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Unformatted text preview: PHYSICS 133 EXPERIMENT NO. 9
GAS THERMOMETRY, OR THE QUEST FOR THE
The kinetic theory of gases states that an ideal gas will obey the relation
pV = nRT (1) where, in SI units, p is the pressure in Pascals, V is the volume in m3, n is the number of moles of
gas, R is the gas constant (8.31 J/mol K), and T is the absolute temperature in K. When V and n
are kept constant, we see that equation (1) gives a linear relationship between p and T. Using the
pressure and temperature characteristics of air, we will estimate the absolute zero of temperature
on the Celsius scale. Equipment
• Hot plate,
aluminum gas cell,
large graduated cylinder with reservoir,
ice water. Method
The pressure transducer employed in this experiment is a device that uses piezoelectric crystals.
Piezoelectric crystals produce an electric voltage across their faces when squeezed or stretched.
By orienting a number of them cleverly inside the transducer, one can measure the applied gas
pressure from the produced output voltage. Briefly stated, the pressure transducer outputs an
electric voltage proportional to the applied pressure. The transducers are calibrated so that they
will output about 0 volts at 1 atm pressure. The linearity of the transducers will be checked over
a small range by changing the height of a column of water pressing on the air inside a plastic
tube connected to the transducer.
Next, the tube will be evacuated by attaching it to a vacuum pump (effectively reducing the
pressure almost to zero), and the change in output voltage output will be noted. Finally, the
pressure of the gas in the aluminum gas cell will be measured after placing the aluminum gas cell
into boiling water and ice water, at temperatures of 100oC and 0oC, respectively. Procedure
I. Linearity of pressure transducer
Attach the pressure transducer to the T-connector at the bottom of the large graduated cylinder
and open the clamp leading to the pressure transducer. Notice that there is another tube leading
to a metal can on the supporting rod. By moving the can up and down, you can change the level
of the water in the graduated cylinder. Explain how this apparatus works.
Measure the voltage output from the pressure transducer at 5 different water levels. Using the
relation that 1 atm corresponds to 1033 cm of water, calculate the pressure in the transducer for
these different heights in atms. Graph the change in voltage vs. the change in water pressure that
caused the voltage change.
Q1. Is the graph linear? Calculate the slope of the graph.
Q2. What can you say about the linearity of the transducer?
II. Zero pressure
To ensure that no water has entered the transducer, we will use a second transducer for the
remainder of the experiment. (Do not use the same transducer you used in Part I above.)
Attach another transducer to the vacuum pump, open the valve, and record the voltage after
several minutes, once the value has become stable. The lowest pressure that the mechanical
pump can reach is approximately 0.0001 atm, which is small enough to be considered zero for
our purposes. Find a linear equation relating pressure and voltage which includes the voltage at
1atm. and the voltage at 0 atm. Compare the slope with that obtained in part 1.
III. Pressure thermometry
The pressure inside the aluminum gas cell will now be measured at 0oC and 100oC. Immerse the
gas cell in the boiling water. CAUTION!: boiling water is as dangerous in the physics lab as
it is in the kitchen. Proceed with care! Avoid making any sudden or impulsive moves that
might knock over the apparatus. Be careful not to touch hot objects.
After waiting a few minutes for the gas to reach the temperature of the water, attach the same
pressure transducer (i.e., the one that you just used in Part 2 above) to the gas cell and
record the voltage reading. You might measure the temperature of the water with a thermometer,
but they are only accurate to 1oC. Next, put the gas cell (with the transducer still attached)
into the bucket of ice water and wait for it to come to equilibrium. Record the voltage. From the
equation that you determined for voltage vs. pressure in part 2, calculate the pressure at both
temperatures. Graph the pressure versus temperature with these two points and extend the line to
p = 0.
Q3. At what temperature (in oC) would the pressure go to zero?
Q4. How does this compare to the expected value of absolute zero? ...
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