Physicspunks

[An Metet]

Tim May graciously wrote:
> The physics cited by Anonymous is hand-waving.

Absolutely.  It's my weak understanding of a beginning physics book.
Thank you for your reply.

>> If a block of a metal is hollowed out and a small port is drilled to
>> see in, the radiance of the cavity is substantially higher than that
>> of the surface of the metal.  As if that weren't shocking enough, it
>> turns out that the radiance of cavities is the same no matter what
>> kind of metal is used.  (This is so counterintuitive that I almost
>> don't believe it!)
>
> It is not correct to say the radiance is either higher or lower than
> some other material: the radiance approximates that of a perfect
> black body.

My book defines "radiance" in terms of the amount of energy radiated
per surface area.  (It likes to use W/cm^2.)  The radiance of the
surface of different materials at various temperatures can be
compared.

The radiance of a cavity to the surface material can be compared and
it is higher.  The radiance of two cavities is the same, but this is
not immediately obvious to the uninitiated.  It's a reasonable thing
to measure and discuss.

> Nothing mystical at all.

If you don't already know, it's actually surprising.

> The "perpetual motion" part is a non sequitor.

> There are many cases where a material of higher radiance, e.g. the
> surface of the earth, is "looking at" (in the sense of the drawing
> above) a material or thing of lower radiance, e.g., deep space.

> And guess what: the earth radiates more energy toward deep space
> than deep space radiates toward the earth. This is one reason
> deserts get so cold so fast at night.

It's not surprising when a hot body and a cold body approach the same
temperature.

But, in the case described the two bodies start out at the same
temperature.  One radiates more energy towards the other one at that
particular temperature.  So, you would expect that one body would
become hotter than the other.

This effect (if it really occurred) could be exploited to make an
engine which would return the two materials back to the same
temperature, but also do some work in the meantime - a perpetual
motion machine.

>From the hints you've dropped I see the general outline of the
solution.  The photons going between the two blocks of metal will
"thermalize" and the volume between the two blocks will look like the
inside of a cavity.  The rate of energy transfer in each direction
will then be the same.

In fact, if the two blocks were contained in a large thermos which
perfectly reflected the photons, the same effect would occur.  It
would be like an inside out cavity.  Each block would end up at the
same temperature.  (Perhaps slightly lower than the start temperature
because it must take some energy to fill the space with thermalized
photons.)