printingoffice, Warbngmn, equals I kmol~m".'I'hr pH of pure water would still be 7. If IW7.n 21 chemists would agree to measure pressurc in I'ascals, hut continue to measure vulume in liters, temperaturr in Kelvins, and "amount of substance" in moles, then the universal gas constant would hnve the same value whether exprrssed in ur in SI units I'am' IK. conventional units Pa.l,/tKmoll .. (71 Page.C. H..Arnar J. Phys., 46.78(1978). kmol). These minor changes in the classification of the m h e (81 Evenson, K. M , d d ,Phys. Re". Lett., 29,1346 (19721. 19) Hellwig, H., E v e n ~ nK. , M ,and Wineland, D. L,Phys. Tdoy,31 (12),21(1978). would seem to strike a compromise between the preferences
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662 1 Journal of Chemical Education
