Differential Temperature Error in Weighing ELLIS BLADE Columbia University, 3-ew York, 5 . 1..
In the second group of observations an attempt was made to stifle convection currents in t,he vicinity of the right-hand pan. T o limit air currents from belov, a cardboard plat,form 12.5 em. ( 5 inches) square \vas placed Ivithin about 0.5 mm. of the lowest part of the pan. Currents from the sides were prevented by curved vertical cardboards several inches high, resting on the platform close t o the pan on each side. The maximum errors under this arrangement are shoir-n by items 11, 12, and 13 of Table I. In the third group the plummet was not placed on the pan at all, but on an asbestos pad directly beneath t,he right pan, and no load was on the balance pan. The response of the pointer under these conditions indicated the existence of air currents from the plummet,. Folloring these experiments a standard glazed porcelain crucible was weighed under conditions similar to the first group above. Four runs lvere made, and as shown in Table I1 and Figure 3 the maximum error n-as nearly three times that for the plummet, but t,he phenomenon was of shorter duration.
Weighings of a specially prepared steel plummet and a standard porcelain crucible. on a magnetically damped balance, indicate that a temperature difference between object and balance causes a weighing error proportional to the magnitude of the difference, which may persist a half hour, and which dissipates logarithmically with time. The 17-gram plummet exhibited a constant maximum error of 0.05 mg. per degree, and the 17-gram crucible, 0.19 mg. per degree.
I
T IS recognized that prior to weighing, objects should be
brought to balance temperature. B u t in quantitative terms, what is the penalty for disregarding the old axiom? On the freely swinging balance, the problem was difficult, if not impossible, to study properly because of the transient nature of the temperature difference. The following investigation was carried out on a magnetically damped balance (Figure I), using the counterpoise method of weighing. The object was a highly polished alloy steel plummet, which was brought to temperature in a specially constructed thermostat, and then transferred to the balance pan. Observations of the pointer were begun a t the end of the first minute and continued a t regular intervals.
TABLEI. So
1 0.16 2 3
0.12 0.18 0.14
D
0.18 0 04 0.44
4
6
7 8 0.36 9 0.48 10 0 . 7 4 11 0 . 2 0 12 0 . 2 6 13 0 . 1 6
In the first group of observations, the plummet was merely weighed, xith temperature differences ranging from 1O to 15'. Table I shows the maximum errors observed for each weighing. The duration of the phenomenon and its time rate of variation are shown by the curves of Figure 2.
14
0.30
hI.&XI>KMERRORS WITH P L E l f > I E T
C.a
Xg./' C.
3 OC 2 7w
0.0533 0.0144 0,0139 0.0667 0.0613 0.0144 0.0624 0.0537 0,0461 0.0514
hlg
4
1c 1c
2 2 sw 0 9 n' 8 4c 6 7TV 10.4 TV 14 4 C
Mean 7.8W 9 6 W
Remarks
Polished Ni-Cr steel plummet (17.376 grams) resting directly on balance pan (normal weighing)
0.0521, average deviation 0.0019 0.0256 Same as above except cardboard 0.0292 shielding used t b diminish convection 0.0197 currents
8.1 Mean 6 . 8 \V
0,0248, average deviation 0,0020 0.0441 Normal weighing of plummet
16 0 . 3 0 1 0 . 4 W 0 . 0 2 8 6 J V Polished plummet on asbestos pad, 9.5C 0,0021 C directly beneath balance pan, hence 16 0.02 affecting i t b y convection only 17 0 . 0 0 9 . 1 C 18 0 . 3 6 1 1 . 6 ~ 0.63iOw 19 0.01 1 4 . 8 C 0.0026 C
Mean 0,0300 K, 0.0025 C 0.54 11.0 C 0,0491 Kormal weighing of plummet W, plummet warmer t h a n balance. C, plummet colder than balance.
20 a
TABLE 11. KO.
1
2 3 4 a
RIB.
c.0.
0 . 8 6 4 . 7 V0.92 5 3 C 0 54 3.0I T 0 91 4 . 6 C LIean
hIAXI3iIUJI
lIg./O
ERRORS WITH CRUCIBLE
c.
Remarks
0 163 Porcelain crucible, of approximately hame 0.174 weight as plummet (16.456 grams), 0 180 placed directly on balance pan (normal 0 PO4 weighing) 0.185, average dwiation 0 , 0 0 5
K crucible warmer t h a n balance. C,'crucible colder t h a n balance.
Discussion The temperature difference can produce a weighing error either through expansion or by deflection of the moving system by air currents. Expansion of the pan and bows is trivial, n-hile the beam is, thermally speaking, only indirectly connected with the object on the pan and hence is not noticeably affected. On the other hand, an updraft of air produced by a marm object would tend to lift the pan, thereby making the object appear too light, Such convection may arise directly from the object, or indirectly through conduction from the pan. The time variation of the error depends in part upon the manner in which the heat divides between the two paths, and is therefore a complex function of heat capacity, conductivity-,emissivity, and geometry.
DAMPED B~LASCE FIGURE 1, ~\IAGNETIC~ALLY 330
JUNE 1.5, 1940
ANALYTICAL EDITION
20
IO
331
30
MINUTES
FIGURE2. ERRORIN SCALEDIVISIONS DUE TO WARMOR COOLPLUMMET 10, middle of scale 1 division = 0.4 m g .
I
The effect of cutting down the convection was shown by the second group of experiments, in which shields were used about the pan, and b y the third group, in xhich conduction to the pan was eliminated by keeping the object out of contact with the pan. It is assumed that perfect shielding R-ould have eliminated the error entirely in the former case, and it seems reasonable to suppose the full error would have been produced in the latter case, if the full force of the convection had been felt by the pan.
MINUTES
I N SCALE I~IVISIOSS DUE TO W.4RM FIGURE 3. ERROR COOLCRCCIBLE
OR
1 0 , middle of soale 1 division = 0 4 mg
-4pparatus The plummet was ground down from a 0.9-cm. (0.375-inch) alloy steel rod, and buffed to a high polish. -4large eye in one end enabled it to be hooked from the bottom of the therniostat by means of a bent wire. The plummet's weight was 17.376 grams. The thermost,at was a 1.25-em. (0.5-inch) copper tube, 17.5 cm. (7 inches) long, with a soldered-in closed bottom. The copper tube and a thermometer were immersed in a water bath contained in a Fisher outer tube (Figure 4). A bent xire vias used for agitation of the bath. The whole assembly was arranged so that a beaker of warm or cold water could be brought up around the Fisher tube for adjusting and controlling the temperature. Temperatures were obtained by the bath thermometer and a balancecase thermometer, previously compared. The crucible, which n-as of a common type, weighed 16.486 grams or slightly less than the plummet. A second thermostat, made for the crucible, was similar in every respect to the first, except that it was larger. A wire cradle with a long stem was used to place and remove the crucible, the cradle being so constructed that the crucible was allowed t o rest directly on the bottom of the thermostat.
Summary When a temperature differential exists between object and balance, a weighing error occurs which is linear with the magnitude of the differential and of opposite sign, referred to the balance temperature as standard. A highly polished plummet weighing 17.376 grams gave a maximum error of 0.05 mg. per degree C., for differences u p to l 5 O in either direction. Thus in analytical work, where calibrations of brass weights are depended upon to the nearest 0.1 mg., a difference of only a few degrees is very objectionable. For the larger differ-
FIGCRE4. APPARATUS ences, the error may persist u p to a half hour, while small ones may last 10 minutes. A common glazed porcelain crucible weighing 16.486 grams gave a maximum error of 0.19 mg. per clegree C. For a temperature difference of so,this amounts to 1 mg. Fortunately, the effect vanishes much more rapidly than in the case of the plummet, and will usually be gone in 15 minutes. The zero point of a balance shifts temporarily when a warm or cold object is weighed, thereby subjecting subsequent n-eighings to error. The magnetically damped balance, operating on a null principle, is especially suitable for analyzing weighing problems in which time is a n element, since readings may be taken as frequently as desired. If external influences such as temperature and vibration are controlled, the precision of this balance is potentially higher than that of the freely swinging type.
