V. K. Brown                    Lindbloom T. H. S.  
                               6130 S.Wolcott Ave.  
                               Chicago IL 60636 

     Show:  (1) alternative method of temperature measurement,  (2) thermal 
expansion of gasses.  

     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.  

     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 
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 
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 
     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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