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slartibartfasz
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PostPosted: Tue Jun 24, 2003 5:59 pm    Post subject: physic/chemistry/math wizzards - solve this... Reply with quote

in order to compute the viscosity of gas mixtures at various temperatures i need to determine the reduced dipol momentum of a substance. in namly formula i have to use* the dipol momentum of the substance in a very strange unit:

1 Debye = 10^-18 * SQRT(10^-13 J m^3) 8O

this seems to be correct since i get sensible results when looking at the resulting unit and the computed values are within 1 or 2% of the measured values.

my problem is that i simply cannot see how the above unit conversion can be achieved. i've read through all definitions i could find, trashed more paper, than a whole forest can deliver and emptied several pens. but still ... how :?: i'm sure its not really complicated it just has a vicious twist somwhere...i'm curious if and how fast this one gets solved here :)

links:
http://physics.nist.gov/Pubs/SP811/appenB8.html
http://www.bipm.fr/enus/welcome.html
http://physics.nist.gov/cuu/Units/
http://www.chemie.fu-berlin.de/chemistry/general/si_en.html

^...power
SQRT()...square root
Debye...Unit of the dipol momentum [C*m]
J...Joule [kg m^2 s^-2]


* formulas and units are out of the VDI Wärmeatlas (german) - the german standard book for everything concerning engineering and heat...

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far
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PostPosted: Tue Jun 24, 2003 6:32 pm    Post subject: Reply with quote

sqrt(kg * m^5 * s^-2) is not equal to A * s * m
It does not make sense. Perhaps the constants in the expression have units?
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slartibartfasz
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PostPosted: Tue Jun 24, 2003 6:53 pm    Post subject: Reply with quote

far wrote:
sqrt(kg * m^5 * s^-2) is not equal to A * s * m
It does not make sense. Perhaps the constants in the expression have units?


seconded - it doesnt seem to make sense...

but if i look up a dipol momentum somewhere [D], mangle it through this and use the resulting value i get a correct solution in the numerical and the unit context. if i use sqrt(J m^3) as a unit in the formula of the reduced dipol momentum, i get an dimensionless figure, which looks sensible to me for a 'reduced' figure.

there has to be some connection...

i put part of my work on my server (pdf) - the formula in question is in the first line page 4 - its not corrected yet, i'm sure there are some errors in the text.
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PostPosted: Tue Jun 24, 2003 7:07 pm    Post subject: Reply with quote

Firstly the formule u gave is not very vivid,

Is this somekind of proofing question?, looks like u have to use dipol equition which i dont really like to see the shape to find "viscosity" and by entering the variables and constants base on your gas mixture condition then all you have to do is twist them until the formula match

just a theory
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far
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PostPosted: Tue Jun 24, 2003 7:13 pm    Post subject: Reply with quote

slartibartfasz wrote:
i put part of my work on my server (pdf) - the formula in question is in the first line page 4 - its not corrected yet, i'm sure there are some errors in the text.

Is this what you are referring to?
Code:
were <foo> is the reduced dipol momentum ...

It doesn't look like the one above.

It is "where <foo> is the reduced dipole moment," btw.
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slartibartfasz
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PostPosted: Tue Jun 24, 2003 7:42 pm    Post subject: Reply with quote

far wrote:
Is this what you are referring to?
Code:
were <foo> is the reduced dipol momentum ...

It doesn't look like the one above.


yes - the thing above is the unit of mu to be used in <foo> - its only a small note in the book. its not in the text because i noticed it after i did the first test with a prog i wrote. it turned out that i have to use the dipol moment in the exact unit of my original post to get a correct result...

[EDIT:] if u take <foo> (the reduced dipol moment) and assume that the dipol moment (mu) has the dimension on the right side of the first equation in this thread u will see that <foo> becomes dimensionless as it should be for a 'reduced' value

Quote:

It is "where <foo> is the reduced dipole moment," btw.


thx - technical terms can be quite tricky...

@vers_iq:

yes it is a proof-question. i know that the rest works and i actually get correct results for mixtures of 15 different gases and temperatures higher than 1000°C... what i dont know is WHY it is correct - i understand every single step involved save the unit of the dipol moment ---> see first post
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PostPosted: Tue Jun 24, 2003 8:10 pm    Post subject: Reply with quote

slartibartfasz wrote:
[EDIT:] if u take <foo> (the reduced dipol moment) and assume that the dipol moment (mu) has the dimension on the right side of the first equation in this thread u will see that <foo> becomes dimensionless as it should be for a 'reduced' value

:?
Here is <foo>: mu_R = mu^2 * p_c / (k * T_c)^2
Lets start with the denominator. I am assuming that k is Boltzmann's constant and that T_c is a temperature, then the denominator is J^2.
If mu^2 is J * m^3 then if mu_R is supposed to be dimensionless, p_c must be J / m^3 (energy density?)

Where does Debye and the electric moment come into this? Does it have anything at all to do with electromagnetism?
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PostPosted: Tue Jun 24, 2003 8:45 pm    Post subject: Reply with quote

far wrote:

Here is <foo>: mu_R = mu^2 * p_c / (k * T_c)^2
Lets start with the denominator. I am assuming that k is Boltzmann's constant and that T_c is a temperature, then the denominator is J^2.
If mu^2 is J * m^3 then if mu_R is supposed to be dimensionless, p_c must be J / m^3 (energy density?)


k...boltzmann constant [J/K]
T_c...critical temperature [K]
p_c...critical pressure [bar]
assume mu^2.... [J m^3]

exactly - only p_c can be written as N/m^2 because of course 1J=N*m

Quote:
Where does Debye and the electric moment come into this? Does it have anything at all to do with electromagnetism?


thats my question ;) - if i would not have found the strange unit conversion from the first post, i would have inserted the dipol moment mu in Debye [C*m] which is clearly wrong. the formula only works if i use mu as [SQRT(J m^3)] and this is the step i dont understand.

the general influence of the dipol moment is clear - it influences the way gas molecules bump into each other ---> influences friction ---> influences viscosity. i just dont know why the equation in the first post is correct - and as u may have noticed i hate to work with math i dont understand ;)
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Last edited by slartibartfasz on Tue Jun 24, 2003 8:47 pm; edited 1 time in total
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PostPosted: Tue Jun 24, 2003 8:46 pm    Post subject: Reply with quote

Well, here's the dipole momentum per mol (Jackson Eq. 4.81):
Code:
p_mol=1/3*p_0^2*E/kT

where p_0 is the permanent dipole moment of a single molecule in the fluid, E is applied electric field and T is the absolute temperature . Obviously, the units work out if you consider that the units of E is J/C/m in SI.

Hope that helps ... are you trying to derive the permanent dipole moment, which would be related to the local electrodynamics, and hence the viscosity? If you invert the formula above, it looks something like your original formula ...
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PostPosted: Tue Jun 24, 2003 9:00 pm    Post subject: Reply with quote

Hypnos wrote:
Well, here's the dipole momentum per mol (Jackson Eq. 4.81):
Code:
p_mol=1/3*p_0^2*E/kT

where p_0 is the permanent dipole moment of a single molecule in the fluid, E is applied electric field and T is the absolute temperature . Obviously, the units work out if you consider that the units of E is J/C/m in SI.


this looks great :D - can u please give me the whole citation of the book (or enough that i can find it)... this the best hint i found so far - thx a lot :D
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PostPosted: Tue Jun 24, 2003 9:05 pm    Post subject: Reply with quote

slartibartfasz wrote:
this looks great :D - can u please give me the whole citation of the book (or enough that i can find it)... this the best hint i found so far - thx a lot :D


I'm a silly physicist -- I thought "Jackson Eq. 4.81" would be more than sufficient! :P

_Classical Electrodynamics_, Jackson, John David, 2nd edition, John Wiley & Sons, New York (1975).

Some notes:

* There is a newer, 3rd edition, which is partly in SI units (2nd edition is all in Gaussian, i.e. "God's units.")

* Jackson is a professor emeritus here, and he's somewhat intimidating. :D
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PostPosted: Tue Jun 24, 2003 9:14 pm    Post subject: Reply with quote

Hypnos wrote:
I'm a silly physicist -- I thought "Jackson Eq. 4.81" would be more than sufficient! :P


hehe - i am a chemist - i dimly recall that i had to sign a paper - vowing never to learn anything a physicist might call standard electrodynamics *urg* - but i have to admit that i may be handy from time to time :)

thx again - i keep u updated if i figure it out completely - tomorrow...
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PostPosted: Wed Jun 25, 2003 12:47 am    Post subject: Reply with quote

42
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PostPosted: Wed Jun 25, 2003 4:22 am    Post subject: Reply with quote

carambola5 wrote:
42


LOL

that was - of course - the first thing i tried :P
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