Newton's Law of Cooling Model
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.
Please note that this resource requires at least version 1.5 of Java.
4 supplemental documents are available
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 1136kb .jar
Last Modified: June 9, 2012
A pdf file that provides additional documentation regarding customization of this simulation.
download 184kb .pdf
Published: July 12, 2012
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 46kb .pdf
Published: October 10, 2010
Rights: Copyright by Barbara Christian. Free for non-commercial use with attribution.
2 source code documents are available
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 22kb .zip
Last Modified: June 24, 2010
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 117kb .zip
Last Modified: June 9, 2012
AAAS Benchmark Alignments (2008 Version)
4. The Physical Setting
4D. The Structure of Matter
4E. Energy Transformations
AAAS Benchmark Alignments (1993 Version)
4. THE PHYSICAL SETTING
E. Energy Transformations
NSES Content Standards
Con.B: Physical Science
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Newton's Law of Cooling Model:
Is Based On Easy Java Simulations Modeling and Authoring Tool
The Easy Java Simulations Modeling and Authoring Tool is needed to explore the computational model used in the Newton's Law of Cooling Model.relation by Wolfgang Christian
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