AN ALTERNATIVE TEMPERATURE MEASUREMENT
V. K. Brown Lindbloom T. H. S.
6130 S.Wolcott Ave.
Chicago IL 60636
1-312-624-6264
OBJECTIVES:
Show: (1) alternative method of temperature measurement, (2) thermal
expansion of gasses.
EQUIPMENT:
500 ml flask, ring stand, test tube clamp, half-meter-long glass tube, one-
hole rubber stopper, thermometer, beaker, graduated cylinder, 2 lb coffee can (or
other container large enough to hold sufficient warm water to cover the flask),
stamp pad ink or other water coloring substance.
STRATEGY:
This is probably best done as a demonstration, at least for the first time.
Fill the beaker mostly full of water, and add enough coloring to make water in
the glass tube clearly visible. Insert the glass tube into the stopper. Fill the
coffee can with water at about 30oC, and hold the empty flask almost
completely under water with the test tube clamp. Put the stopper in the flask
with perhaps 35 cm or so of the glass tube sticking up out of the stopper.
Measure the temperature of the room as exactly as possible, and then after
perhaps 5 minutes, carefully measure the temperature of the water. Now place
a wet finger over the end of the tube and then remove the flask, tube, stopper and
all, from the coffee can. Immerse the open end of the tube in the colored water
in the beaker, and then remove your finger. Finally, place the neck of the
flask in the test tube clamp so that you don't have to stand there holding it
and looking foolish. As time passes, the colored water will climb slowly up the
glass tube toward the flask.
The exact form for discussing this phenomenon will of course depend on both
the instructor and the class. Students might be asked why the water rises, for
example. When temperature is suggested, perhaps the class could be asked
whether the flask warmed up or cooled off as the water rose. After this, a
student might wish to test the temperature of the water in the coffee can
with a finger, and then put a hand on the flask to see whether the flask is
warmer or cooler than the water. Because of the relatively small difference
between the two temperatures, it may be necessary to reveal both the initial
(warm) and final (cold) readings of the flask temperature. While the student
holds his or her hand on the flask, it may be observed that the water height
decreases, and the class may again be asked for the reasons. If more than one is
suggested, the students may be asked to propose experiments that might determine
what the most important factor actually is.
The class may wish to use the device to measure relative temperatures of
the hands of different individuals. If they do, it should be suggested that
they determine afterward whether the height of the water at room temperature
is still what it was in the beginning. (It won't be, in all probability.)
QUANTITATIVE TREATMENT of the topic turns out to be decidedly non-trivial,
and is not recommended for most high school classes. If one or more
advanced students wish to try, however, the example below uses results
obtained during a trial in the summer of 1986. The capacity of the flask with
the stopper inserted was 541 ml. The glass tube (one of unusually large
diameter) was 48.3 cm long and, when full, held 18.5 ml of water. Room
temperature that day was 21.6oC, and the temperature of the warm water was 28.3oC.
The colored water rose 17.7 cm in the tube while the flask was inverted. Allowing
2
for the air in the tube, the warm volume was thus about 554.4 ml. Atmospheric
pressure is normally about 76.0 cm of mercury. Since we were using water,
and mercury is about 13.6 times as heavy as an equal volume of water, normal
atmospheric pressure would be about 1034 cm of water. Initial warm volume would
thus be about 554.4 ml, and final cold volume would be 547.6 ml. It would seem
that the Ideal Gas Law should apply, especially over such a small
temperature range. If it did, then we could use the Ideal Gas Law equation
PHVH/TH=PcVc/Tc,
where P=pressure, V=volume and T=temperature on the Kelvin scale. Then
assuming the original pressure to be atmospheric pressure, we could calculate the
final pressure. Using the values supplied above, the result is 1023.56 cm of
water. On reflection, however, this just can't be. The atmosphere actually
provides not only the pressure on the air inside the flask, but also enough
to support that 17.7 cm of water as well. The actual pressure on the air inside
the inverted flask must therefore be less than 1034 cm of water by 17.7 cm, or
1016.3 cm of water. What's wrong?
The main culprit is the fact that water vapor (from the moisture of the
stopper, flask, tube, etc.) is by no means an ideal gas, and it therefore does
not follow the equation given (although air works quite well). The Handbook
of Chemistry and Physics gives the vapor pressure of water at 21.6oC as 19.349
cm of mercury, and that of water at 28.3oC as 28.848 cm of mercury. Since water
vapor pressure at room temperature made up 2.59% of the 1016.3 cm of water
(74.70 cm of mercury) that was the total pressure, then the same percentage of the
contents of the flask must have been water vapor - which would come to about
14.18 ml, leaving the volume of air as only 533.4 ml at room temperature.
Similarly, using the actual warm pressure of 1034 cm of water (or 76.0
cm of mercury) and the actual combined air-and-vapor warm volume of 554.4 ml gives
us a volume of warm water vapor of 21.04 ml, almost 50% more. This means
the volume of warm dry air was really 533.36 ml, virtually unchanged despite the
difference in temperatures!
Using 533.4 ml as the volume of warm dry air and the gas law, along with
the reduced pressure after cooling, we find that the final volume of the cold
dry air alone should have been 530.6 ml. This, added to the 14.2 ml volume
of water vapor, would give a final volume of 544.8 ml, instead of the 547.6 ml
actually observed. Considering the volume-per-centimeter of the glass tube,
that would mean that the water should rise about 7.3 cm more than it actually
did.
The latter figure is not entirely accurate either, however. If the water
in the tube rose further, the pressure would have been lessened and the total
volume of the cold sample increased because of that reason, and thus the
deficiency in height would be less. Further, as time went on, the height of
the water in the tube dropped visibly, indicating some leakage in the system.
Additionally, the original and final temperatures were measured only
indirectly and may not have been entirely accurate. During the demonstration, a
calculation based upon the coefficient of linear expansion of Pyrex glass
indicated a negligible effect.
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