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Andrew Usher
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 Posted: Fri Jul 25, 2008 12:11 am Post subject: Boltzmann>s constant is evil! |
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In science, I have always thought, equations benefit by being as
simple
as possible, without extraneous 'magic numbers'. This is a
justification
given for choosing the maetic system over English units (when a
rational
justification is used at all for that). And yet, Boltzmann>s constant
is
clearly such a 'magic number'.
For example, I write the Boltzmann function
f(E) = exp(-E/T)
where the standard way would be
f(E) = exp(-E/kT)
and the k serving as a meaningless constant or conversion factor.
More than that, it affects the notion of entropy, which is really
fundamental. More than physics, actually - entropy is a mathematical
concept at root, and therefore is always dimensionless. And yet,
idiot
thermodynamics force us to write 'J/mol-K'; as if those units matter
one
bit. Presenting a dimensionless number as otherwise is positively
misleading.
Heat capacity is also unitless, at least if measured on a molecular
basis, which is preferable at least for gases. I have given the
criterion
for convective stability
d log T / d log P = - 1/Cp
and this works only if Cp is dimensionless. Not only is this the
simplest
possible form but it expresses without words why it is correct, if
one
only looks at it.
Avogadro>s number is similar, and I believe things should never be
measured on a molar basis when they can reasonably be done on a
molecular
basis. The heats on chemical reactions, for example, can be given in
molecular units just as sensibly as in molar units. Indeed, electron
volts are already used for related purposes often by astrophysicists,
and
the band gap of solids is normally given in ev, and that is a
sort of chemical reaction. That unit also has a particular advantage
that
it is also used for the energy of photons, and therefore one can
correlate the two without the need of any conversion factor.
Andrew Usher |
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Andrew Usher
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| Posted: Fri Jul 25, 2008 6:00 am Post subject: Re: Boltzmann>s constant is evil! |
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On Jul 24, 11:09 pm, Salmon Egg <Salmon...@sbcglobal.net> wrote:
[quote]The concept of setting fundamental constants equal to one is an old
practice among theoretical physicists. Typically the speed of light, c,
and electron charge, among others, is set to one.
[/quote]
No, Boltzmann>s constant is not a 'fundamental constant', it is
a conversion factor. For comparison, the speed of light has units
(length/time) that can>t be defined away, though it can be set = 1.
Andrew Usher |
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Salmon Egg
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| Posted: Fri Jul 25, 2008 7:03 am Post subject: Re: Boltzmann>s constant is evil! |
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™™In article
<2453af29-1cbf-4648-adda-c543e4be44bd@v39g2000pro.googlegroups.com>,
Andrew Usher <k_over_hbarc@yahoo.com> wrote:
[quote]In science, I have always thought, equations benefit by being as
simple
as possible, without extraneous 'magic numbers'. This is a
justification
given for choosing the maetic system over English units (when a
rational
justification is used at all for that). And yet, Boltzmann>s constant
is
clearly such a 'magic number'.
For example, I write the Boltzmann function
f(E) = exp(-E/T)
where the standard way would be
f(E) = exp(-E/kT)
[/quote]
<snip> I just cannot read allof this and stay awake.
The concept of setting fundamental constants equal to one is an old
practice among theoretical physicists. Typically the speed of light, c,
and electron charge, among others, is set to one.
Bill |
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dlzc
Guest
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| Posted: Fri Jul 25, 2008 2:59 pm Post subject: Re: Boltzmann>s constant is evil! |
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On Jul 24, 11:00 pm, Andrew Usher <k_over_hb...@yahoo.com> wrote:
[quote]On Jul 24, 11:09 pm, Salmon Egg <Salmon...@sbcglobal.net> wrote:
The concept of setting fundamental constants equal
to one is an old practice among theoretical
physicists. Typically the speed of light, c, and
electron charge, among others, is set to one.
No, Boltzmann>s constant is not a 'fundamental
constant', it is a conversion factor. For
comparison, the speed of light has units
(length/time) that can>t be defined away, though it
can be set = 1.
[/quote]
C / Co = e( -tau / t )
Evil set to one.
David A. Smith |
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Lloyd
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| Posted: Fri Jul 25, 2008 7:49 pm Post subject: Re: Boltzmann>s constant is evil! |
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On Jul 24, 8:11 pm, Andrew Usher <k_over_hb...@yahoo.com> wrote:
[quote]In science, I have always thought, equations benefit by being as
simple
as possible, without extraneous 'magic numbers'. This is a
justification
given for choosing the maetic system over English units (when a
rational
justification is used at all for that). And yet, Boltzmann>s constant
is
clearly such a 'magic number'.
For example, I write the Boltzmann function
f(E) = exp(-E/T)
where the standard way would be
f(E) = exp(-E/kT)
and the k serving as a meaningless constant or conversion factor.
More than that, it affects the notion of entropy, which is really
fundamental. More than physics, actually - entropy is a mathematical
concept at root, and therefore is always dimensionless. And yet,
idiot
thermodynamics force us to write 'J/mol-K'; as if those units matter
one
bit. Presenting a dimensionless number as otherwise is positively
misleading.
Heat capacity is also unitless, at least if measured on a molecular
basis, which is preferable at least for gases. I have given the
criterion
for convective stability
d log T / d log P = - 1/Cp
and this works only if Cp is dimensionless. Not only is this the
simplest
possible form but it expresses without words why it is correct, if
one
only looks at it.
Avogadro>s number is similar, and I believe things should never be
measured on a molar basis when they can reasonably be done on a
molecular
basis.
[/quote]
Yeah, because if I have 100 mL of water and I want to know how much
heat it absorbs, or how much Na it will react with, figuring it out
per individual atom is so much more convenient! Not!
Why not price everything in pennies instead of dollars? Why not use
the wt of an atom as the standard and report your weight as xxx many
of those? Why not use the diameter of an atom as the standard for
length?
[quote]The heats on chemical reactions, for example, can be given in
molecular units just as sensibly as in molar units. Indeed, electron
volts are already used for related purposes often by astrophysicists,
and
the band gap of solids is normally given in ev, and that is a
sort of chemical reaction. That unit also has a particular advantage
that
it is also used for the energy of photons, and therefore one can
correlate the two without the need of any conversion factor.
Andrew Usher[/quote] |
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Andrew Usher
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| Posted: Fri Jul 25, 2008 8:19 pm Post subject: Re: Boltzmann>s constant is evil! |
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On Jul 25, 1:37 pm, Salmon Egg <Salmon...@sbcglobal.net> wrote:
[quote]In article
77cfdcfd-2e5b-4bb9-ac24-2438403ea...@n33g2000pri.googlegroups.com>,
Andrew Usher <k_over_hb...@yahoo.com> wrote:
No, Boltzmann>s constant is not a 'fundamental constant', it is
a conversion factor. For comparison, the speed of light has units
(length/time) that can>t be defined away, though it can be set = 1.
So the Boltzman constant has dimensions of energy/temperature. Big deal!
[/quote]
Wrong, 'temperature' is not a physical quantity. The Boltzmann
constant
is dimensionless.
Andrew Usher |
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Andrew Usher
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| Posted: Fri Jul 25, 2008 8:26 pm Post subject: Re: Boltzmann>s constant is evil! |
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On Jul 25, 1:49 pm, Lloyd <lpar...@emory.edu> wrote:
[quote]Avogadro>s number is similar, and I believe things should never be
measured on a molar basis when they can reasonably be done on a
molecular basis.
Yeah, because if I have 100 mL of water and I want to know how much
heat it absorbs, or how much Na it will react with, figuring it out
per individual atom is so much more convenient! Not!
[/quote]
For the first, it actually would be no harder to convert from
molecular
than molar quantities, though I wouldn>t insist on it. Your second
example is irrelevant, as is requires only ratios.
I maintain that an equation written like
2 H2 + O2 -> 2 H2O + 584 kJ/mol
is actually incorrect, while
2 H2 + O2 -> 2 H2O + 6.05 ev
is perfectly clear.
Andrew Usher |
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Andrew Usher
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| Posted: Fri Jul 25, 2008 11:21 pm Post subject: Are scientists really this DUMB? (was Re: Boltzmann>s consta |
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On Jul 25, 2:44 pm, Sam Wormley <sworml...@mchsi.com> wrote:
[quote]Andrew Usher wrote:
In science, I have always thought, equations benefit by being as
simple as possible, without extraneous 'magic numbers'.
See:http://en.wikipedia.org/wiki/Boltzmann_constant
http://scienceworld.wolfram.com/physics/BoltzmannEquation.html
http://scienceworld.wolfram.com/physics/Stefan-BoltzmannLaw.html
http://scienceworld.wolfram.com/physics/Maxwell-BoltzmannDistribution...
[/quote]
What the hell kind of reply is that? All those equations are indeed
simpler
without using Boltzmann>s constant, and theoretically more elegant.
Andrew Usher |
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Andrew Usher
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| Posted: Fri Jul 25, 2008 11:23 pm Post subject: Re: Boltzmann>s constant is evil! |
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On Jul 25, 2:45 pm, Sam Wormley <sworml...@mchsi.com> wrote:
[quote]Andrew Usher wrote:
The Boltzmann constant is dimensionless.
Andrew Usher
http://scienceworld.wolfram.com/physics/BoltzmannsConstant.html
[/quote]
Since energy and temperature have the same units, that is
dimensionless.
If you don>t believe me, try to calculate temperature in terms
of M, L, and T.
Andrew Usher |
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Salmon Egg
Guest
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| Posted: Sat Jul 26, 2008 12:37 am Post subject: Re: Boltzmann>s constant is evil! |
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In article
<77cfdcfd-2e5b-4bb9-ac24-2438403ea45e@n33g2000pri.googlegroups.com>,
Andrew Usher <k_over_hbarc@yahoo.com> wrote:
[quote]No, Boltzmann>s constant is not a 'fundamental constant', it is
a conversion factor. For comparison, the speed of light has units
(length/time) that can>t be defined away, though it can be set = 1.
[/quote]
So the Boltzman constant has dimensions of energy/temperature. Big deal!
Bill |
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Andrew Usher
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| Posted: Sat Jul 26, 2008 1:14 am Post subject: Re: Boltzmann>s constant is evil! |
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On Jul 25, 6:55 pm, Fred Kasner <fkas...@sbcglobal.net> wrote:
[quote]I maintain that an equation written like
2 H2 + O2 -> 2 H2O + 584 kJ/mol
is actually incorrect, while
2 H2 + O2 -> 2 H2O + 6.05 ev
is perfectly clear.
You apparently never bothered to stay awake during the single college
chemistry course you took. The equation 2H2 + O2 -> 2H2O + delta H is
well understood to be a NOT a molecular equation but a molar equation
[/quote]
That>s ridiculous semantics. Moles are only meaningful BECAUSE
they correspond to a certain number (an arbitrary magic number) of
atoms or molecules.
[quote]wherein the statements are: 2 moles of H2 react with one mole of O2 to
produce 2 moles of water plus some specific amount of heate stated in
kilojoules (or as it used to be in kilocalories).
[/quote]
Molecules are reacting. Moles are not a physically meaningful
concept.
[quote]As you wrote it it is
ambiguous as you can>t tell whether the number of moles refers to the H2
or the H2O or refers to the O2. You are either stupid, or careless, or
ill educated.
[/quote]
So you agree with me, then call me stupid etc. ? Wow.
Andrew Usher |
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Sam Wormley
Guest
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| Posted: Sat Jul 26, 2008 1:44 am Post subject: Re: Boltzmann>s constant is evil! |
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Andrew Usher wrote:
[quote]In science, I have always thought, equations benefit by being as
simple as possible, without extraneous 'magic numbers'.
[/quote]
See: http://en.wikipedia.org/wiki/Boltzmann_constant
http://scienceworld.wolfram.com/physics/BoltzmannEquation.html
http://scienceworld.wolfram.com/physics/Stefan-BoltzmannLaw.html
http://scienceworld.wolfram.com/physics/Maxwell-BoltzmannDistribution.html |
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Sam Wormley
Guest
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| Posted: Sat Jul 26, 2008 1:45 am Post subject: Re: Boltzmann>s constant is evil! |
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Andrew Usher wrote:
[quote]The Boltzmann constant is dimensionless.
Andrew Usher
[/quote]
http://scienceworld.wolfram.com/physics/BoltzmannsConstant.html |
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Andrew Usher
Guest
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| Posted: Sat Jul 26, 2008 3:00 am Post subject: Re: Boltzmann>s constant is evil! |
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On Jul 25, 8:41 pm, "Landy" <no...@nowhere.net> wrote:
[quote]"Andrew Usher" <k_over_hb...@yahoo.com> wrote in message
news:e91c4504-a1cc-44e8-89e2-8f1dbf40f704@x41g2000hsb.googlegroups.com...
On Jul 25, 2:45 pm, Sam Wormley <sworml...@mchsi.com> wrote:
Andrew Usher wrote:
The Boltzmann constant is dimensionless.
Andrew Usher
http://scienceworld.wolfram.com/physics/BoltzmannsConstant.html
Since energy and temperature have the same units, that is
dimensionless.
No they don>t. Energy is Joules and temperature is degrees (or Kelvins).
[/quote]
You snipped the important part of the post.
Here it is: If you don>t believe me, try to calculate temperature in
terms
of M, L, and T.
Andrew Usher |
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Andrew Usher
Guest
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| Posted: Sat Jul 26, 2008 4:29 am Post subject: Re: Are scientists really this DUMB? (was Re: Boltzmann>s co |
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On Jul 25, 9:42 pm, Sam Wormley <sworml...@mchsi.com> wrote:
[quote]Andrews, you are a bit short on education. Boltzmann>s constant has
physical units... And there are more base units than LMT, including
thermodynamic temperature.
[/quote]
I know all this. The physical dimension of Boltzmann>s constant is 1,
since both energy and temperature are ML^2/T^2.
[quote]http://physics.nist.gov/cuu/Units/units.html
Base quantity Name Symbol
------------------------------------------------
length meter m
mass kilogram kg
time second s
electric current ampere A
thermodynamic temperature kelvin K
amount of substance mole mol
luminous intensity candela cd
[/quote]
While the first four are derived from the physical quantities
M, L, T, and Q, the last three do not correspond to anything
physically real.
The candela, especially, is defined using the CIE
luminosity function for the eye. Even if it were a perfect
description of the human eye>s sensitivity, it obviously would
not be a fundamental quantity.
Andrew Usher |
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