🚀 go-pugleaf

> Let us consider a black surface exposed to the solar radiation (say f.i.
>F=1000 W/m2).

> Without concentration it reaches an equilibrium temperature calculated by :
>                    4
>             sigma*T  = F   (about 100 deg. Celsius)
>
> In a perfect concentrator, with a given concentration factor f, we have :
>                    4
>             sigma*T  = f * F
>
>For a given (great but non infinite) value of f, we can then obtain very great
>calues of T (we know that temp. > 3000 K are "easilly" obtained) but the
>problem is that in the formula herover it is theoretically possible to obtain
>for T a value of f.i. 7000 K, i.e. a temperature wich is over the sun
>temperature.

>We know on another hand that this is strcitly impossible due to the 2nd
>principle of thermodynamics.

        If one looks at the object and image of a simple lens system,
the brightness (watts/sq.cm/steradian) is the same.  Concentrating
by making a smaller image area increases the steradian measure of
the incident light cone.  Conversely, concentrating by reducing
the solid angle of incident light results in a larger image area.

        This implies that an imaging optical system consisting of simple
lenses doesn't break the second law of thermodynamics with respect
to radiant heat flow.  I suspect that generalizing to non-imaging
optics is possible, but the more puzzling case is nonlinear optical
effects (like holograms).  I think the second law of thermodynamics
is rather easier to apply than a full analysis of possible optical
concentrators!

        John Whitmore