### About

http://weelookang.blogspot.sg/2014/11/ejss-cube-block-cooling-model.html

image of

copper shiny https://c1.staticflickr.com/1/164/362133253_77585f5429_z.jpg?zz=1

copper dull https://www.colourbox.com/preview/10760507-196481-golden-copper-shiny-abstract-vertical-background.jpg

al shiny http://preview.cutcaster.com/cutcaster-photo-100709683-metal-texture.jpg

al dull http://pixabay.com/p-432524/?no_redirect

fe shiny http://www.burningwell.org/gallery2/d/11247-6/img_0571.jpg

fe dull http://upload.wikimedia.org/wikipedia/commons/1/1d/Old_dirty_dusty_rusty_scratched_metal_iron.jpg

### For Teachers

### Translations

### Software Requirements

Android | iOS | Windows | MacOS | |

with best with | Chrome | Chrome | Chrome | Chrome |

support full-screen? | Yes. Chrome/Opera No. Firefox/ Samsung Internet | Not yet | Yes | Yes |

cannot work on | some mobile browser that don't understand JavaScript such as..... | cannot work on Internet Explorer 9 and below |

### Credits

This email address is being protected from spambots. You need JavaScript enabled to view it.; christian wolfgang

### end faq

### Sample Learning Goals

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### For Teachers

## Newton's Law of Cooling

The Newton's Law of Cooling model computes the temperature of an object of mass M as it is heated or cooled by the surrounding medium.

### Assumption:

### Validity:

### Convection-cooling "Newton's law of cooling" Model:

\( T_{background} \) is the temperature of the surrounding background environment; i.e. the temperature suitably far from the surface is the time-dependent thermal gradient between environment and object.

### Definition Specific Heat Capacity:

The specific heat capacity of a material on a per mass basis is\( m \) is the mass of the body

\( c \) specific heat capacity of a material

\( T_{final} \) is the \(T_{background}\)

\( T_{initial}\) is the \( T(t) \)

\( \frac{mc ( T_{background}- T(t) ) }{\delta t} = h A( T(t) - T_{background} )\)

assuming mc is constant'

\( mc \frac{ \delta ( T_{background}- T(t) ) }{\delta t} = h A( T(t) - T_{background} )\)

\( \frac{ ( T_{background}) }{\delta t} = 0 \)

negative sign can be taken out of the differential equation.

\( \frac{ ( T(t) ) }{\delta t} = -\kappa ( T(t) - T_{background} )\)

If heating is added on,

the final ODE equation looks like

### Definition Equation Used:

\( V \) is volume of object

\( \rho \) is density of object

\( A \) surface area of object

assumption of increased surface are

## Materials added:

copper shiny \( c_{Cu} \) = 385 \( \frac{J}{kg K}\)\( \rho_{Cu} \) = 8933 \( \frac{kg}{m^{3}}\)

heat transfer coefficient \(h_{Cu}\) = 400 \( \frac{W}{(K m^{2})} \)

copper dull \( c_{Cu} \) = 385 \( \frac{J}{kg K}\)

\( \rho_{Cu} \) = 8933 \( \frac{kg}{m^{3}}\)

heat transfer coefficient \(h_{Cu}\) = 200 \( \frac{W}{(K m^{2})} \)

aluminium shiny \( c_{Al} \) = 903 \( \frac{J}{kg K}\)

\( \rho_{Al} \) = 2702 \( \frac{kg}{m^{3}}\)

heat transfer coefficient \(h_{Al}\) = 400 \( \frac{W}{(K m^{2})} \)

aluminium dull \( c_{Al} \) = 903 \( \frac{J}{kg K}\)

\( \rho_{Al} \) = 2702 \( \frac{kg}{m^{3}}\)

heat transfer coefficient \(h_{Al}\) = 200 \( \frac{W}{(K m^{2})} \)

iron shiny \( c_{Al} \) = 447 \( \frac{J}{kg K}\)

\( \rho_{Al} \) = 7870 \( \frac{kg}{m^{3}}\)

heat transfer coefficient \(h_{Al}\) = 400 \( \frac{W}{(K m^{2})} \)

iron dull \( c_{Al} \) = 447 \( \frac{J}{kg K}\)

\( \rho_{Al} \) = 7870 \( \frac{kg}{m^{3}}\)

heat transfer coefficient \(h_{Al}\) = 200 \( \frac{W}{(K m^{2})} \)

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) . The Newton's Law of Cooling model assumes h=400 for all shiny and h=200 for dull 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.
- EJSS Cube Block Cooling Model was created by Wolfgang Christian and recreated by lookang using the Easy Java Simulations (EJS) version 5.1 authoring and modeling tool

Research

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### Video

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### Version:

### Hands-On Kits

- http://www.addest.com/products/category/Science_Kits by Addest Station Cooling Curve Kit

### Other Resources

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