Vernier Software and Technology
Vernier Software & Technology

Newton's Law of Cooling

Figure from experiment 30 from Physics with Vernier

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.

Additional Requirements

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

Standards Correlations

See all standards correlations for Physics with Vernier »

Physics with Vernier

See other experiments from the lab book.

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

Experiment 30 from Physics with Vernier Lab Book

<i>Physics with Vernier</i> book cover

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