Education Technology

Warming Up to Heating Curves

Published on 06/09/2008

Activity Overview

In this activity, students use the CBL 2™ to collect temperature data as a sensor warms up in a cup of water. They find an appropriate mathematical model for the resulting data set.

Before the Activity

  • Connect the calculator to the CBL 2 unit using the link cables
  • Connect the temperature sensor into channel 1 of the CBL 2 unit and start the DataMate program
  • See the attached PDF file for detailed instructions for this activity
  • Print pages 41 - 47 from the attached PDF file for your class
  • During the Activity

    Distribute the pages to the class.

    Follow the Activity procedures:

  • Place the temperature sensor in a cup of hot water and collect temperature versus time data
  • Model the temperature data using a modified exponential function y = a(1 - b^x) + c where x = time and y = temperature
  • Find c (the starting temperature), and y (the approach temperature)
  • Solve for the value of a
  • Use different values of b and find a value of b such that it gives a graph that best fits the data generated
  • Use the DataMatrix editor to perform an exponential regression
  • Verify if the values of a and b match those from the model
  • Plot the regression curve and compare it with the modeling curve to find how well the equation fits the data
  • After the Activity

    Review student results:

  • As a class, discuss questions that appeared to be more challenging
  • Re-teach concepts as necessary