Activity Overview
In this activity, students investigate Newton's Law of Cooling and determine a model to represent the data.
Before the Activity
Connect the temperature sensor to the DIG/SONIC port of the CBL 2™
Connect the CBL 2™ to the calculator using the Unit-to-Unit cable Use the TI Connect™ software to transfer data from the computer to the calculator
See the attached PDF file for detailed instructions for this activity
Print pages from the attached PDF file for the class
During the Activity
Distribute the pages to the class.
Follow the Activity procedures:
Use calculus to derive the model for exponential growth and decay
Understand that according to Newton's Law, if a chilled object warms to room temperature, the rate at which the object's temperature changes at any given time is proportional to the difference between its temperature and the temperature of the surrounding medium
Collect temperature-time readings and use the Chill89 program to store the data
Plot a graph and trace it to find the room temperature
Study the standard exponential equation and use it to model the data
Calculate the differences between the final and initial values for both data sets
Use the calculator to perform exponential regression on the differences
Derive the equation that models the original data
Use the model to predict temperature at any given time
After the Activity
Review student results.
As a class, discuss questions that appeared to be more challenging
Re-teach concepts as necessary