[ExI] anders' sea of pu

[Anders Sandberg]

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.

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. Near the surface where 
the pressures are low enough for all the other phases there will be even 
more jumps of thermal expansion (*and* contraction). Meanwhile the core 
will melt. Now, low pressure plutonium melt will allow solid plutonium 
phases to float, but I think the high pressure plutonium near the core 
will actually be lighter than the beta phase and start melting its way 
up (or following the thermal expansion rifts): I expect some spectacular 
plutonium volcanism. The initial dynamics will be a fun mess of 
convection that likely make the above thermal conduction model irrelevant.

Now, the temperature difference between the core and the surface ought 
to produce some pretty vigorous convection despite the high viscosity. 
The Coriolis effect might actually cause interesting stirring of the 
upwelling plumes. So while swimming, look out for currents!


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.


On 02/12/2013 16:52, spike wrote:
>
> but somewhere in this discussion, I should
> offer a polite greeting to the local NSA agent who is wondering why I am
> googling about the internets wanting to learn about half-ife of plutonium,
> uranium and neptunium, so hello there Ms. or Mr. NSA agent!

Indeed. Hi there, NSA!


-- 
Anders Sandberg,
Future of Humanity Institute
Oxford Martin School
Faculty of Philosophy
Oxford University