Vernier Software & Technology

# Newton's Law of Cooling

## Introduction

A container of hot water at temperature, T, placed in a room of lower temperature Troom, will result in an exchange of heat from the hot water to the room. The water will eventually cool to the same temperature as the room. You observe this cooling process every time you wait for a hot drink to cool. In this experiment, you will examine the cooling of hot water, with the goal of creating a model that describes the process. You can also predict the time it takes for the hot water to cool to room temperature.

Isaac Newton modeled the cooling process by assuming that the rate at which thermal energy moved from one body to another is proportional (by a constant, k) to the difference in temperature between the two bodies, Tdiff. In the case of a sample of water cooling in room temperature air

${\text{cooling rate}} = -k{T_{diff}}$

From this simple assumption, he showed that the temperature change is exponential in time and can be predicted by

$T_{diff} = T_{0}e^{-kt}$

where T0 is the initial temperature difference. Exponential changes are common in science. Systems in which a rate of change is proportional to the changing quantity show exponential behavior.

To complete this experiment in a short time, you will use a small quantity of hot water, at a temperature about 30°C above room temperature. A Temperature Probe will record the water’s temperature as it cools.

## Objectives

• Use a Temperature Probe to record the cooling process of hot water.
• Test Newton’s law of cooling using your collected water temperature data.
• Use Newton’s law of cooling to predict the temperature of cooling water at any time.

## Sensors and Equipment

This experiment features the following Vernier sensors and equipment.

You may also need an interface and software for data collection. What do I need for data collection?

## Physics with Vernier

See other experiments from the lab book.

 1 Graph Matching 2A Back and Forth Motion 2B Back and Forth Motion 3A Cart on a Ramp 3B Cart on a Ramp 4A Determining g on an Incline 4B Determining g on an Incline 5 Picket Fence Free Fall 6 Ball Toss 7 Bungee Jump Accelerations 8A Projectile Motion (Photogates) 8B Projectile Motion (Projectile Launcher) 9 Newton's Second Law 10 Atwood's Machine 11 Newton's Third Law 12 Static and Kinetic Friction 13 Air Resistance 14 Pendulum Periods 15 Simple Harmonic Motion 16 Energy of a Tossed Ball 17 Energy in Simple Harmonic Motion 18A Momentum, Energy and Collisions 18B Momentum, Energy and Collisions 19A Impulse and Momentum 19B Impulse and Momentum 20 Centripetal Accelerations on a Turntable 21 Accelerations in the Real World 22 Ohm's Law 23 Series and Parallel Circuits 24 Capacitors 25 The Magnetic Field in a Coil 26 The Magnetic Field in a Slinky 27 Electrical Energy 28A Polarization of Light 28B Polarization of Light (Rotary Motion Sensor) 29 Light, Brightness and Distance 30 Newton's Law of Cooling 31 The Magnetic Field of a Permanent Magnet 32 Sound Waves and Beats 33 Speed of Sound 34 Tones, Vowels and Telephones 35 Mathematics of Music

### Experiment 30 from Physics with Vernier Lab Book

#### Included in the Lab Book

Vernier lab books include word-processing files of the student instructions, essential teacher information, suggested answers, sample data and graphs, and more.