Re: [Phys-L] Sunlight Brighter Than The Sun???

[John Denker <jsd@av8n.com>]

On 08/12/2013 08:45 PM, Folkerts, Timothy J wrote:

> Here is a link to Nature that seems to claim to be able to focus
> sunlight on the earth *even* *brighter* than the sunlight leaving the
> sun (72 MW/m^2 vs 64 MW/m^2.  This would seem to me to be a violation
> of the 2nd Law of Thermodynamics.
>
> It comes from the University of Chicago, which is is pretty reputable
> place.  Any thoughts?
>
> http://www.readcube.com/articles/10.1038/346802a0?locale=en

This article is droll, with a capital T.

If we take the article at face value, it violates Liouville's 
theorem (conservation of phase space) and it violates the
brightness theorem, which can be considered a corollary of 
Liouville's theorem.  Anything that violates Liouville's
theorem can be used to violate the second law of thermodynamics
and violate the Heisenberg uncertainty principle.

On 08/14/2013 07:22 AM, Folkerts, Timothy J wrote:

> OK ... a few more numbers
[snip]

Still assuming we take the article at face value, this detailed
analysis is correct, and shows what's wrong with the article.

So, where does that leave us?  The only thing that remains is 
word games.  The article is evidently playing games with terms 
such as "surface", "temperature", "solar collector", and
especially "brightness".

Here's my second-best guess:
By convention, the "surface" of the sun refers to the visible
surface, i.e. the photosphere.  It has a more-or-less well-
defined temperature.  However, the sun as a whole is not a
black body, and is not in equilibrium with itself, so it
does not have a well-defined overall "temperature".  The
corona is 200 times hotter than the photosphere.  You could
in principle build a coronagraph and focus this light to
make something very hot indeed.  However, this would not
be an efficient "solar collector" within the usual practical
meaning of the term ... and this does not appear to be what
they have done.

My best guess is that they're playing games with the idea
of brightness, which has a precise technical definition
in terms of phase space, which involves both position and
angle.  Ultra-strictly speaking the word "brightness" does 
not appear in the article.  Still, though, the key claim 
in the title is "brighter", and unless we are playing the 
silliest of silly word games, that means "more brightness".

At this point I assume they are playing with the difference
between 2π and 4π steradians.

Consider a particular atom on the surface of the sun.
Consider the energy it radiates in various directions.
The direction is crucial, if we are going to talk about
brightness.  For /some/ purposes, it makes sense to 
talk about the power radiated into 2π of solid angle.
However, for the purposes of thermal equilibrium, you
need to consider the entire 4π of solid angle.  That
is, for the atom to be in thermal equilibrium, you need 
to hit it from *every* angle with blackbody radiation
at the equilibrium temperature.

If you have some other object in equilibrium with the
aforementioned atom, you have some choices:  
 a) It can be black on the front and shiny on the 
  back, i.e. thermally insulated, in which case you
  need to hit it from 2π worth of directions.
 b) It can be black on all sides, in which case you
  need to hit it from all 4π worth of directions.
 c) et cetera.

These two choices are equivalent from the point of 
view of thermal equilibrium, but they /might/ 
sometimes be considered inequivalent if the goal 
is to build a "solar concentrator".  In case (b), 
the brightness is not higher and the temperature of 
the target is not higher, but the available power 
delivered to a fixed-size target might be higher, 
in the subset of applications where it makes sense 
to irradiate something from all sides (or at least 
from substantially more than 2π worth of directions).

*) Calling this "brighter" is just wrong.

*) Making extravagant claims about "brighter" without
mentioning the brightness theorem falls far short of
due diligence.

*) Their exotic explanation for the result makes no sense.

Whether there is any practical advantage to irradiating
something from all sides (as opposed to making it black on 
one side and shiny on the other) is a complicated question.
The devil is in the details.  Existing photovoltaics are 
already one-sided by design, so for this application 
there is no advantage irradiating the back.  OTOH in a
specialized application where the target is initially 
cold and the only goal is to heat the target, heating 
it from all sides might make sense.

Other applications would need to be investigated on a
case-by-case basis.