Module 8

How Fast Can You Cool It?

Student Guide

Amanda Beasley, Angela Chomokos, John Zikopoulos,
Mangela Joshua, Pat Shontz

INTRODUCTION

When you place three plastic bottles of water of different sizes in the refrigerator at the same time, which one will cool the fastest? If you place fresh lemons and grapefruit in an ice chest to cool them, which will chill faster, the lemon or the grapefruit? What factors determine the cooling rates of objects?

OBJECTIVES

1. To determine the surface area of a regular geometric object (homework).

2. To investigate the relationship between the geometry of an object and the rate that it cools.

MATERIALS

TI-83 Graphing Calculator	Motion Detector
Calculator Based Laboratory (CBL)	Cable to link TI-83 with CBL
cart	string
scissors	temperature probe
clay	ice
water	PHYSICS program
thermometer	graph paper

PROCEDURE

1. Collect your group's materials, and form

spherically shaped balls of four different sizes from the clay.

2. Discuss with your group all geometric and physical properties about the clay spheres that you think help detemine how fast they will cool in ice water.

3. Set up the equipment by connecting the temperature probe to channel one of the CBL, and linking the CBL to the TI-83 calculator using the cable provided.

4. Discuss with your group how you will use the temperature probe to measure the cooling rate of each clay sphere.

5. Use the PHYSICS program in your TI-83 calculator to perform the experiments on all four clay spheres. Save the temperature-time lists in your calculator after each experiment.

6. Use STATISTICS to fit a curve to each of your T vs t graphs. Record the regression coefficients, and sketch the shapes of the cooling curves for each sphere.

7. With your group prepare a whiteboard, and prepare to share your results and conclusions with the class.

APPLICATION QUESTIONS

Consider a cube with dimensions 1x1x1 cm. Find its surface area to volume ratio. Repeat for cubes of sizes 2x2x2cm and 3x3x3 cm. As the size of an object becomes larger, what happens to the surface area to volume ratio?
Which will cool faster just after it has been removed from a hot oven, a cupcake or a 9 inch circular cake? Explain your answer.
Based on the clay sphere experiment, can you make a statement of the relationship between the cooling rate of an object and its surface area-to-volume ratio? Explain your answer.
Suppose you had three chunks of clay with the same mass. Suppose you shaped each clay chunk into a different regular geometric shapes. Would they cool at the same rate? Explain your answer.
Explain the difference between the concepts of temperature and heat.

Last modified 12 Aug 1997
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