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| James Lerch |
 Posted: Sat Oct 20, 2007 12:54 am |
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Guest
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Greetings Gents.
Given 25mg of aluminum heated via tungsten wire in a room temperature
vacuum chamber operating at 2x10-5 torr, what velocity would the
resulting Aluminum vapor atom have has it traveled thru the chamber on
its way to forming an optical coating?
Background on the question:
I built a vacuum chamber for coating front surface optical mirrors for
Newtonian telescopes. (call me a dedicated amateur, or insane, which
ever make you feel good)
The chamber is 0.6 meter x 0.6 meter x 0.3 meter, fabricated from 12mm
thick mild steel.
The filament used to heat the 25mg Al sample is 0.76mm in diameter,
40mm in length and glows cherry red to orange while the Al sample
evaporates. In total I have 18 filaments in the chamber used to coat
single optic.
I don't know what's needed to calculate the resultant velocity, and
mostly want to know because I was asked during a recent public
outreach event. My answer was "I don't know, I'd guess pretty damn
fast"
Any ball park answer would do, the question just got my curiosity
going, so here I am :)
Thanks for your time!
--
Take Care,
James Lerch
http://lerch.no-ip.com/atm (My telescope construction,testing, and coating site)
http://lerch.no-ip.com/ChangFa_Gen (My 15KW generator project)
"Anything that can happen, will happen" -Stephen Pollock from:
"Particle Physics for Non-Physicists: A Tour of the Microcosmos"
" Press on: nothing in the world can take the place of perseverance.
Talent will not; nothing is more common than unsuccessful men with talent.
Genius will not; unrewarded genius is almost a proverb.
Education will not; the world is full of educated derelicts.
Persistence and determination alone are omnipotent. " |
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| IsaacKuo |
| Posted: Sat Oct 20, 2007 8:03 am |
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Guest
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On Oct 20, 12:54 am, James Lerch <jle...@tampabay.no-spam-
seeds.rr.com> wrote:
[quote:d5584f8d39]Given 25mg of aluminum heated via tungsten wire in a room temperature
vacuum chamber operating at 2x10-5 torr, what velocity would the
resulting Aluminum vapor atom have has it traveled thru the chamber on
its way to forming an optical coating?
[...]
I don't know what's needed to calculate the resultant velocity, and
mostly want to know because I was asked during a recent public
outreach event. My answer was "I don't know, I'd guess pretty damn
fast"
[/quote:d5584f8d39]
The temperature of a gas is the average kinetic energy of each
particle. The mass of the particle in this case is the mass of an
aluminum atom. From this, we can determine the "average"
speed of an aluminum atom. By "average", we mean the
root-mean-square, if anyone asks...the square root of the
mean of the square of all the speeds. This is because
kinetic energy is proportional to the square of the speed.
So, let's start with room temperature. That's about 20 degrees
Celcius, so about 293 degrees Kelvin.
Each degree of Kelvin is equal to 12.47 Joules of energy
per mole, so that gives us 3654 joules per mole. A mole
of aluminum has a mass of about 27 grams, so the kinetic
energy per kilogram is around 135,000 joules. This
corresponds to a velocity of about 520m/s.
That's a speed of 1870km/hour, or 1170 miles per hour.
Just say over a thousand miles per hour.
Isaac Kuo |
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| James Lerch |
| Posted: Sat Oct 20, 2007 1:37 pm |
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On Sat, 20 Oct 2007 06:03:28 -0700, IsaacKuo <mechdan@yahoo.com>
wrote:
[quote:9eff6ca2b7]So, let's start with room temperature. That's about 20 degrees
Celcius, so about 293 degrees Kelvin.
Each degree of Kelvin is equal to 12.47 Joules of energy
per mole, so that gives us 3654 joules per mole. A mole
of aluminum has a mass of about 27 grams, so the kinetic
energy per kilogram is around 135,000 joules. This
corresponds to a velocity of about 520m/s.
[/quote:9eff6ca2b7]
Pretty certain I'll screw this up, but I'm going to attempt to use
your answers to figure out how you solved for it. If I can do that, I
can ask, and possible answer, my follow up question.
Via google 20c in kelvin= 293.15k
293k * 12.47J/mol = 3653 J/mol (12.47J/mol verified via wiki page on
Kinetic theory, btw saying I verified something via a Wiki page makes
me nervous.. :-)
Al atomic weight = 26.98154
kinetic energy per kilogram = 3653J/mol * (1/(26.98g/1000g)) =
135,397J/kg
From here http://www.unc.edu/~rowlett/units/dictJ.html , I learn that
kinetic energy is one half the mass times the square of the velocity.
In this case 135,397J/kg = 0.5kg * v^2 = 520m/s
Cool, I can replicate your answer, which now leads me to attempt to
answer my next question, which is "The above calculation is for room
temperature of ~20c. What is the calculated velocity for Aluminum at
the temperature for a given vapor pressure of 10e-5 torr?"
Going to my suppliers material deposition table, here:
http://www.lesker.com/newweb/Technical_Info/MaterialDeposition.cfm?CFID=236391&CFTOKEN=79259340§ion=materialdeptable&init=skip
I interpolate that Al has a temp of ~900c at a vapor pressure of 10e-5
torr. (10e-5 torr is the pressure my chamber is at during
evaporation, so I think the velocity of Al will be relative to this
temperature of vaporization, yes?)
Running with this assumption:
900c in kelvin = 1,173k
1,173k * 12.47J/mol = 14,627J/mol
14,627J/mol * (1/(26.98g/1000g)) = 542,154J/kg
542,154J/kg = 0.5kg * v^2 = 1,041m/s
So at this point a person may wonder "How and Why did this topic come
about?" So here's the story on that.
When you get a group of astrogeeks together, invariably the
conversation runs to the mental masturbation thought exercise of
returning to the moon, and what to do once you get there.
This invariable leads to the "Stepping stone to the stars" orgasm and
how a moon base would be a great place for raw materials. What raw
materials is the next question, and apparently their is allot of
Aluminum on the moon.
So, the next question after that is "Assume a power source, and
refining capability on the moon, how do you get your finished product
off the moon?"
The above question lead to "What is lunar escape velocity and exactly
how fast is the aluminum vapor in you vacuum chamber traveling?" With
the "wouldn't it be neat" what if idea of taking the pure Al metal,
heating it in the vacuum on the lunar surface into a vapor,
collimating the vapor into a parallel stream, then project the stream
of aluminum vapor to a receiving station at the Earth-Moon L1..
Of course at this point, all semblance to reality departs and the rest
of the conversation turns to coating inflated membranes with Al to
create pressure vessels, the transmission of energy from lunar to L1
via heat recovery from the cooling of the Al vapor, and all kinds of
other insanity 
Yes it was a fun thought, but I think its full of flaws..
--
Take Care,
James Lerch
http://lerch.no-ip.com/atm (My telescope construction,testing, and coating site)
http://lerch.no-ip.com/ChangFa_Gen (My 15KW generator project)
"Anything that can happen, will happen" -Stephen Pollock from:
"Particle Physics for Non-Physicists: A Tour of the Microcosmos"
" Press on: nothing in the world can take the place of perseverance.
Talent will not; nothing is more common than unsuccessful men with talent.
Genius will not; unrewarded genius is almost a proverb.
Education will not; the world is full of educated derelicts.
Persistence and determination alone are omnipotent. " |
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