In this activity, you will evaluate the test data from a cooling experiment using two different types of graphs: a scatter plot of the actual data and a scatter plot of the natural log of the data. This experiment was designed to illustrate the process by which the temperature of an object placed in a cooler external environment would fall until it reached the same temperature as that environment, and to find a mathematical relationship to model that behavior. A 250 mL glass beaker containing 200 mL of water at 70 degrees Celsius was placed in a large square foam container, filled with four liters of ice-cooled water (at 0.4 degrees Celsius). A temperature probe was inserted into the beaker to monitor the change in temperature of the water as time passed. The data was collected and a second set of data was generated by taking the natural log of the raw temperature data. Using Excel or the TI-83, generate scatter plots of both the raw temperature data and the natural log of the raw temperature data versus time. This data exists in three files; one is in Excel Data format, one is in Text format, and one is in TI-83 Group format. If you want to generate the scatter plots using the TI-83, you will have to import the text data into the calculator from the computer after you have downloaded the file. What was the difference between the two graphs? Did you expect this difference? For both graphs, calculate the slope between t=24s and t=54s. Now try it between t=102s and t=126s. What do you notice about the two calculated slopes for each graph? Which graph had a constant slope? Which graph is easier to use? The original idea and data for this activity came from Bill Bishop, a Physics teacher at the Central Virginia Governor's School for Science and Technology. Copyright © 1998 Central Virginia Governor's School for Science and Technology Lynchburg, VA |