1
Algebra I: Strand 3. Quadratic and Nonlinear Functions; Topic 4. Inverse Variation; Task
3.4.2
TASK 3.4.2: HEAT AND PRESSURE
Solutions
Students in a chemistry class performed an experiment to see if there was a relationship
between the temperature of a gas and the volume that it occupied. They set up an
apparatus that allowed them to change the temperature of a quantity of air and then
measure its volume while keeping the pressure constant. The data from their experiment
is listed in the table below.
Temperature (°C)
30
40
50
60
70
80
90
100
Volume (cm3)
52.0
54.3
56.7
58.4
60.9
63.1
65.2
66.1
Using your calculator enter the data using temperature as the independent variable and
volume as the dependent variable. In this situation, why is the temperature the
independent variable?
Students selected and controlled the temperature, they had no control over the volume;
the volume depended on the temperature.
1. What domain and range are appropriate for this problem situation? Why? What
window did you use?
The domain for this data is 30° to 100 ° and the range for this data is 52 cm3 to 66.1
cm3. The domain is the temperature and it would be continuous from 30 degrees to 100
degrees. The volume would also be continuous data. There are a variety of windows that
would be appropriate as long as the maximum and minimum points can be seen.
2. Does there appear to be a relationship between the temperature of the air and its
volume? If so, describe the relationship.
There is a relationship between the temperature and the volume. As the temperature
increases the volume increases. The volume appears to be increasing by 2 cm3 for each
10 degrees in temperature.
November 24, 2004. Ensuring Teacher Quality: Algebra I, produced by the Charles A. Dana Center at The University
of Texas at Austin for the Texas Higher Education Coordinating Board.
2
Algebra I: Strand 3. Quadratic and Nonlinear Functions; Topic 4. Inverse Variation; Task
3.4.2
3. Graph the parent function that best fits the data. Use parameter changes to adjust
the line to fit the data. What rule best models this data?
Students’ answers may vary. For example, starting with y = x translate the function up
42 units (y = x + 42). Applying this parameter change does translate the graph up, but
the slope is not correct. Change the slope of 1 to .2 and try the graph again. This slope
has not been increased enough yet.. Try y = .3x + 42. This slope seems a little too
steep. y = .27x + 42 is a good estimate.
4. Using your graph, what would you approximate the volume of the air to be at
75°C? At 110°C?
75 degrees would have a volume 62.25 cm3 At a temperature of 110 degrees, the volume
would be 71.7 cm3.
The students then performed an experiment to see if there was a relationship between the
pressure of a gas and its volume while the temperature was held constant. They collected
the following data.
Pressure
(Newtons/m2)
0.5
1.0
2.0
3.0
4.0
5.0
6.0
7.0
8.0
Volume (cm3)
41.0
19.0
10.0
7.0
5.0
4.0
3.0
2.9
2.4
Plot the data points with pressure as the independent variable and volume as the
dependent variable.
5. Look at the data for pressure and volume to complete the following sentence: As
the pressure is doubled, the volume is ___________.
Divided by 2.
6. Enter pressure into L1 and volume into L2. Using what you know about data and
different functions, justify whether or not this data is best represented by a linear,
quadratic, exponential, or inverse function.
November 24, 2004. Ensuring Teacher Quality: Algebra I, produced by the Charles A. Dana Center at The University
of Texas at Austin for the Texas Higher Education Coordinating Board.
3
Algebra I: Strand 3. Quadratic and Nonlinear Functions; Topic 4. Inverse Variation; Task
3.4.2
The finite differences show that this data is not linear or quadratic. There is not a
common ratio for the data representing the volume, so the data is not exponential. The
inverse function models this data.
Pressure is put on the plunger for the syringe while there is a stopper on the opposite end.
Use the data from the table above and explain what happens to the volume of the gas.
7. If the stopper remains in place, will the volume of gas ever become zero?
Explain.
As the plunger is pushed in the pressure becomes greater. The volume of gas is
compressed as pressure is added to the plunger. No matter what force is exerted on the
plunger, the volume will never go away completely. Since the gas does not dissolve but is
only compressed, some volume will always remain.
November 24, 2004. Ensuring Teacher Quality: Algebra I, produced by the Charles A. Dana Center at The University
of Texas at Austin for the Texas Higher Education Coordinating Board.
4
Algebra I: Strand 3. Quadratic and Nonlinear Functions; Topic 4. Inverse Variation; Task
3.4.2
TASK 3.4.2: HEAT AND PRESSURE
Students in a chemistry class performed an experiment to see if there was a relationship
between the temperature of a gas and the volume that it occupied. They set up an
apparatus that allowed them to change the temperature of a quantity of air and then
measure its volume while keeping the pressure constant. The data from their experiment
is listed in the table below.
Temperature (°C)
30
40
50
60
70
80
90
100
Volume (cm3)
52.0
54.3
56.7
58.4
60.9
63.1
65.2
66.1
Using your calculator enter the data using temperature as the independent variable and
volume as the dependent variable. In this situation, why is the temperature the
independent variable?
1. What domain and range are appropriate for this problem situation? Why? What
window did you use?
2. Does there appear to be a relationship between the temperature of the air and its
volume? If so, describe the relationship.
3. Graph the parent function that best fits the data. Use parameter changes to adjust the
line to fit the data. What rule best models this data?
4. Using your graph, what would you approximate the volume of the air to be at 75°C?
At 110°C?
November 24, 2004. Ensuring Teacher Quality: Algebra I, produced by the Charles A. Dana Center at The University
of Texas at Austin for the Texas Higher Education Coordinating Board.
5
Algebra I: Strand 3. Quadratic and Nonlinear Functions; Topic 4. Inverse Variation; Task
3.4.2
The students then performed an experiment to see if there was a relationship between the
pressure of a gas and its volume while the temperature was held constant. They collected
the following data.
Pressure
(Newtons/m2)
0.5
1.0
2.0
3.0
4.0
5.0
6.0
7.0
8.0
Volume (cm3)
41.0
19.0
10.0
7.0
5.0
4.0
3.0
2.9
2.4
Plot the data points with pressure as the independent variable and volume as the
dependent variable.
5. Look at the data for pressure and volume to complete the following sentence: As the
pressure is doubled, the volume is ___________.
6. Enter pressure into L1 and volume into L2. Using what you know about data and
different functions, justify whether or not this data is best represented by a linear,
quadratic, exponential, or inverse function.
Pressure is put on the plunger for the syringe while there is a stopper on the opposite end.
Use the data from the table above and explain what happens to the volume of the gas.
7. If the stopper remains in place, will the volume of gas ever become zero? Explain.
November 24, 2004. Ensuring Teacher Quality: Algebra I, produced by the Charles A. Dana Center at The University
of Texas at Austin for the Texas Higher Education Coordinating Board.