Wednesday, December 20, 2017

Sun Capture

The Sun's spectrum peaks at about \(5.99584916e14\,Hz\).  From the post "Photons With Kinetic Energy?" dated 5 Dec 2017,

\(f=\sqrt{\cfrac{c^3}{8\pi}*{density}*{Z}*3.4354}\)

The best material to absorb this frequency is,

\({density}*{Z}=f^2\cfrac{8\pi}{c^3}*\cfrac{1}{3.4354}=(5.99584916e14)^2*\cfrac{8\pi}{c^3}*\cfrac{1}{3.4354}\)

\({density}*{Z}=97611.69\)

where \(density\) is in \(kgm^{-3}\) and \(Z\) is the atomic number or the sum of all atomic numbers in a molecule.

At this high value, water (\(Z=10\)) cannot act as a good absorber because of its low density \(1000\,kgm^{-3}\)

Titanium \(Z=22\) and density \(4506\,kgm^{-3}\), on the other hand,

\({density}*{Z}=22*4506=99132\)

comes close to this value,  so a suspension of \(Ti\) or \(TiO_2\) (\(Z=22+2*8=38\), density \(4230\,kgm^{-3}\) (Rutile) and \(3780\,kgm^{-3}\) (Anatase)) in a suitable fluid such that its adjusted density is,

\(suspension\,density=\cfrac{97611.69}{Z}\)

will absorb at the Sun's peak frequency.

For the case of \(Ti\),  by weight, a portion,

\(\cfrac{97611.69}{99132}=0.98466\)

of the suspension is \(Ti\) and the rest by weight is fluid.  Given the high density of \(Ti\), it might still be possible for a good suspension that flow with low viscosity.

For the case of \(TiO_2\), Anatase, in a suspension of,

\(\cfrac{97611.69}{38*3780}=0.67956\)

portion \(TiO_2\) by weight.  A light weight fluid will hold this material in suspension that flows well.

It is best that the suspension flows to prevent settlements.

But what is captured from the Sun's spectrum?