Newton's Law of Cooling Model 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 heated or 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.  

Newton assumed that the rate of thermal energy transfer at the object's surface is proportional to the surface area and to the temperature difference between the object and the surrounding medium.
 
where h is the heat transfer coefficient and A is the area of the object.  Combing Newton's law of cooling with the definition of specific heat C and assuming that the specific heat is constant gives


Users can select the mass of the object and the material and the model computes the surface area assuming a cubic shape. The model plots the object's temperature as a function of time as the user heats and cools the object.  A data-tool button on the temperature graph allows users fit the data to analytic functions.

Note:  A typical (rough) heat transfer coefficient h for still air and iron is 6 W/(K m^2) and 400 W/(K m^2) for still water and iron. The Newton's Law of Cooling model assumes h=400 for all materials.  The actual value of h depends on many parameters including the material, the fluid velocity, the fluid viscosity and the condition of the object's surface.
References:
"Measuring the Specific Heat of Metals by Cooling," William Dittrich, The Physics Teacher, (in press).
Credits:
The Newton's Law of Cooling model was created by Wolfgang Christian using the Easy Java Simulations (EJS) version 4.2 authoring and modeling tool.

You can examine and modify a compiled EJS model if you run the model (double click on the model's jar file), right-click within a plot, and select "Open EJS Model" from the pop-up menu.  You must, of course, have EJS installed on your computer.  Information about EJS is available at: and in the OSP ComPADRE collection .

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