Re: [Sci.nanotech] Nanofuture question
- From: "Perry E. Metzger" <perry@xxxxxxxxxxxx>
- Date: Wed, 05 Apr 2006 16:45:07 -0000
"Richard Poff" <richardpoff@xxxxxxxxxxxxxx> writes:
I am reading Josh Halls interesting book on this subject. I ran
across this fact noted in Chapter 12: "A spherical balloon of
diamond with two square meters of surface area would need to be less
than half a micron thick to hold sea level pressure". I wonder if a
balloon of this sort filled with nothing (ie a vaccuum) would also
be able to withstand sea level pressure without imploding.
If the balloon was filled with gas, it would not need any particular
strength to avoid implosion, since the inside gas pressure would
cancel the exterior gas pressure. The sentence in the book makes sense
only if one is speaking of an evacuated volume enclosed by a thin
shell of diamond.
I was also wondering how much the vacuum filled 'balloon' would
weigh,
That isn't hard to calculate. Note that you have a surface of two
square meters and a thickness of half a micron, which is to say, half
a millionth of a meter. Multiply and you will have the volume. Look up
the density of diamond and divide and you will know the mass.
I will leave the actual calculation as an exercise, not wanting to
take away anyone's fun, but I will note that the density of several
allotropes of carbon, including diamond, are on Wikipedia and can be
found in a few seconds.
and what would happen to it if you took it outside and let it go.
Objects that displace a mass of fluid or gas that exceeds their own
mass are buoyant, for quite obvious reasons.
Even without a calculator, one could easily guess that the balloon in
question would be buoyant. The mass it could lift at sea level can be
easily calculated by determining its volume (you know the surface area
and thus the volume is a simple bit of plugging in numbers), the mass
determined from the previous step, and the fact that most gases have
a molar volume of 22.4 litres at standard temperature and
pressure. (The atomic mass of nitrogen is about 14, and the atomic
mass of oxygen is about 16. For these purposes, if you just assume 75%
N and 25% O you'll be fine.)
The amount the balloon could carry would go down radically as the
atmosphere thins -- it can never exceed the height where the mass of
the system equals the mass of gas displaced. Thus, at a height where
the atmosphere is half as dense, the system can only have half the
mass. The height that a given balloon can attain is thus dependent on
how large a payload you attach.
Would this not be a useful method of moving things to the upper
atmosphere?
Balloons are already used for such purposes, so one doesn't have to
guess the answer to that.
Perry
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