Newton's Law Of Cooling and The Calculus Behind It

Published on
07/21/2005

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