Re: muonic matter questions

On Tue, 16 Jun 2009 15:13:02 -0700, Erik Max Francis <max@xxxxxxxxxxx>
wrote:

Jonathan L Cunningham wrote:
On Mon, 15 Jun 2009 16:16:57 -0700 (PDT), Luke Campbell
<lwcamp@xxxxxxxxx> wrote:

On Jun 15, 2:29=A0pm, Mike Williams <nos...@xxxxxxxxxxxxxxxxxx> wrote:

I suspect that the system is going to run hot. To start with, it's going
to generate at least as much heat as a conventional 26th century
mircochip, but in a volume 200^3 times smaller. The larger mass of the
muons and the higher voltages may well also act to increase the
temperature. I expect the temperature might approach a billion degrees,
which might be a little problematical.
Nah. The atomic bonds in the muonic matter are much stronger, and
require about 200 times more energy to break, and thus can withstand
much higher temperatures. Further, with higher temperatures and
smaller dimensions, heat can be conducted and radiated from the chip
much faster.

If everything scales by 200, then it looks to me like it runs 200 times
hotter. My first thought was that an electronic matter processor running
at, say 350K would scale to 35000 K -- not quite a billion degrees, but
quite warm.

If the scale factor is 200, then it's the _power_ that would increase by
200, not the temperature. The thermodynamic temperature goes by the
inverse fourth power of the energy, that would increase by a factor of
about 4.

But do you see anything wrong with the BOTE sanity check? Here it is
again, to save you searching:

:Ok, small BOTE sanity check: it runs 200 times as fast, at 200 times the
:voltage, so dissipates 200^2 times as much power, but that's ok, because
:it can run 200 times as hot, without failing. Being 200 times smaller,
:it has only 1/200^2 as much area, but each unit area radiates 200^4
:times as much heat, which works out as 200^4/200^2 times = 200^2
:times as much heat in total.
:
:Summary: it uses 200^2 times as much power, and radiates 200^2 times as
:much heat. Neat. All the numbers fit together. :-)

You are right that not everything can scale as 200. In this case, given
that energy levels scale linearly, and temperature scales linearly with
energy, I think it likely that the temperature scales linearly, and the
power as a square. I don't find it very obvious... despite Luke's
reference to Atomic units, but my "sanity check" convinced me!

Of course, it's possible that the figures balance under your assumptions
too... but it's not obvious that power is as fundamental as the energy
levels (band gap?) etc. So I'll leave that for you or someone else to
check.

Jonathan

--
http://chromomancer.livejournal.com
.

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