a) Talking about "stability" of a sample of uranium, large or small,
is silly. The answer is no, it's not stable. There are no stable
isotopes of uranium. (If you want to talk about criticality rather
than stability, that's discussed below.)
b) To suggest that uranium would be more stable at low temperatures is
insane. The reactivity of uranium goes *up* at low temperatures, over
a wide range of temperatures, from zero up to and beyond the boiling
point of metallic uranium.
c) ²³⁵U and ²³⁸U are mainly alpha emitters, if left alone, i.e. in the
absence of a chain reaction or other provocation. The energetic alphas
get stopped very near where they are created, and the energy gets
turned into heat.
The thermal conductivity of metallic uranium is pretty good but not
infinite. So the internally-generated heat has some trouble getting
out. For a sphere one meter in radius, I estimate the temperature in
the middle would be 3725 K, even if the outside is dead shorted to
zero kelvin. (You can get very nearly the right answer by dimensional
analysis. Or you can do the super-easy integral.)
That temperature is far above the melting point, and almost to the
boiling point. And it increases like r squared.
So a 4 meter diameter uranium sphere is impossible. It would destroy
itself faster than you could assemble it.
There was some mention of a 100 meter sphere. That is beyond
impossible ... for the most prosaic reasons, having nothing to do with
criticality or chain reactions or fission of any kind.
=================================
As a separate matter, it was claimed that a 100 meter sphere would
exceed the critical mass. That's actually not true, assuming we are
talking about standard (non-enriched) uranium.
By "standard" I mean the pure metallic element, with the present-day
natural abundance of isotopes:
99.3% ²³⁸U
0.7% ²³⁵U
(The ratio changes over geological timescales, so it's worth
specifying "present day".)
Here are some true facts:
1) Standard uranium will not go critical. If you tried to quantify the
critical mass, the answer would be "more than infinite", in the sense
that an infinite sample will be subcritical, with some margin to
spare.
2) Contrary to naïve intuition, uranium when it is less pure is more
reactive. In particular, to achieve a chain reaction with standard
uranium, you need a /moderator/. That's because the cross-section for
induced fission of ²³⁵U is orders of magnitude larger for slow
neutrons than fast neutrons.
3) ²³⁵U is fissile, whereas ²³⁸U is not. Indeed, ²³⁵U is the only
naturally-occurring fissile nuclide. In this context, fissile means you
can sustain a fission chain reaction.
Tangential remark: Actually you can induce fission in ²³⁸U using very
fast neutrons. Some large so-called "fusion" weapons (e.g. Ivy Mike)
get most of their energy from induced fission of ²³⁸U, using very fast
neutrons from a relatively small-scale fusion stage. Even so, the fact
remains that fission reactions don't produce enough such neutrons to
sustain a chain reaction in natural uranium.
4) If you want to make a reactor using natural uranium, with no
enrichment, you need a lot of uranium (and a lot of moderator). The
infamous RBMK design used at Chernobyl was big enough to use natural
uranium (although in practice it used slightly enriched fuel). It
contained about 190 tons of uranium dioxide and 2000 tons of graphite.
Size matters because you care about the "neutron economy". The more
neutrons that leak out the sides, the harder it is to achieve
criticality.
5) Light elements such as hydrogen, beryllium, and carbon make good
moderators. You can understand this in terms of high-school
kinematics. Energy transfer scales like recoil velocity /squared/.
In contrast, ²³⁸U is not a good moderator. For one thing, it's not
exactly a light element. More importantly, an incident neutron is
likely to be /absorbed/, creating ²³⁹U. In a few minutes that
beta-decays into ²³⁹Np, and in a couple days that beta-decays into
²³⁹Pu. The latter is fissile, but it takes /another/ neutron to induce
it to fission.
6) ²³⁵U, ²³⁸U, and ²³⁹Pu — if left alone — are mainly alpha emitters.
Alpha decay produces no free neutrons. There is some small chance of
spontaneous fission, but not much.
To achieve criticality, you have to rely on /induced/ fission. One
neutron in, two or three neutrons out.
Tangential remark: The small rate of spontaneous fission makes it a
bit tricky to /start/ a reactor the first time.
7) So, to an excellent first approximation, a sample of present-day
natural uranium just sits there and alpha-decays. The energetic alphas
get stopped very near where they are created, and the decay energy
gets converted to heat.
To a second approximation, some small percentage of the ²³⁵U will
spontaneously fission. The resulting neutrons will turn a small amount
of the ²³⁸U into ²³⁹Pu, but the chance of that nuclide catching a
/second/ neutron is at most small squared. Actually it's even less
than that, because the Pu decays almost as fast as you can make it. So
it doesn't hang around long enough to catch the second neutron.
²³⁵U : 704 million years
²³⁸U : 4500 million years
²³⁹Pu : 0.24 million years
8) The famous "natural reactor" at Oklo, Gabon did not involve the
pure metal. The uranium ore consists of pitchblende aka uraninite aka
UO₂ with some admixture of U₂O₃, along with a bunch of clay minerals
and other stuff. It is believed that criticality depended on
moderation by groundwater. It was therefore self-limiting, since if it
got too hot the moderator would boil off. Also note that the reaction
took place 1.7 billion years ago, when the percentage of ²³⁵U in
natural uranium was higher.
This was before the emergence of plants or animals of any kind, so it
wasn't as much of a biohazard as it could have been.
===============
Bottom line: If you have a moderate-sized chunk of standard uranium,
at the end of 700 million years you have lost half of your ²³⁵U with
not much to show for it except some helium and some heat.
A larger chunk will vaporize itself, not due to criticality, not due
to a chain reaction, not due to fission of any kind, but simply due to
the steady-state heating from spontaneous alpha decay.