written by Wolfgang Christian

The Newton's Law of Cooling model computes the temperature of an object of mass M as it is heated by a flame and cooled by the surrounding medium.  The model assumes that the temperature T within the object is uniform.  This lumped system approximation is valid if the rate of thermal energy transfer within the object is faster than the rate of thermal energy transfer at the surface.  Users can select the mass or volume of the object and the type of material, and the model computes the temperature as a function of time. The model plots this temperature as a function of time as the user heats and cools the object.  It is a supplemental simulation for an article by William Dittrich in The Physics Teacher (TPT).  

The sphere heats and cools by exchanging thermal energy with the surrounding fluid by convection and this energy exchange is proportional to the difference between the sphere's surface temperature Ts and the temperature of the fluid Tf.  Inside the sphere the thermal energy is transported by diffusion.   The temperature inside is uniform if thermal energy transfer within the sphere is faster than thermal energy transfer at the surface.

The simulation shows how a temperature gradient appears if the heat transfer coefficient or the transfer coefficient are large.  The Heating and Cooling a Sphere model allows users to select copper, aluminum, and iron material properties and to set the sphere's radius and its heat transfer coefficient to observe these effects.

The Heating and Cooling a Sphere model was created using the Easy Java Simulations (EJS) modeling tool.  It is distributed as a ready-to-run (compiled) Java archive.  Double clicking the ejs_heat_HeatingAndCoolingSphere.jar file will run the program if Java is installed.

• Download ejs_heat_NewtonLawOfCooling.jar - 1704kb Java Archive File

Last Modified June 10, 2014

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A customizable heating and cooling simulation that allows teachers to set the display parameters.  The customized simulation is automatically saved with associated curricular in a new jar file that can be redistributed.

• Download ejs_thermo_teacher_HeatingAndCooling.jar - 1136kb Java Archive File

Last Modified June 9, 2012

This file has previous versions.

A pdf file that provides additional documentation regarding customization of this simulation.

• Download heating_and_cooling_documentation.pdf - 184kb Adobe PDF Document

Published July 12, 2012
Last Modified August 9, 2012

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A middle school science lesson plan that uses to Newton's Law of Cooling model to explain why we must continually heat our houses in winter and cool them in summer.

• Download Heating_and_Cooling_Simulation.pdf - 46kb Adobe PDF Document

Released under a Copyright by Barbara Christian.  Free for non-commercial use with attribution.

Published October 10, 2010
Last Modified October 12, 2010

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This file has previous versions.

Answer key with screen shots for the middle school science lesson plan.

• Download Heating_and_Cooling_Simulation_Key.pdf - 74kb Adobe PDF Document

Released under a Copyright Barbara Christian.  Free for non-commercial use with attribution.

Published October 10, 2001
Last Modified October 12, 2010

This file is included in the full-text index.

The source code zip archive contains an XML representation of the Newton's Law of Cooling model.   Unzip this archive in your EJS workspace to compile and run this model using EJS.

• Download ejs_heat_NewtonLawOfCooling.zip - 22kb Compressed File

Last Modified June 24, 2010

This file has previous versions.

The source code zip archive contains an XML representation of the Customizable Heating and Cooling Model.  Unzip this archive in your EJS workspace to compile and run this model using EJS.

• Download ejs_thermo_teacher_HeatingAndCooling.zip - 117kb Compressed File

Last Modified June 9, 2012

This file has previous versions.