Re: Can a Lens focus light to the temperature of the sun?

Greetings Patrick:

References:
1. F. W. Sears, Optics, Addison-Wesley, NY, 1958

2. US National Solar Thermal Test Facility (NSTTF)

http://www.nrel.gov/docs /fy99osti/24646.pdf

3. Photograph of the Odeillo France Solar Furnace

http ://www.tourinfos.com/gb/r0011/d0066/m0001/j0007/p001796.htm

4. Toward the Large Scale Production of Fullerenes and Nanotubes by
Solar Energy, Proceedings of the Solar Forum 2001, Cedex, France
Information : guillard@imp.cnrs.fr

Your question relates to what is technically called a Solar Furnace. Solar furnaces are
in operation all over the world and are being used for materials research and testing
of materials at very high temperatures. If you look up Solar Furnace with a search
engine you will find over 4000 references to solar furnace technology that ranges
from amateur kits to leading edge semiconductor materials research.
The US the Department of Energy has established the National Solar Thermal Test Facility
(NSTTF) which is discussed in Reference 2. The facility at the Sandia National Laboratory
in New Mexico can produce solar flux ranging from 2000 to 20,000 suns.

The largest Solar Furnace in the world is located in the Pyrenees mountains near Odeillo,
France. Reference 3 is a picture of the 2 story high parabolic mirror used in the French
solar furnace. The paper in Reference 4 presents graphs of the power in the focal plane of
the French facility which can reach power densities as high as 12 million watts
(12 megawatts) watts per square centimeter!!

Temperature is a measurement of the kinetic energy (KE) in the vibration of molecules,
atoms and particles that make up matter. As the KE of a material increases while being
heated by some external energy source, the vibrations of a typical solid material will
cause the atoms and molecules to come apart and melt into a liquid. At higher KE the
material will boil and give off gas. At even higher KE the atoms and molecules in the
gas will be ionized and torn apart to form a plasma such as we see on the sun's surface.
While we can use various instruments to measure the temperature of solids, liquids and
gasses, when we reach plasma temperatures our KE measuring devices will also be dissolved
and we have to use remote viewing pyrometers to determine plasma temperatures of the
surface of the material as we observe it.

A pyrometer measures the power in the electromagnetic spectrum of the radiation from matter
at very high temperatures and we can find then find the wavelength of the maximum power
output of the matter and call it the black body temperature. A black body is a perfect
absorber of radiation which in turn must also be a perfect emitter of radiation. This is
discussed in standard physics text books such as Reference 1. In science we use
temperatures measured in Degrees Kelvin (K) which is the temperature above absolute zero
where the KE is near zero but not zero because of quantum mechanical issues. Absolute
zero is - 273.15 degrees Celsius (C) and the Kelvin (K) scale follows the Celsius scale.
Thus boiling water at 100 degrees C = 373.15 degrees K etc.

The Odeillo facility has been used to measure hypersonic aircraft and missile parts and
other high temperature materials. One advantage of a solar furnace is that it can almost
instantly provide maximum heating (KE) were conventional furnaces may take hours to reach
similar temperatures. Also the power in the focal plane of the Odeillo facility must be
reduced so that the materials being tested are not totally destroyed instantly.

Although the sun is millions of degrees in its core pyrometric measurment of the surface
of the sun produces a black body temperature of about 6000 degrees K and the maximum power
wavelength of the black body curve from Reference 1 is:

Wavelength (max) = (0.0029)/T = .0029/6000 = 483 nanometers (nm)

Thus the sun appears white hot because the peak radiation output is in the blue/green
portion of the visible spectrum.

As an exercise, what would be a rough estimate of the black body temperature of a material
placed at the maximum power point in the focal plane of the Odeillo solar furnace if we
could make one square centimeter of a theoretical material that could survive long enough
for us to make a pyrometric measurement? We will assume that the sample is in a vacuum
and that thermal conduction and convection are not an issue.

Reference 1 teaches us:

W =s A T^4

Where W = power radiated per second (Watts)
s is the Stefan- Boltzman constant = 5.67x 10^-8 watts / (square meter x T^4)
A is the radiating area in square meters
T^4 is the temperature in degrees Kelvin to the 4th power

We know that the Odeillo power is 12 million watts per square cm and our material area
is one square cm (1x10^-4 square meters)

If we solve for T we get:

T = [ W/(s A)]^0.25 = [(12 x 10^6)/(5.67x10^-8 x 1 x 10^-4)]^0.25
= 38, 142 degrees K

Wavelength (max power) = (0.0029)/T = .0029/38142 = 76 nanometers (nm)

The wavelength of the maximum power is in the middle of the ultraviolet range of the
electromagnetic spectrum and the material would appear blue hot; however, the
greatest amount power is in ultraviolet radiation and would be invisible and very dangerous
to human eyes and tissue. Thus great care must be taken when working with solar furnaces!

Thank you for your interesting question.

Best regards, Your Mad Scientist
Adrian Popa