ESTIMATION OF ABSOLUTE ZERO FROM THE RELATIONSHIP BETWEEN PRESSURE AND TEMPERATURE
PURPOSE
To determine the relationship between pressure and temperature for a closed, rigid container.
To extrapolate the value of absolute zero.
The Chemistry Sensor will be used to measure the pressure of the gas inside a rigid container and use a temperature
probe to measure the temperature of the water bath in which the container is immersed. A graph of Absolute
Pressure versus Temperature data will then be analyzed to determine the relationship between pressure and
temperature and to estimate the value of absolute zero.
THEORY
In solids and liquids, the atoms or molecules are very close to each other leaving no room between them. For this reason, solids
and liquids cannot be measurably compressed. Gases, on the other hand, have relatively large distances between the atoms or
molecules as they bounce around into each other and the walls of their container. This fact allows gases to be compressed. In
this experiment you will use modern equipment to recreate the experiment first done by Boyle. Robert Boyle discovered that
there is a mathematical relationship between gas pressure and volume in 1661. Another important property of a gas is that its
volume will also change when its temperature changes. Jacques Charles quantified this in about 1787 (Charles's law). The
combination of these two laws led to the discovery of the Ideal Gas Law by Emil Clapeyron in 1834. This law described the
predictable relationship of pressure, temperature, and volume of a gas.
Gas pressure is related to how often gas molecules bounce into surfaces. When the volume of a container of gas is changed, the
distance between the walls changes and the amount of time it takes for a particle to get from one wall to another changes, which
results in a different number of collisions per second and, results in, a different amount of pressure. The pressure of a constant
volume of gas will be affected by changes in temperature. Since temperature is a measure of the average kinetic energy (and
therefore the average speed) of gas molecules, a change in temperature will change how much time it takes for molecules to
move wall to wall in a container. This implies that if the molecules stopped moving, they would no longer hit the walls and the
pressure would be zero. The colder something gets, the slower the molecules move, thus the temperature at which all motion
stops must be the coldest temperature possible. This temperature is called "absolute zero".
In this activity, you will investigate the Ideal Gas Law by determining the relationship between pressure and
temperature for a fixed volume of gas. The gas you will study as a model of an “ideal gas” is air, and a heated water
bath will be used to increase the temperature of your gas sample. You will also attempt to determine the relationship
between pressure and temperature and also to determine the numerical value of absolute zero.
VARIABLES
MATERIALS
Dependent:
Air Pressure, P, inside Erlenmeyer flask, using Absolute Pressure Sensor (10 samples/s)
Independent:
Temperature, T, outside Erlenmeyer flask, using stainless steel (10 samples/s)
Range: continuous from lowest (–10C) to maximum (50C or until the stopper pops off)
Constants:
Equipment: same hardware and sensors used for all trials.
Air sample: random air sample; same sample used continuously – changed if stopper releases
Data collection: temperature sensor tip near the middle of the Erlenmeyer flask, away from edges
Assumptions:
Temperature range in the flask is small; the temperature probe readings are near the mean value.
Environmental conditions (P, T, air flow) remain relatively constant throughout data collection
Probes were properly calibrated for the range of measurements used.
The stopper and tubes maintained a closed system (no leaks)
Sensors
• Xplorer GLX datalogger or SPARK
• PASPORT Absolute Pressure Sensor
• PASPORT Stainless Steel Temperature Sensor
Consumables
• glycerin (C3H5(OH)3), 1 drop
• water, 1.0 L
(optional) ice/snow and salt
Hardware
• Small Tripod Base & Rod
• large beaker, 1-L
• Three Finger Clamp
• hot plate
• large Erlenmeyer flask & stopper
• spoon
Safety gear
• lab glasses
• lab aprons
• PASPORT Chemistry Sensor
• quick-release connector & tubing
• tongs / mitts
SAFETY
Remember, follow the directions for using the equipment.
Keep water away from electrical outlets, the datalogger, and the PASPORT equipment.
Be very careful when using the hot plate.
Wear safety glasses and follow all standard laboratory safety procedures.
PROCEDURE
Cool the Erlenmeyer flask in a sub-zero snow/salt slurry
Some fresh snow was gathered and placed in the large beaker.
Some salt was added to the snow and the snow and salt was mixed with a spoon.
The Erlenmeyer flask was placed in the snow/salt mixture and the two-hole stopper was placed on the flask
A thermometer or temperature probe was used to monitor the temperature of the slurry.
Setup datalogger and sensors
The Chemistry Sensor was inserted into the Xplorer GLX datalogger (or SPARK) and the interface was turned on.
Absolute Pressure Sensor was selected and the sample rate was set to 10 samples/s
The Temperature Sensor was connected to the side of the interface.
4. Choose the appropriate DataStudio
configuration file entitled
05 Ideal Gas Law CF.ds
and proceed with the following instructions.
Note: Configuration files automatically launch the appropriate
display(s), sampling rate(s), etc.
To computer
To computer
5. Ideal Gas Law
PS-2808
Student Instruction Sheet 137
A MOLE IS A MOLE ...TRUST NO ONE
Equipment Setup
1. Put a drop of glycerin on the barb
end of a quick-release coupler. Put
the end of the coupler into one end
of a short piece (about 15 cm) of
plastic tubing that comes with the Absolute Pressure Sensor.
2. Put a drop of glycerin on the barb end of the other type of plastic
connector that comes with the sensor. Push the barb end of the
connector into the other end of the tubing. Fit the end of the
connector into the one-hole rubber stopper.
3. Push the rubber stopper firmly into the air chamber (aluminum
can).
4. Align the quick-release connector on one end of the plastic tubing
with the pressure port of the Pressure Sensor. Push the
connector onto the port, and then turn the connector clockwise
until it clicks (about one-eighth turn).
5. Use a rubber band to attach the Temperature Sensor to the air chamber
(aluminum can).
6. Set the air chamber/Temperature Sensor into the beaker.
7. Fill the beaker with water until half of the air
chamber is submerged.
Note: Do not let the rubber stopper get
wet.
8. Set the beaker/air chamber assembly on the
hot plate (but don’t turn on the hot plate yet).
9. Use the Three Finger Clamp to hold the air
chamber in the water.
5. Ideal Gas Law
PS-2808
138 Student Instruction Sheet
A MOLE IS A MOLE . . .TRUST NO ONE
Record Data
1. Click the Start ( ) button to begin recording data.
2. Turn on the hot plate to “High” (or its hottest setting).
3. Continue to record data until the water begins to boil (or the rubber stopper
is pushed out). Click the Stop ( ) button to end data recording.
4. Turn off the hot plate.
Note: Be very careful not to touch the hot plate, beaker, or
hot water.
Analyze
Record calculations in your Data Table on the Student Response Sheet as you
complete your analysis.
1. Use the Graph Display to examine the plot of Pressure versus Temperature.
Use the Fit ( ) menu to determine the relationship of pressure and
temperature.
Hint: Start with Linear Fit. If the coefficient of linear
regression, r, is not close to 1.000, try a different choice.
2. Select the Smart Tool ( ) button. Use the Smart Tool ( ) cursor to find
where the Linear Fit line crosses the x axis. You will need to stretch the
graphs to find the intersection point. Record the x-coordinate of the point
where your line crosses the x axis as your estimate for absolute zero on the
Student Response Sheet.
3. Save your DataStudio file (on the File menu, click Save Activity As...) to the
location specified by your teacher.
4. Answer all the questions on the Student Response Sheet.
5. Follow your teacher’s instructions regarding cleaning up your work space.
5. Ideal Gas Law
PS-2808
Student Response Sheet 143
A MOLE IS A MOLE... TRUST NO ONE
Student Response Sheet
Name: ______________________________
Date:_______________________________
A Mole Is a Mole...
Trust No One
Vocabulary
Use available resources to find the definitions of the following terms:
absolute zero: _________________________________________________
___________________________________________________________
intermolecular forces: __________________________________________
___________________________________________________________
kinetic energy: ________________________________________________
___________________________________________________________
pressure: ____________________________________________________
___________________________________________________________
temperature: _________________________________________________
___________________________________________________________
volume: ______________________________________________________
___________________________________________________________
5. Ideal Gas Law
PS-2808
144 Student Response Sheet
A MOLE IS A MOLE... TRUST NO ONE
Predict
How do you think the pressure of the gas inside a rigid container changes as the
temperature of the gas is changed?
___________________________________________________________
___________________________________________________________
___________________________________________________________
Data
Make a sketch of your graph of Pressure versus Temperature. Label the x axis
and y axis and the most significant features of the graph.
In your graph of Pressure versus Temperature, use the Fit menu to find a
mathematical fit for your data.
Hint: Think about the equation of the Ideal Gas Law.
Resize the graph until you can see where the line crosses the x axis of the graph.
5. Ideal Gas Law
PS-2808
Student Response Sheet 145
A MOLE IS A MOLE... TRUST NO ONE
Use the Smart Tool to find the x-coordinate
of the point on the Linear Fit line where it
crosses the x axis. The x coordinate is your
estimate for absolute zero.
Analyze
1. Based on your Pressure versus
Temperature data, what is your estimate
for absolute zero?
___________________________________________________________
___________________________________________________________
___________________________________________________________
2. How does your estimate for absolute zero compare to the accepted value of
–273.15ºC?
___________________________________________________________
___________________________________________________________
___________________________________________________________
Synthesize
1. Based on your Pressure versus Temperature data, how is the pressure related
to the temperature?
___________________________________________________________
___________________________________________________________
___________________________________________________________
2. Do your results support your predictions? Why or why not?
___________________________________________________________
___________________________________________________________
___________________________________________________________
5. Ideal Gas Law
PS-2808
146 Student Response Sheet
A MOLE IS A MOLE... TRUST NO ONE
5. Ideal Gas Law
PS-2808