# Cooling sphere

#### MarkL

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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#### mgb_phys

Homework Helper
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

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