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- The following instructions have been taken, with minor editing,
from: Minor, Ralph S. Physical Measurements: A Laboratory
Manual in General Physics for Colleges. Part II: Heat, Mechanics
and Properties of Matter. Berkeley, Calif. (1919) pp. 26-30.
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- Copyright © 1998 Richard A. Paselk
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-
- Prior to modern manufacturing methods uniform
tubing (todays precision bore tubing) was not generally available.
Thus the following proceedures for calibration in which determining
the uniformity of the tubing is a major portion.
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-
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- ABSOLUTE CALIBRATION OF A THERMOMETER
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- To plot a curve from which the true temperature
may be obtained corresponding to each scale-reading of a given
mercurial thermometer.
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- Such a curve is called the calibration curve
of the thermometer. The process of obtaining it is absolute since
it does not involve comparison with a standard thermometer. This
process consists, first, in determining the absolute corrections
for two separate scale-readings on the thermometer, preferably
near its fixed points, that is, the points on its scale corresponding
to the temperature of melting ice and the temperature of water
boiling under standard pressure. The thermometer tube between
the two points is then calibrated because of the possibility
that its bore may not be uniform, and the relative corrections
thus determined are superimposed graphically upon the correction
curve resulting from the absolute corrections at or near the
two fixed points.
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- (a) Calibration of the Tube.--Break
off a portion of the thread of mercury about ten degrees in length.
For this purpose, first invert the thermometer and let enough
mercury flow into the small cistern to fill it about half full;
then, holding the thermometer in a horizontal position, tap or
jar it lightly lengthways to break the mercury in the small cistern
loose from the rest. The mercury in the stem will now flow back
into the bulb and leave the stem free for the thread of mercury
which must be jarred loose from the mercury in the small cistern.
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- Ask for assistance, if necessary. Jar the
lower end of the thread to the zero-point of the scale and read
the position of the upper end (which will be near the 10°
mark) to tenths of a degree. Then jar the lower end of the thread
to the 10° mark and read the upper end. Repeat with the lower
end at the successive points 20°, 30°, 40°, etc.,
up to 90°. Then take the readings in the reverse order, setting
the upper end of the thread successively at 100°, 90°,
etc., down to 10°, and reading the position of the lower
end each time. The object of these readings is to find the length
of the thread in each of the ten intervals between 0° and
100°; by means of the two series it is possible to find the
average value of the length of the thread for each interval.
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- (b) Correction at the Lower Fixed Point.--Put
the thermometer through the cork in a test-tube, having filled
the latter about half full of distilled water. Place the tube
in a freezing mixture of shaved ice and salt, and stir the water
around the thermometer until it begins to freeze. Read the thermometer.
By warming the tube in the hand and repeating the freezing process,
obtain several readings.
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- (c) Correction Near the Upper Fixed Point.--Place
the thermometer through the cork in the tube at the top of the
boiler, with the bulb well above the surface of the water. Boil
the water so that the steam issues freely, but not with any perceptible
pressure, from the vent. Read the thermometer when it becomes
steady. Allow the boiler to cool slightly, and repeat, making
three readings in all. If the instrument be provided with a water-manometer,
take the manometer-reading simultaneously with the temperature-reading.
Read the barometer.
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- (d) Let the thermometer cool slowly to about
the temperature of the room, and repeat (b). If the freezing
point observed now is different from that observed in (b), use
the mean of the two values in the calibration that follows.
- ____________
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- (e) Assume that the temperature of freezing
water is O°C. From the Tables take the true boiling-point
temperature for the pressure observed in (c), find the corrections
of the thermometer for the scale-readings observed in (b) and
(c). Record these two corrections by points on coordinate paper,
having as abscissae the
- scale-readings of the given thermometer in
degrees, and as ordinates the corresponding corrections in tenths
of a degree but on a magnified scale. (See Fig. 2). Corrections
should be plus (+) if they are to be added to the observed to
give the true temperatures, minus (-) if they are to be subtracted.
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- Connect these two points by a straight line.
The ordinate of this straight line at any point gives the correction
of the thermometer at that scale-reading on the assumption that
the bore of the thermometer is uniform throughout the whole range.
In general this assumption is not justified, and there must be
added to this correction at each point another correction due
to the inequalities of the diameter of the bore. In order to
find the bore correction, proceed as follows. Determine the mean
length of the thread in all of its different positions. If the
bore were uniform, each of the observed lengths would equal this
mean value. From the deviation between the observed and mean
thread lengths, calculate the length which a thread whose mean
length was exactly ten degrees would have when placed in the
first interval. This would be in the same ratio to the observed
thread length as ten degrees is to the mean thread length. We
will call this the reduced thread length. An actual rise of exactly
ten degrees in temperature will produce an apparent rise equal
to this amount. The difference between this reduced thread length
and ten degrees when the sign is reversed, gives the bore correction
for a temperature of approximately ten degrees. Proceed similarly
with each interval. The total correction which must be applied
at any point of the scale is found, by adding together the corrections
for all the intervals below that point. Since, by definition,
the mean thread length is one tenth the sum of all the observed
thread lengths, the total bore correction at 100° will necessarily
be zero. The sample set of data given below will illustrate the
method. l is the observed thread length in a given interval,
which may be an average of several determinations. L is
its mean value for all intervals; r is the reduced thread
length in a given interval. Its mean value is ten degrees. 10
- r gives the correction for each interval, and the sum
of all such corrections gives the total at a certain point of
the scale.
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| Intervals |
Average l |
r |
Dif.(10-r) |
Bore-Corrections |
| 1st |
14.16 |
10.01° |
-0.01° |
At 0°= .00° |
| 2nd |
14.25 |
10.07 |
-.07° |
" 10°=-.010 |
| 3rd |
14.27 |
10.09° |
-.09° |
" 20°=-.O8° |
| 4th |
14.42 |
10.19° |
-.19° |
" 30°=-.17° |
| 5th |
14.27 |
10.09° |
-.09° |
" 40°=-.36° |
| 6th |
14.13 |
9.99° |
+.01° |
" 50°=-.45° |
| 7th |
14.13 |
9.99° |
+.01° |
" 60°-.44° |
| 8th |
14 |
9.89 |
+.11° |
" 70°=-.43° |
| 9th |
14 |
9.89 |
+.11° |
" 80°=-.32° |
| 10th |
13.85 |
9.79° |
+.21° |
" 90°=-.21° |
| Mean = 14.15°= L 10.00° |
|
|
|
" 100° = .00° |
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- The curve showing the resultant corrections
for all scale-readings from 0 to 100 can therefore be obtained
by super-imposing the bore-corrections just found upon the line
drawn to show the corrections due to the errors in the fixed
points. For this purpose plot points whose abscissae are 10°,
20°, 30°, etc., and whose corresponding ordinates are
found by measuring from the slanting line, already drawn, distances
equal to the corresponding bore- corrections--measuring up or
down from this line according as the corrections are plus or
minus. The smooth curve, which should now be drawn through these
plotted points, is the calibration curve of the thermometer.
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- What are the true temperatures corresponding
to the scale-readings 0°, 25°, 50°, 75° and 100°
on the given thermometer ?
- © R. Paselk
- Last modified 22 July 2000
