[ExI] anders' sea of pu

[spike]

-----Original Message-----
From: extropy-chat-bounces at lists.extropy.org
[mailto:extropy-chat-bounces at lists.extropy.org] On Behalf Of Anders Sandberg
Subject: Re: [ExI] anders' sea of pu

>...The temperature distribution of Plutonia is also pretty interesting. If
you solve the heat diffusion equation for a sphere with internal heat
generation you get T(r) = T_S + (q/6k)(R^2-r^2) where T_0 is the surface
temperature, q is the volume heat generation and k thermal conductivity. 
It is hottest in the centre with a temperature of T(0)=T_S + R^2 q/6k...
T_S can be calculated due to energy conservation: the heat production is
balanced by emission to space. 4 pi R^2 sigma T_S^4 = 4 pi q R^3 / 3 gives
T_S =  (q R / 3 sigma)^.25. So the surface temperature grows slowly with
radius, but the core temperature increases with the square of the radius...

Ja, this is a more formal way to do what I did with a Bessel function.
Under the circumstances, that function predicts that 10km down from the
surface, any cubic cm of Pu would act like any other: it wouldn't know or
care that it was a mere 10km from a radiating surface.

>...So cold Plutonia starts to heat up. As the core gets hotter it shifts to
the beta phase, jumping up in volume - expect some magnificent rifting as
the hot core grows faster than the surface...

Possibly, but there might be phases of plutonium we know nothing about,
since we have little experience with super high pressures on this particular
metal.

>...By the way, Spike, you know about
https://en.wikipedia.org/wiki/Bateman_Equation
, right? Seems we could model the reaction chain fairly easily this way...


COOL!  Thanks for the reminder.  It's in my Modern Physics textbook from my
misspent youth.  I did something like this, noting that the 240Pu and
everything beyond it is negligible for this oddball scenario: you have the
initial alpha decay and two betas that happen quickly.  In the short few
year span, it is close enough to say one part per million of the original
244Pu has converted, so the fact that 240Pu has a thousandth the half-life
doesn't much matter: a thousandth the half-life with a millionth the
material, contribution about a thousandth to the activity.

In any case, the plutonium sphere would heat up, then about five years into
the experiment there would be some spectacular eruptions of molten Pu,
followed by the surface melting, while hot helium radiated into space, and
possibly some alpha particles would have enough energy for escape velocity
(I haven't done the calcs on this, tomorrow's fun.)  But if so, it would
leave behind a net negatively charged body, which is cool too.  Then the net
negative charge of the planet would hold the alpha particles much more
effectively than gravity, so the escape velocity would be much higher.

Cool Anders, what a fun mental exercise you spawned merely by mentioning
seas of plutonium.


On 02/12/2013 16:52, spike wrote:
>
>> but somewhere in this discussion, I should offer a polite greeting to 
> the local NSA agent...hello there Ms. or Mr. NSA agent!

>...Indeed. Hi there, NSA!
--
>...Anders Sandberg,

_______________________________________________

Ja, sure easy for you to say: you don't have to worry about them arranging
an IRS audit.  {8-[

{8-]  

I confess