Model a Cooling Sphere: Finding Resources

In summary, to model a cooling sphere that loses heat through radiation, you can use the Stefan-Boltzmann law and consider the mass and specific heat capacity of the sphere. The rate of cooling will constantly change and can be calculated using differentiation or a computer. If the sphere is not in space, the heat flow from the surrounding area must also be considered. The calculation for this can be found on a webpage that allows you to input values.
  • #1
MarkL
34
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I would like to model a cooling sphere, losing heat at the boundary through radiation. Is there a book that can help me?
 
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  • #2
It's fairly simple.
The heat given off by a hot surface is given by the Stefan–Boltzmann law and depends on the temperature and the emmisivity ( blackness ) of the surface.
For a perfectly black sphere:
Power = s 4 pi r^2 t^4
where s=5.6e-8 r is radius in metres and t is absolute temperature in kelvin.
You then just need to know the mass and specific heat capacity of the sphere.

As the sphere cools the rate of heat loss from the above equation drops and so the rate of cooling constantly changes. You can either differentiate to get a new equation or use a computer to calculate the temperate and power at each time interval.

If you aren't in space you will also have to consider the heat flowing back onto the sphere from the area around it. This is found from the same equation but T is the temperature of the room.

For better formatted equations see: http://en.wikipedia.org/wiki/Stefan-Boltzmann_law
 
  • #3

FAQ: Model a Cooling Sphere: Finding Resources

How does the cooling sphere model work?

The cooling sphere model works by simulating the transfer of heat from a hot object to its surroundings. It takes into account factors such as the object's initial temperature, its specific heat capacity, and the temperature of its surroundings to calculate how long it will take for the object to cool down to a certain temperature.

What resources are needed to create a cooling sphere model?

To create a cooling sphere model, you will need a computer with modeling software, data on the object's initial temperature and specific heat capacity, and knowledge of the surrounding environment's temperature. You may also need to gather additional resources such as materials to build a physical model or conduct experiments to collect data.

How accurate is the cooling sphere model?

The accuracy of the cooling sphere model depends on the accuracy of the data and assumptions used in the model. If the initial temperature and specific heat capacity are accurately measured, and the surrounding temperature is constant, the model can provide a fairly accurate prediction of the cooling process. However, it may not account for other factors such as changes in the environment or energy loss during the cooling process.

Can the cooling sphere model be applied to real-world situations?

Yes, the cooling sphere model can be applied to real-world situations. It can be used to predict the cooling process of various objects, such as food items, electronic devices, or even celestial bodies. However, the accuracy of the model may vary depending on the complexity of the situation and the accuracy of the data used.

Are there any limitations to the cooling sphere model?

Like any other model, the cooling sphere model has its limitations. It assumes that the object and its surroundings are in a closed system and that the temperature is constant. It also does not account for factors such as external energy sources or changes in the surrounding environment. Additionally, the model may not accurately represent the cooling process of objects with irregular shapes or complex compositions.

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