Assuming that the focused sun beam can reach a temperature higher
than the temperature of the sun itself. A machine can be designed like this:
A focusing sunlight system is used to focus sunlight. The assumption
gives that the beam can reach a higher temperature than the
sun. Hence, the sun with the focusing system can be used as a heat source
and the sun itself can be used as a heat sink. A heat engine receives
heat (QH) from the heat source, outputs work (Wout)
and rejects the waste heat (QL) to the sun. The heat engine
needs to satisfy the first law first. That is,
QH = QL + Wout
The combined system of the lens and the heat engine gives a new heat
engine. In this design, the sun is the heat source and
also the heat sink. The sun gives heat QH and has QL back.
The net heat transfer to the new heat engine from the sun is:
QH - QL = (QL + Wout) -
QL = Wout
Hence, the new heat engine works like this: It receives
heat from the sun only and convert it totally to work. This
design violates the Kelvin-Planck statement of the second law and the new heat engine
is a perpetual-motion machine of the second kind. It means the assumption
that the focused sun beam could become hotter than the sun
itself is obviously wrong.
This case gives an idea that a focusing system can not produce a temperature
higher than the source itself.