| Topic: |
Science > Physics |
| User: |
"" |
| Date: |
31 Jul 2006 05:22:29 AM |
| Object: |
Temperature and Pressure at atomic level? |
I am not a physicist.
I remember that temperature is average (RMS?) molecular velocity.
In that case, is it absurd to talk of temperature of an atom in most
cases? How about pressure?
Atomic world must be really weird where you can talk of Volume but not
of Temperature and perhaps Pressure!
TIA,
-Bhushit
.
|
|
| User: "tadchem" |
|
| Title: Re: Temperature and Pressure at atomic level? |
31 Jul 2006 03:51:56 PM |
|
|
wrote:
I am not a physicist.
I remember that temperature is average (RMS?) molecular velocity.
In that case, is it absurd to talk of temperature of an atom in most
cases? How about pressure?
"Temperature" is the *average* kinetic energy per particle.
"Pressure" is the average rate of transfer of momentum across a unit
area.
Atomic world must be really weird where you can talk of Volume but not
of Temperature and perhaps Pressure!
You can talk about the average number of times that a tossed coin will
come up heads being 0.5, but you will never see an individual toss
come up with 0.5 heads, and it won't tell you what will come up on the
*next* toss.
You simple cannot argue from statistics to individual cases, although
you can work in the other direction. Once you are talking about a
statisitical quantity you lose contact with the individual cases.
Tom Davidson
Richmond, VA
.
|
|
|
| User: "" |
|
| Title: Re: Temperature and Pressure at atomic level? |
31 Jul 2006 04:55:41 PM |
|
|
In article <1154379116.003026.227110@s13g2000cwa.googlegroups.com>, "tadchem" <tadchem@comcast.net> writes:
joshipura@gmail.com wrote:
I am not a physicist.
I remember that temperature is average (RMS?) molecular velocity.
In that case, is it absurd to talk of temperature of an atom in most
cases? How about pressure?
"Temperature" is the *average* kinetic energy per particle.
Not really, but will do for the current discussion.
"Pressure" is the average rate of transfer of momentum across a unit
area.
Atomic world must be really weird where you can talk of Volume but not
of Temperature and perhaps Pressure!
You can talk about the average number of times that a tossed coin will
come up heads being 0.5, but you will never see an individual toss
come up with 0.5 heads, and it won't tell you what will come up on the
*next* toss.
You simple cannot argue from statistics to individual cases, although
you can work in the other direction. Once you are talking about a
statisitical quantity you lose contact with the individual cases.
Tom Davidson
Richmond, VA
Mati Meron | "When you argue with a fool,
meron@cars.uchicago.edu | chances are he is doing just the same"
.
|
|
|
| User: "tadchem" |
|
| Title: Re: Temperature and Pressure at atomic level? |
31 Jul 2006 06:25:10 PM |
|
|
wrote:
In article <1154379116.003026.227110@s13g2000cwa.googlegroups.com>, "tadchem" <tadchem@comcast.net> writes:
joshipura@gmail.com wrote:
I am not a physicist.
I remember that temperature is average (RMS?) molecular velocity.
In that case, is it absurd to talk of temperature of an atom in most
cases? How about pressure?
"Temperature" is the *average* kinetic energy per particle.
Not really, but will do for the current discussion.
I chose not to confuse the non-physicist with reference to Bolzmann's
factor.
Tom Davidson
Richmond, VA
.
|
|
|
| User: "" |
|
| Title: Re: Temperature and Pressure at atomic level? |
31 Jul 2006 11:14:25 PM |
|
|
In article <1154388310.717519.88490@s13g2000cwa.googlegroups.com>, "tadchem" <tadchem@comcast.net> writes:
mmeron@cars3.uchicago.edu wrote:
In article <1154379116.003026.227110@s13g2000cwa.googlegroups.com>, "tadchem" <tadchem@comcast.net> writes:
joshipura@gmail.com wrote:
I am not a physicist.
I remember that temperature is average (RMS?) molecular velocity.
In that case, is it absurd to talk of temperature of an atom in most
cases? How about pressure?
"Temperature" is the *average* kinetic energy per particle.
Not really, but will do for the current discussion.
I chose not to confuse the non-physicist with reference to Bolzmann's
factor.
Yes, for sure, but that's not what I meant. That just falls under
"proportional to", not very interesting. Neither was it my intention
to get to more formal definitions involving derivativs of enthropy
with respect to energy and the like. So, staying away from exotic
stuff I would say "under common conditions temperature is proportional
to average energy per particle". Note, "energy", not "kinetic
energy". There is nothing separating kinetic energy from any other
kind, here.
It so happens that the first (and, unfortunately, often the last)
statistical physics example students encounter is this of an ideal
gas. In this specific case the *only* degrees of freedom are those of
translational motion and, therefore, the *only* energy present is
kinetic. So there, indeed, temperature is just the average kinetic
energy per particle. This, however, is just a very specail, very
simple case. Not the general one.
Mati Meron | "When you argue with a fool,
meron@cars.uchicago.edu | chances are he is doing just the same"
.
|
|
|
| User: "tadchem" |
|
| Title: Re: Temperature and Pressure at atomic level? |
01 Aug 2006 04:07:53 PM |
|
|
wrote:
<snip>
So, staying away from exotic
stuff I would say "under common conditions temperature is proportional
to average energy per particle". Note, "energy", not "kinetic
energy". There is nothing separating kinetic energy from any other
kind, here.
Yes there is. Motion.
It so happens that the first (and, unfortunately, often the last)
statistical physics example students encounter is this of an ideal
gas.
If they take physical chemistry (as *every* chemist must, and most
physicists *should*) they also get into rotational, vibrational, and
electronic partition functions, each of which freely exchanges energy
with the other forms, rapidly reaching thermal equilibrium - unless of
course the particles (atoms,. molecules, ions) are *maintained* in a
non-equilibrium state.
In this specific case the *only* degrees of freedom are those of
translational motion and, therefore, the *only* energy present is
kinetic. So there, indeed, temperature is just the average kinetic
energy per particle. This, however, is just a very specail, very
simple case. Not the general one.
At thermal equilibrium the temperature is the same for translation,
rotation, vibration, and electronic states. The energy levels will
differ, of course, but the distribution of particles among those energy
levels will be governed by Boltzmann statistics. Only in the cases in
which the spins of the particles becomes relevant to particle energy
will Bose-Einstein or Fermi-Dirac statistics come into play.
Tom Davidson
Richmond, VA
.
|
|
|
| User: "" |
|
| Title: Re: Temperature and Pressure at atomic level? |
01 Aug 2006 04:25:34 PM |
|
|
In article <1154466473.218041.267040@i42g2000cwa.googlegroups.com>, "tadchem" <tadchem@comcast.net> writes:
mmeron@cars3.uchicago.edu wrote:
<snip>
So, staying away from exotic
stuff I would say "under common conditions temperature is proportional
to average energy per particle". Note, "energy", not "kinetic
energy". There is nothing separating kinetic energy from any other
kind, here.
Yes there is. Motion.
It so happens that the first (and, unfortunately, often the last)
statistical physics example students encounter is this of an ideal
gas.
If they take physical chemistry (as *every* chemist must, and most
physicists *should*) they also get into rotational, vibrational, and
electronic partition functions, each of which freely exchanges energy
with the other forms, rapidly reaching thermal equilibrium - unless of
course the particles (atoms,. molecules, ions) are *maintained* in a
non-equilibrium state.
Yes, of course they reach equilibrium. None of this contradicts
anything I said.
In this specific case the *only* degrees of freedom are those of
translational motion and, therefore, the *only* energy present is
kinetic. So there, indeed, temperature is just the average kinetic
energy per particle. This, however, is just a very specail, very
simple case. Not the general one.
At thermal equilibrium the temperature is the same for translation,
rotation, vibration, and electronic states. The energy levels will
differ, of course, but the distribution of particles among those energy
levels will be governed by Boltzmann statistics. Only in the cases in
which the spins of the particles becomes relevant to particle energy
will Bose-Einstein or Fermi-Dirac statistics come into play.
Again, non of this contradicts anything I said.
If you'll say "the average kinetic energy of a particle equals (up to
proportionality coefficients etc.) the temperature", this is correct.
If you'll say "temperature is the the average kinetic energy of a
particle", this is misleading, since temperature can be many other
things as well.
Mati Meron | "When you argue with a fool,
meron@cars.uchicago.edu | chances are he is doing just the same"
.
|
|
|
| User: "tadchem" |
|
| Title: Re: Temperature and Pressure at atomic level? |
02 Aug 2006 04:39:09 AM |
|
|
wrote:
In article <1154466473.218041.267040@i42g2000cwa.googlegroups.com>, "tadchem" <tadchem@comcast.net> writes:
wrote:
<snip>
So, staying away from exotic
stuff I would say "under common conditions temperature is proportional
to average energy per particle". Note, "energy", not "kinetic
energy". There is nothing separating kinetic energy from any other
kind, here.
Yes there is. Motion.
It so happens that the first (and, unfortunately, often the last)
statistical physics example students encounter is this of an ideal
gas.
If they take physical chemistry (as *every* chemist must, and most
physicists *should*) they also get into rotational, vibrational, and
electronic partition functions, each of which freely exchanges energy
with the other forms, rapidly reaching thermal equilibrium - unless of
course the particles (atoms,. molecules, ions) are *maintained* in a
non-equilibrium state.
Yes, of course they reach equilibrium. None of this contradicts
anything I said.
In this specific case the *only* degrees of freedom are those of
translational motion and, therefore, the *only* energy present is
kinetic. So there, indeed, temperature is just the average kinetic
energy per particle. This, however, is just a very specail, very
simple case. Not the general one.
At thermal equilibrium the temperature is the same for translation,
rotation, vibration, and electronic states. The energy levels will
differ, of course, but the distribution of particles among those energy
levels will be governed by Boltzmann statistics. Only in the cases in
which the spins of the particles becomes relevant to particle energy
will Bose-Einstein or Fermi-Dirac statistics come into play.
Again, non of this contradicts anything I said.
If you'll say "the average kinetic energy of a particle equals (up to
proportionality coefficients etc.) the temperature", this is correct.
If you'll say "temperature is the the average kinetic energy of a
particle", this is misleading, since temperature can be many other
things as well.
Mati Meron | "When you argue with a fool,
meron@cars.uchicago.edu | chances are he is doing just the same"
So, please enlighten us all.
Assuming the presence of thermal equilibrium, in what more general case
is the average kinetic energy per particle *not* proportional to the
temperature? Or, alternatively, when is temperature *not* proportional
to the average kinetic energy per particle?
Tom Davidson
Richmond, VA
.
|
|
|
| User: "Edward Green" |
|
| Title: Re: Temperature and Pressure at atomic level? |
02 Aug 2006 07:05:33 PM |
|
|
tadchem wrote:
Assuming the presence of thermal equilibrium, in what more general case
is the average kinetic energy per particle *not* proportional to the
temperature? Or, alternatively, when is temperature *not* proportional
to the average kinetic energy per particle?
Ultra-cold particle in a box.
.
|
|
|
| User: "tadchem" |
|
| Title: Re: Temperature and Pressure at atomic level? |
03 Aug 2006 04:30:45 AM |
|
|
Edward Green wrote:
tadchem wrote:
Assuming the presence of thermal equilibrium, in what more general case
is the average kinetic energy per particle *not* proportional to the
temperature? Or, alternatively, when is temperature *not* proportional
to the average kinetic energy per particle?
Ultra-cold particle in a box.
Using a singular particle sort of takes the steam out of the word
"average", doesn't it?
Tom Davidson
Richmond, VA
.
|
|
|
| User: "G=EMC^2 Glazier" |
|
| Title: Re: Temperature and Pressure at atomic level? BH absolute Zero |
03 Aug 2006 09:08:24 AM |
|
|
Gravity creates heat(fusion of stars) Gravity takes away all heat. The
coldest spot of the cosmos is inside a black hole. Only gravity is
inside a black hole. There is not the smallest vibration(wave) of any
kind. It is gravity all the way down. Bert
.
|
|
|
| User: "=?UTF-8?Q?Jeff=E2=80=A6Relf?=" |
|
| Title: Nothing is hotter than Planck density/temperature. |
03 Aug 2006 10:50:46 AM |
|
|
Hi G_EMC_2_Glazier, Nothing is hotter than Planck density/temperature.
Ideal black holes don't exist, just as as ideal vacuums don't exist.
( Both involve infinite energy, which is impossible )
.
|
|
|
| User: "Phineas T Puddleduck" |
|
| Title: Re: Nothing is hotter than Planck density/temperature. |
03 Aug 2006 11:27:37 AM |
|
|
In article <Jeff_Relf_2006_Aug_3_8qMk@Cotse.NET>, Jeff’ĶRelf
<Jeff_Relf@Yahoo.COM> wrote:
Hi G_EMC_2_Glazier, Nothing is hotter than Planck density/temperature.
Ideal black holes don't exist, just as as ideal vacuums don't exist.
( Both involve infinite energy, which is impossible )
Jane Relf - shut up. You continually espouse this nonsense.
--
Relf's Law? -+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+
"***** repeated to the limit of infinity asymptotically approaches
the odour of roses."
Corollary -+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+
³It approaches the asymptote faster, the more Œpseduos¹ you throw in
your formulas.²
--
Posted via a free Usenet account from http://www.teranews.com
.
|
|
|
|
|
|
| User: "Edward Green" |
|
| Title: Re: Temperature and Pressure at atomic level? |
03 Aug 2006 05:46:05 PM |
|
|
tadchem wrote:
Edward Green wrote:
tadchem wrote:
Assuming the presence of thermal equilibrium, in what more general case
is the average kinetic energy per particle *not* proportional to the
temperature? Or, alternatively, when is temperature *not* proportional
to the average kinetic energy per particle?
Ultra-cold particle in a box.
Using a singular particle sort of takes the steam out of the word
"average", doesn't it?
Consider an ensemble, or a single system averaged over time, occupying
energy levels in accordance with some small positive T.
.
|
|
|
|
|
|
|
| User: "" |
|
| Title: Re: Temperature and Pressure at atomic level? |
02 Aug 2006 05:07:46 AM |
|
|
In article <1154511549.700037.197820@p79g2000cwp.googlegroups.com>, "tadchem" <tadchem@comcast.net> writes:
mmeron@cars3.uchicago.edu wrote:
In article <1154466473.218041.267040@i42g2000cwa.googlegroups.com>, "tadchem" <tadchem@comcast.net> writes:
mmeron@cars3.uchicago.edu wrote:
<snip>
So, staying away from exotic
stuff I would say "under common conditions temperature is proportional
to average energy per particle". Note, "energy", not "kinetic
energy". There is nothing separating kinetic energy from any other
kind, here.
Yes there is. Motion.
It so happens that the first (and, unfortunately, often the last)
statistical physics example students encounter is this of an ideal
gas.
If they take physical chemistry (as *every* chemist must, and most
physicists *should*) they also get into rotational, vibrational, and
electronic partition functions, each of which freely exchanges energy
with the other forms, rapidly reaching thermal equilibrium - unless of
course the particles (atoms,. molecules, ions) are *maintained* in a
non-equilibrium state.
Yes, of course they reach equilibrium. None of this contradicts
anything I said.
In this specific case the *only* degrees of freedom are those of
translational motion and, therefore, the *only* energy present is
kinetic. So there, indeed, temperature is just the average kinetic
energy per particle. This, however, is just a very specail, very
simple case. Not the general one.
At thermal equilibrium the temperature is the same for translation,
rotation, vibration, and electronic states. The energy levels will
differ, of course, but the distribution of particles among those energy
levels will be governed by Boltzmann statistics. Only in the cases in
which the spins of the particles becomes relevant to particle energy
will Bose-Einstein or Fermi-Dirac statistics come into play.
Again, non of this contradicts anything I said.
If you'll say "the average kinetic energy of a particle equals (up to
proportionality coefficients etc.) the temperature", this is correct.
If you'll say "temperature is the the average kinetic energy of a
particle", this is misleading, since temperature can be many other
things as well.
Mati Meron | "When you argue with a fool,
meron@cars.uchicago.edu | chances are he is doing just the same"
So, please enlighten us all.
Assuming the presence of thermal equilibrium, in what more general case
is the average kinetic energy per particle *not* proportional to the
temperature? Or, alternatively, when is temperature *not* proportional
to the average kinetic energy per particle?
I did not say that it is not proportional. Mmind you, cases like this
can be easily found, when you're tlaking about the electrons in solid,
then even under normal conditions the distribution is not even close
to MB, in fact it is Fermi-Dirac to a good approximation. But I do
not intend to engage in nitpicking here. All I mean here is that
there is a difference between "the tmeperature is proportional to the
mean kinetic energy ..." and "the temperature *is* the mean kinetic
energy". The first is fine for most standard situations, the second
conveys the meaning that temperature represents kinetic energy alone,
which is false. Not a big problem for those who know what they're
doing but the second has the potential to completely mislead laymen,
and laymen constitute a big part of the crowd here.
Mati Meron | "When you argue with a fool,
meron@cars.uchicago.edu | chances are he is doing just the same"
.
|
|
|
| User: "tadchem" |
|
| Title: Re: Temperature and Pressure at atomic level? |
02 Aug 2006 05:48:54 PM |
|
|
wrote:
<snip>
But I do
not intend to engage in nitpicking here. All I mean here is that
there is a difference between "the tmeperature is proportional to the
mean kinetic energy ..." and "the temperature *is* the mean kinetic
energy".
....as long as you are not nit-picking...
<grin>
Tom Davidson
Richmond, VA
.
|
|
|
|
|
|
|
| User: "Aristotle Eisenglas" |
|
| Title: Re: Temperature and Pressure at atomic level? |
03 Aug 2006 11:23:34 AM |
|
|
wrote:
Yes, for sure, but that's not what I meant. That just falls under
"proportional to", not very interesting. Neither was it my intention
to get to more formal definitions involving derivativs of enthropy
with respect to energy and the like. So, staying away from exotic
stuff I would say "under common conditions temperature is proportional
to average energy per particle". Note, "energy", not "kinetic
energy". There is nothing separating kinetic energy from any other
kind, here.
It so happens that the first (and, unfortunately, often the last)
statistical physics example students encounter is this of an ideal
gas. In this specific case the *only* degrees of freedom are those of
A has the meaning that temperature represents kinetic energy
alone, which is false. You added the caveat "in the absence of
friction". That contention is false. Point me to the airport.
The driver began, "You a physicist?
Does this make sense or am I missing something?
.
|
|
|
|
|
| User: "tj Frazir" |
|
| Title: Re: Temperature and Pressure at atomic level? |
31 Jul 2006 11:53:12 PM |
|
|
equal to the force it takes to pull it aapart.
.
|
|
|
|
|
|
|
| User: "" |
|
| Title: Re: Temperature and Pressure at atomic level? |
31 Jul 2006 06:49:41 AM |
|
|
wrote:
I am not a physicist.
I remember that temperature is average (RMS?) molecular velocity.
In that case, is it absurd to talk of temperature of an atom in most
cases? How about pressure?
Atomic world must be really weird where you can talk of Volume but not
of Temperature and perhaps Pressure!
TIA,
-Bhushit
There are properties of a single system such as an atom, then there are
properties of vast collections of those systems, such as a gas, which
are emergent upon the metasystem transition. Cybernetics 101.
.
|
|
|
|
| User: "" |
|
| Title: Re: Temperature and Pressure at atomic level? |
31 Jul 2006 12:03:14 PM |
|
|
In article <1154341349.742736.19280@i42g2000cwa.googlegroups.com>, writes:
I am not a physicist.
I remember that temperature is average (RMS?) molecular velocity.
Not quite but close enough for the present topic.
In that case, is it absurd to talk of temperature of an atom in most
cases?
Indeed.
How about pressure?
Same. Both temperature and pressure are statistical properties,
characterizing large ensambles of atoms, no single atoms.
Atomic world must be really weird where you can talk of Volume but not
of Temperature and perhaps Pressure!
That's the least of the weirdness.
Mati Meron | "When you argue with a fool,
meron@cars.uchicago.edu | chances are he is doing just the same"
.
|
|
|
|
| User: "" |
|
| Title: Re: Temperature and Pressure at atomic level? |
08 Aug 2006 05:02:42 AM |
|
|
Now my other questions:
As it does not make sense to talk of pressure or temperature over a
single atom, can we say
PV=nRT
and its refinements go on losing meaning as we talk about smaller and
smaller volume?
Thus, the gas laws apply for some "big enough" volume.
One symmetry question: If laws can't be applied to some smallest
volume, can they be applied only till a largest volume? i.e. the gas
laws apply for some "small enough" volume too?
Then another symmetry question: Are there conditions where only
pressure makes sense and V and T don't? Or only temperature makes sense
and P and V don't?
-Bhushit
joshipura@gmail.com wrote:
I am not a physicist.
I remember that temperature is average (RMS?) molecular velocity.
In that case, is it absurd to talk of temperature of an atom in most
cases? How about pressure?
Atomic world must be really weird where you can talk of Volume but not
of Temperature and perhaps Pressure!
TIA,
-Bhushit
.
|
|
|
| User: "" |
|
| Title: Re: Temperature and Pressure at atomic level? |
08 Aug 2006 04:26:02 PM |
|
|
In article <1155031362.801865.5200@i42g2000cwa.googlegroups.com>, writes:
Now my other questions:
As it does not make sense to talk of pressure or temperature over a
single atom, can we say
PV=nRT
and its refinements go on losing meaning as we talk about smaller and
smaller volume?
Yep.
Thus, the gas laws apply for some "big enough" volume.
As it stands, yes.
One symmetry question: If laws can't be applied to some smallest
volume, can they be applied only till a largest volume? i.e. the gas
laws apply for some "small enough" volume too?
No, there is no such limitation.
Then another symmetry question: Are there conditions where only
pressure makes sense and V and T don't? Or only temperature makes sense
and P and V don't?
No, not really. Volume is a geometric property and it always makes
sense. Both pressure and temperature, on the other hand, are
statistical properties of an ensamble, and represent the ensamble
better and better as the number of degrees of freedom grows.
Mati Meron | "When you argue with a fool,
meron@cars.uchicago.edu | chances are he is doing just the same"
.
|
|
|
|
|
|
Related Articles |
|
|
