VERY interesting physics problem!!! :O

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angle.alpha
Posts: 21
Joined: Tue Mar 08, 2011 8:28 pm

VERY interesting physics problem!!! :O

There are two identical chambers, A and B containing identical metal balls initally at the same temperature. Each chamber is a perfect vacuum and has thermally conducting walls at a lower temperature than the balls.

In A the ball is resting on the floor, which is made of material which is a perfect thermal insulator.

In B the ball is affixed to the ceiling which is also made of perfectly insulating material.

Which ball cools down faster?

Both balls lose energy by radiation at the same rate. If there were no other form of energy involved, this would be accounted for by a change in thermal energy and therefore a change in temperature.

However, the centre of mass of one ball (B) rises while the other falls (thermal expansion of metal). This means B does work against gravity while A has work done on it. Since the rate of radiative loss is the same for both, this means that the thermal energy lost by B must be greater than A, so it must cool quicker.
joe
Posts: 755
Joined: Fri Aug 29, 2003 11:57 am
Location: Sydney

Re: VERY interesting physics problem!!! :O

Very nice!

I think that there's another tiny effect (though I'd like to ask an expert on general relativity about it). In a gravitational field, the distribution of energy in a black box is not quite uniform, and is higher at the bottom. So the radiation from the field into B would be slightly greater than that into A. (What GR says about the radiation out I don't know.)

Note that the two effects depend differently on the geometry: this one depends on the size of the box, the thermal expansion one depends on the size of the balls.

Joe