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Direct or Inverse Proportionalities
Purpose: The relationship between a set of variables can be direct or inverse. In part one of this activity, the relationship between the volume of a confined air pocket and applied pressure will be determined. In part two, the relationship between the volume of a confined air pocket and its temperature will be determined.
The data will be analyzed and plotted in order to learn the characteristics associated with each type of relationship.

Time Required: 2 days

Group Size: 2 students

Materials Needed Per Group:

  • One thin stem pipette filled with colored water, sealed at one end.
  • Centimeter ruler
  • Set of 5 books per group
  • A disposable cup
  • Thermometer or temperature probe
Prior Knowledge: Students should be able to plot a graph.

Procedure

Day 1 Activities
  1. Obtain a thin stem pipette. Measure the length of the air pocket. (The length of the air pocket is proportional to the volume of confined air.) Record the length in the data table.


  2. Stack one book on the bulb of the pipette. This will be recorded as one book of applied pressure. Notice that the volume of air in the pipette has changed. Measure the length of the air pocket and record the value.


  3. Repeat, adding a second book to the stack. Measure and record the length of the pocket of air.


  4. Add books, one at a time, recording the volume after each, until 5 books have been stacked onto the pipette.
    Pressure
    (# of books)
    012345
    Length of
    air pocket
    (cm)
          


Day 1 Analysis:
  1. Graph the data using pressure (number of books) as the independent variable and volume (length of air pocket) as the dependent variable. Label each axis and give the graph a name.


  2. Determine whether the relationship between pressure and volume is a direct or an inverse proportionality.
Day 2 Activites:
  1. Obtain a plastic cup. Fill the cup ¾ of the way with water. Put the thin stem pipette into the cup, bulb end down. Insert a thermometer (or use a temperature probe) and record the temperature of the water. Measure and record the length of the confined air pocket.


  2. Lower the temperature of the water by adding a small amount of ice to the cup. Allow the pipette to sit in the ice water for about 2 minutes. Take it out and measure the length of the air pocket. Record the length and the temperature.


  3. Lower the temperature by adding more ice. Allow the pipette to sit in the water for about 2 minutes. Take it out and measure the temperature and record the length of the air pocket.


  4. Continue the process until a total of five data points have been collected.
    Temprature
    (°C)
          
    Volume
    (cm)
          
Day 2 Analysis:
  1. Make a plot of length (y axis) versus temperature (x axis). Label each axis and give the plot a title.


  2. Does the shape of this graph reflect a direct or an inverse relationship between volume and temperature?


  3. Use a graphing utility to find the best fitting linear function for your data. What does the slope represent? What does the y-intercept represent? (In a classroom, have students compare their slope and y-intercept with those from the other groups.)



E Saylor

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