Velocity of Aluminum vapor in a vacuum?

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James Lerch - 20 Oct 2007 06:54 GMT

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!

Signature

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 - 20 Oct 2007 14:03 GMT

> 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"

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 - 20 Oct 2007 19:37 GMT

>So, let's start with room temperature. That's about 20 degrees
>Celcius, so about 293 degrees Kelvin.
[quoted text clipped - 4 lines]
>energy per kilogram is around 135,000 joules. This
>corresponds to a velocity of about 520m/s.

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&C
FTOKEN=79259340&section=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..

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tadchem - 20 Oct 2007 22:52 GMT

> >So, let's start with room temperature. That's about 20 degrees
> >Celcius, so about 293 degrees Kelvin.

That may be the temperature of the hardware that contains the vacuum,
but that is not the temperature of the boiling aluminum. The aluminum
will boil at whatever temperature is appropriate for the absolute
pressure of the *contents* of the vacuum chamber, and remain at that
temperature until it strikes some object at a different temperature.

> >Each degree of Kelvin is equal to 12.47 Joules of energy
> >per mole, so that gives us 3654 joules per mole. A mole
[quoted text clipped - 32 lines]
> evaporation, so I think the velocity of Al will be relative to this
> temperature of vaporization, yes?)

Very good.

> Running with this assumption:
>
[quoted text clipped - 5 lines]
>
> 542,154J/kg = 0.5kg * v^2 = 1,041m/s

The kinetic molecular theory of gases ((chapter 2 or so in a good
textbook on Physical Chemistry) will recognize three distinct
"average" velocities from the distribution of velocities in a
Boltzmann gas of molecular mass m at temperature T (k is the Boltzmann
constant):

v(p) = sqrt(2*k*T/m) is the 'most probable' velocity of a given
molecule [molecules with this velocity outnumber molecules with any
other velocity]

v(avg) = sqrt(8*k*T/pi*m) is the 'average' velocity [half the
molecules have a higher velocity and half have a lower velocity]

v(rms) = sqrt(3*k*T/m) is the 'root-mean-square' velocity [molecules
with this velocity have average energy]

v(p) is the smallest, v(avg) is about 13% larger than v(p). and v(rms)
is about 22% larger than v(p). Always.

You are free to take the values of these constants (m, k, T, and P)
and plug them into the expressions to find out how fast the gaseous
aluminum atoms are moving. Please note that these are only average
speeds. Some molecules will be going MUCH faster.

For a gas at 173 K with a molecular weight of 26.98 g/mole I calculate
v(p) = 85027 cm/sec

However, this only applies when the gas can be treated as individual,
non-interacting molecules. If the dimensions of the vacuum chamber
exceed the mean free path of the gas molecules, then the individual
velocity of gas molecules (which only applies *in between* collisions
with other gas molecules, which serve to randomize the direction of
the velocity) then you must treat the gas as a bulk fluid. The
relevant velocity then becomes the speed of sound (the speed at which
a pressure wave travels through the gas cloud):
http://en.wikipedia.org/wiki/Speed_of_sound

v(sound) = sqrt(gamma*k*T/m)

For a monatomic gas such as aluminum vapor gamma is exactly 5/3,
giving us v(sound) equal to about 91% of v(p). When you think about
it, it should be obvious that a pressure wave in a gas cannot move
faster than the gas itself.

For may years I used a mass spectrometer which had a 30 cm ion path,
and thus required pressures of <10^-9 Torr to function properly.

> So at this point a person may wonder "How and Why did this topic come
> about?" So here's the story on that.
[quoted text clipped - 7 lines]
> materials is the next question, and apparently their is allot of
> Aluminum on the moon.

Yes. It is bound up as aluminum oxide, the same as here on earth.
Those oxides are themselves part of more complex pyroxenes - mixed
oxides of silica and aluminum.,

> So, the next question after that is "Assume a power source, and
> refining capability on the moon,

Currently aluminum can only be refined electrochemically. This
requires converting the aluminum into a form which not only allows the
individual movement of aluminum ions (a liquid) but the necessary
electric current to reduce the aluminum from the +3 oxidation state to
the 0 oxidation state. Since aluminum oxide is an insulator, some
anion must be introduced that forms an ionic melt with aluminum +3
ions. Usually this anion is fluoride.

> how do you get your finished product
> off the moon?"
>
> The above question lead to "What is lunar escape velocity

2.38 km/s
http://en.wikipedia.org/wiki/Moon
(Wiki can be a good friend)

> 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..

Your aluminum vapor will become a cloud which will rapidly disperse.

> Of course at this point, all semblance to reality departs and the rest
> of the conversation turns to coating inflated membranes with Al to
[quoted text clipped - 6 lines]
> Take Care,
> James Lerchhttp://lerch.no-ip.com/atm(My telescope construction,testing, and coating site)http://lerch.no-ip.com/ChangFa_Gen(My 15KW generator project)

Tom Davidson
Richmond, VA

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BradGuth - 30 Oct 2007 19:44 GMT

> > >So, let's start with room temperature. That's about 20 degrees
> > >Celcius, so about 293 degrees Kelvin.
[quoted text clipped - 143 lines]
>
> Your aluminum vapor will become a cloud which will rapidly disperse.

But there is already something of a cool mass at the moon's L1, that's
also highly electrostatic worthy to boot.
- Brad Guth -

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Natural Science Forum / Physics / General Physics / October 2007

Velocity of Aluminum vapor in a vacuum?