From: Anders Sandberg (asa@nada.kth.se)
Date: Thu Oct 24 2002 - 02:33:24 MDT
On Wed, Oct 23, 2002 at 10:02:22PM -0400, Alexander Sheppard wrote:
> What kind of efficiency rates can you get by using a small black hole for
> conversion into Hawking radiation? You ought to get half matter and half
> antimatter, right? So shouldn't be possible, theoretically (now, not
> practically) to combine them and get 100% conversion?
Thermodynamics makes things troublesome. While you can convert matter to
energy, there will always be entropic losses and efficiency is never
100% even if the conversion is. As a first approximation a black hole
housed in a Dyson shell that captures the Hawking radiation is a heat
engine, using the rest of the universe as a heat sink and the black hole
as the heat source. The Carnot efficiency of this device is (1-T_cold /
T_hot), where T_hot is the temperature of the black hole and T_cold the
temperature of space (~3 Kelvin). So if the black hole is 10^6 K, then
the efficiency is 0.999997 - quite good. But this does not take material
properties into account - the Dyson shell would not stand more than a
few thousand Kelvins if it is made of molecular matter. So T_hot might
actually be the hottest part of the shell, and for a 7000 K shell the
efficiency is just 0.99957. OK, that was still rather perfect :-) The
big efficiency loss would be energy capture by the shell - the neutrino
part of the radiation would escape (are there any estimates of the
composition of the radiation?).
-- ----------------------------------------------------------------------- Anders Sandberg Towards Ascension! asa@nada.kth.se http://www.nada.kth.se/~asa/ GCS/M/S/O d++ -p+ c++++ !l u+ e++ m++ s+/+ n--- h+/* f+ g+ w++ t+ r+ !y
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