# Cooling of spheres

1. Dec 18, 2011

### SandeshPhy

Why is it that two spheres,one hollow and other solid having same material and size and heated to same temperatures cool differently?
Precisely,why does hollow sphere cool faster than solid sphere?

2. Dec 18, 2011

### technician

The solid sphere has greater mass and therefore contain more energy when heated to a certain temp.
More energy to get rid if than a hollow sphere

3. Dec 18, 2011

### SandeshPhy

But my question was about rate of cooling and not about total heat.
Why the hollow sphere cools at a faster "rate"?

4. Dec 18, 2011

### 256bits

What rate are we talking about here? You have to be more specific when asking certain questions.

Are you asking why the hollow sphere cools down from a higher temperature to a lower temperature in less time than a solid sphere? In which case you have the answer from the previous posts - a solid sphere has more mass to cool down.
Here the rate dT/dt for hollow is > than that for solid sphere , where is temp of sphere.

Or are you asking why the hollow sphere looses more heat energy per degree in temperature differential between the sphere and the air - assuming it is in air - than the solid sphere. And in this case, the rates are the same - both spheres lose the same amount of heat energy with regards to the temperature differential at the surface.
Here the rate dQ/dT are the same for both spheres, where dQ is the amount of heat lost from the sphere, and dT is the temperature differential at the surface between air and sphere.

The solid sphere will thus take longer to cool since it has more heat energy to lose. Realize that heat energy from the solid sphere is moving from the interior to the surface via the temperature differential from the surface to the interior. A hollow sphere has no "heat" in its interior.

Last edited: Dec 18, 2011
5. Dec 18, 2011

### SandeshPhy

I was talking about rate of cooling with respect to time.

6. Dec 18, 2011

### Rap

Then the explanation is that the interior of the hollow sphere is not heating the hollow sphere, but for the solid sphere, the interior is continually heating the surface, replacing energy that is extracted from the surface by cooling.

7. Dec 18, 2011

### JHamm

If the two spheres have the same total temperature then the solid one has all of this energy distributed throughout the entire volume but a hollow sphere has all of this temperature concentrated at the surface. The rate of transfer of heat is proportional to the amount of energy that is exposed, since the hollow sphere has all of this energy sitting at the top it radiates off very quickly whereas the solid sphere has very little energy at the surface, this radiates slowly and is then replaced by some more heat as it goes.
You can try thinking of it as two hollow spheres, one has a whole lot of temperature at the surface while the other has a lot less but has a pile of hot coals sitting inside.

8. Dec 18, 2011

### DaveC426913

You could consider the solid sphere to be identical to a hollow sphere except that it is continually having its lost heat replenished by an internal heat source. So this hollow sphere is not going to cool until its internal heat source cools significantly.