Powered sphere completely surrounded by perfect mirrors

[KLindem]

I humbly ask for people's opinions on the following hypothetical setup:

A solid black body sphere in space is supplied by an internal nuclear energy source with a constant power flux to its surface of 459 W/m². It's surface temperature is accordingly 300K. The power released (to space) balances exactly the power supplied (from the nuclear source) at the sphere's surface. The temperature thus remains constant.

Then we place a shell around the sphere, enclosing it totally. For argument's sake, the temperature of the shell can be considered to be equal to that of the surrounding space (0 K - impossible, yes, but bear with me). The surface of the sphere and the shell is equidistant all around and the gap between the two bodies is a vacuous space. Now, let's say the radius of the sphere is 1000 km and the radius of the shell 1001 km. This means that the distance between the surface of the sphere and the inner surface of the shell is 1 km, allowing us, for simplicity's sake, to disregard the difference in area between the two facing surfaces (amounting to 0,2 %). (If it turns out to matter at all.)

My question is this:

What would happen to this sphere/shell system if the entire inner surface of the shell were a perfect mirror, i.e. a perfect insulator of thermal radiation?

Cheers.

 

[Drakkith]

Then the sphere would heat up, higher and higher, until it melted. No energy would escape since you have "perfect" mirrors.

 

[KLindem]

Thanks for answering.

Yes, that would of course be my guess too. Ever-increasing temperature.

But what actually happens to the energy returning from the mirror to the sphere? And how is the temperature actually raised? By what mechanism? Is it just from piling up of energy of equal level of intensity (frequency/vibration) on the surface of the sphere?

I guess it has to be caused somehow by ever increasing concentration of energy rather than increasing intensity ...? The internal power output after all remains constant. And the sphere's surface area will always be the same. So its inherent 'vibrational' (KE) temperature should stay the same as well.

Does that sound reasonable? Concentration vs. intensity of energy with regards to temperature ...

 

[Dale]

But what actually happens to the energy returning from the mirror to the sphere?

It is absorbed since the sphere is a black body.

And how is the temperature actually raised? By what mechanism?

By conduction from the nuclear plant. The reflected radiation serves to prevent any cooling, but does not actually raise the temperature by itself.

Is it just from piling up of energy of equal level of intensity (frequency/vibration) on the surface of the sphere?

I guess it has to be caused somehow by ever increasing concentration of energy rather than increasing intensity ...?

I don't understand the distinction you are trying to draw here.

The internal power output after all remains constant. And the sphere's surface area will always be the same. So its inherent 'vibrational' (KE) temperature should stay the same as well.

No, it is getting hotter, so its "'vibrational' (KE) temperature" will increase.

Does that sound reasonable? Concentration vs. intensity of energy with regards to temperature ...

I still don't get the distinction.

 

[Drakkith]

Note that an object that is warmer than its surroundings will lose heat. Out in space, this can only be done by radiative cooling, where thermal radiation takes energy from the object. However, if you reflect all that radiation back on the object, as you have done in your example, it can no longer cool itself. As Dalespam said, you can treat this as if the object were incapable of cooling itself.

 

[KLindem]

Yup, thanks!