Air Thermometer
Historically it was found that the relationship between pressure and temperature for a fixed volume of a
gas was linear, so could be expressed by the equation:
p = po + a T
In this equation p is the absolute pressure of the gas, po is the absolute pressure at zero degrees Celsius,
and T is the temperature in degrees Celsius. The slope α is determined from:
p - po
a= b
100
pb is the absolute pressure of the gas at the boiling point of water which is chosen to be 100 oC. Thus, the
equation relating pressure and temperature can be written:
p - po o
p = po + b
T C
100
In this experiment the student will see how well a constant volume gas thermometer (with air being the
gas, and the pressure approximately atmospheric) obeys this relationship.
In particular, do three samples of air at different pressures agree on the temperature at which p = 0, and do
they give the same value for an in-between temperature (approximately room temperature)?
Overview of Procedure:
A pressure sensor will be used to measure the pressure of the air thermometer. The pressure
sensor must be calibrated. The data will consist of recording the pressure in three different
water baths. One will be a mixture of ice and water in a Dewar flask (0 oC). One will be a can of
boiling water (100 oC). The third will be a can of water at room temperature (approximately).
Procedure:
Put your setup together:
1) Start heating a 46 oz can of water (your boiling water bath): It must be boiling to be sure its
temperature is 100 oC for the data points you will take. Use a can or beaker for the room
temperature water bath, and a one liter Dewar for the ice bath.
2) Plug the pressure sensor into channel A on the MPLI box.
3) Setup the Software: Open the MPLI program (on Physics Lab toolbar at the bottom of the
screen). Under Experiment / Select Channels: Click to turn arrows off on B and C. If there’s
a “Text Window” showing in the lower right-hand part of the screen, remove it by clicking on the
upper left (-) symbol in the “Text Window”, choose “Close”.
4) Calibrate channel A: Select the button for channel A. Select “Calibrate Now”. Type in
“Pressure”, hit [ENTER], type in “mm Hg”, hit [ENTER]. Connect a vacuum pump (with a
pressure gauge attached) to the "T" valve. NOTE: The “T” valve connects any two of the
ports. The handle points to the closed port. Align the handle so that the vacuum pump is
connected to the pressure sensor. Turn on the pump. When the reading stabilizes, type in 0
Air Thermoneter – p.2
and hit [ENTER]. Disconnect the tubing from the "T" valve and turn off the vacuum pump.
When the reading stabilizes, type in the barometer reading in mm Hg and hit [ENTER]. Put
your name in “done by”, save the calibration to disk. When it asks “save to______”, what you
type in becomes the calibration file name.
5) Backup your calibration file. Put your floppy disk in drive A. Minimize MPLI program and
open “My Computer”. Double click on drive C. Double click on Mpli. Find your calibration files and
copy to drive A. That way if your computer gets shut off, you can copy the file into the
Mpli folder when you boot it back up and then load it as a calibration file. Restore
MPLI program. You have now calibrated your pressure sensor. The calibration file is valid
for your pressure sensor connected to your computer.
Run the Experiment:
1)
Click “Timing” at the top right of the screen, and change the experiment length to
approximately 20 seconds. Connect your glass (Pyrex) bulb to the “T” valve.
2)
Place the bulb in the room temperature bath. IT IS IMPORTANT THAT THE BULB BE
COMPLETELY IMMERSED IN THE BATH. Swing the valve handle to point at the sensor
and then back to where it points at the open port. Repeat. (This vents the gas bulb to
atmospheric pressure at room temperature.) Click on the “START” button, or hit the [ENTER]
key. Repeat the data collection until the readings are relatively constant. When the pressure
readings have stabilized, click and drag to encompass the graphical data, a dotted box will
appear around the selected area. Then, select “Statistics” from the “Analysis” menu and record
the “Mean”, “Standard Deviation”, “Minimum”, and “Maximum”. You can record these values
by hand on a data sheet, and then enter them into a spreadsheet later for analysis.
3)
Move the bulb to the hot (boiling water) bath and repeat step 2. REMEMBER: THE
BULB MUST BE COMPLETELY IMMERSED IN THE BATH. Do not leave in boiling
water longer than necessary, as vinyl tubing softens and can expand, changing the
volume of the container. However, be sure it’s in the boiling water long enough
that the pressure has stabilized. Actually, you can hold the tubing while recording the
data to keep it from overheating. You may want to check the boiling water with, a
thermometer to be sure it has stabilized. Also, it’s a good idea to keep a thermometer in
the room temperature water to be sure that its temperature remains constant.
4)
Move the bulb to the ice bath and repeat step 2. You now have readings in room
temperature water (W), boiling water (H), and ice bath (C), in the sequence W→H→C.
5)
With the bulb in the ice bath, vent the bulb to atmosphere, increasing the number of
moles of gas. Then gather another set of points: C→W→H.
6)
Repeat with the bulb vented while in boiling water bath: H→W→C. This will give you
three sets of data.
Air Thermoneter – p.3
Data Analysis:
You may use a spreadsheet to analyze your data. Remember, a graph of p vs T must extend to about
minus 275 degrees Celsius. Calculate the temperature corresponding to a pressure of zero for each of your
runs. Be sure to include an estimate of the uncertainty in this value. Also, check on the temperature of the
room temperature bath for each run. How consistent is it? What’s the uncertainty in your values?