VERY interesting physics problem!!! :O

[angle.alpha]

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?








answer given:
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]

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