What temperature means
Compilation. What temperature means
Date: Tue, 7 Mar 2006
From: Karrie Anderson, Chemistry Instructor, Kiel High School, Wisconsin
Subject: Temperature of One Molecule
Does the concept of temperature apply to one molecule? I really had to think on that (my
classes had a great debate), but I wanted to make sure that I was thinking correctly. I thought the
answer is no. Can anyone verify this for me?
-------------------Date: Thu, 9 Mar 2006
From: Andrew Schuetze, El Paso, Texas
Does the average K.E. concept of temperature break down when you have a set of just
one? Isn't the average of a set of one the K.E. of just that one item in the set? What else in your
models do I not have in my thought process that causes this to be a problem? Or maybe my
arithmetic is badly formed?
-------------------Date: Fri, 10 Mar 2006
From: Andy Edington, Mequon, WI
The problem we are seeing (with both quantum models and temperature-energy) is that
people forget the sequence: observation first, followed by model creation. Temperature is what
you measure with a thermometer. Everything else is simply a constructed model, which is why
the mathematical model becomes difficult to use at the parameter extremes. In this case, the
extreme of one molecule. Several people have said "students could understand this if they had
physics first." I disagree. My evidence is the number of teachers (including college professors)
who don't "get it."
If you have time to study the historical development of chemistry models and physics
models, you begin to understand some of the match-up difficulties. Sometimes the mathematical
models are just defined models set up strictly for calculation-tabulation-communication
convenience or for 'matching up' slightly different measurement methods or mathematical
models. The relationship of these defined mathematical models to visualizable physical models
is often tenuous or nonexistent. We also have mathematical models that are only valid for large
numbers of particles.
At this point I can't resist passing on some valuable wisdom I received from an 'elder
statesman of chemistry' when I first started teaching: "Remember, we are teaching high school
chemistry, not physical chemistry."
-------------------Date: Fri, 10 Mar 2006
From: Carmela Minaya, Hanalani Schools
Andrew Schuetze wrote:
Does the ave. K.E. concept of temperature break down when you have a set of just one?
Isn't the average of a set of one the K.E. of just that one item in the set….”
DavidMichael Boyer also wrote:
Yes, we sometimes idealize gas molecules as 'points', forgetting they are really not.
You spoke of the rotational KE. Are you are saying that Guy says the SUM of KE
linear and KE rotational comprise KE total? Also, in a 'single molecule system'
wouldn't the average KE be equal to the KE of the particle (just as the average of any
single value equals itself?)
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What temperature means
We are given to believe that the square of the velocity of the particle is proportional to
the average KE. How does this line up if the KE rot is part of the total package?
Finally, do you know how Guy explained the vibrational component? (in a non
monatomic). Can one further argue that vibrational motion is also Kinetic?
Consider a particle traveling, rotating AND BUMPING into something. (like a gas
molecule into a solid wall). Consider a model of this molecule having bonds that are
like springs. Would not collisions at certain angles increase vibrational KE while
rotational and/or translational are lowered?
The collision has to be perfectly elastic, so both momentum and KE are conserved.
Since the total energy is constant before and after the collision, I am now painted into a
corner for I now have a translationally SLOWER molecule than before. OK, I am
supposed to because some energy is shared with the wall. But wait, this is where the
'springs' come in. Energy was STORED as PE (compressing the 'springs') upon the
impulse, and released back to the molecule as KE.
If the molecule truly 'slowed down' translationally, it could conceivably reach a point
after subsequent collisions in which all KE is rot and vib. What is it's 'temperature'
now?"
Carmela Minaya responded:
David, you are right about the single molecule too, but we don't measure temperature
microscopically like that. We cannot measure macroscopically a single molecule system. In
chemistry modeling we are constantly relating the macroscopic observation to microscopic
behavior and diagramming the behavior of the multi-particle system with particle diagrams and
energy diagrams. That is, we don't have a thermometer sensitive enough to measure the
temperature of one atom or molecule, but we can and do measure temperature by implying the
motion of many, many, many particles. By the same token, we don't have a balance that can
measure the mass of one atom or molecule, but we can mass moles of atoms or moles of
molecules.
To me, there are parallels between looking at atomic or molecular behavior or amounts
theoretically and qualitatively and looking at them quantitatively through the mole or molar mass
and macro temperature, thereby making actual observations on that basis. Temperature is
looking at all of the particles and implying their behavior based on that observation; it's not
looking at only one particle.
My own personal belief is that we have to treat the system as multi-particulate and not as
a single molecule because we cannot physically measure a single particle. However, I suppose if
technology eventually enables us to measure a single particle system in chemistry, then this
discussion will become moot.
Your point about vibrational kinetic energy is true as well. The vibrational motion must
be considered as well as the linear motion on each possible plane. Bottom line from what I
learned in Guy's discussion, the temperature is really a probability related to the sum of all types
of motion. I'm not super clear on the math of it all, but I have a conceptual understanding. My
gut says if I understood geometric algebra better, then I could probably bring math into the
picture in a simpler form than calculus might currently allow. The types of motion that should
be considered are the ones that are relevant.
--------------------Date: Sat, 11 Mar 2006
From: Don Yost, Sacramento, CA
Just a thought: If you have one molecule and you are moving with it, with respect to
your frame of reference, the temperature must be zero. This situation could not exist with two or
more randomly moving molecules.
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What temperature means
-------------------Date: Sat, 11 Mar 2006
From: Jim Ford, a professor of Chemistry
This morning the discussion of the temperature of one molecule got to me. Temperature
is a measure of the translational energy of the molecules. We can see this when we heat various
ideal gases: diatomic gases have a higher heat capacity than monatomic ones. Our models
explain this by saying that some of the thermal energy being added is going into exciting the
rotational and vibrational motions. So while there is energy associated with, or stored, in these
other motions, they aren't measured by the thermometer stuck into the sample.
The modes will interact, occasionally, but on average, equal amounts of energy are in
each possible mode of storage. So while a vibrationally compressed bond might lose some of its
energy to translation on a collision, there's an equal possibility that a collision will excite a
vibrational mode and cause a decrease in the translational energy.
It all makes perfect sense.
So I hit the ‘Reply to List’ and began with "Temperature is a measure of the translational
energy of the molecules." This seemed adequate to me, but I felt it would benefit from additional
support. Surprisingly, I couldn't find exactly what I was looking for, online or on desk.
Reluctantly, I began to think. WHY is temperature a measure of just the translational energy?
How does the thermometer know? If rotating and/or vibrating molecules can donate energy to
translational modes (see above), why can't they donate that energy to the thermometer, and
thereby contribute to the measured temperature?
I suspect the answer lies in the thermodynamic definition of temperature, T = dq(rev)/dS.
Somewhere in late September we come up with T = dE/dS, and I'm sure that sheds light on this
whole thing. In fact, yeah, that's the ticket. I'd explain, but the margins are too small.
-------------------Date: Sun, 12 Mar 2006
From: Brenda Royce, University High, Fresno, CA
From our discussion last summer with Guy at ASU, the part that made sense to me
regarding why only translational Ek applies to temperature measurements (please correct me if
I'm mistaken) is that the transfer of energy to the thermometer requires collisions, and collisions
require translation.
Applying a 'balls connected by springs' model of a molecule to this, it seems to me that
the rotational and vibrational modes could affect the force of the collision at the point of contact
for a given molecule. But the energy transfer due to a collision during a vibrational stretch in a
bond or during a forward rotation relative to the collision - which should increase the impact
(and subsequent energy transfer) - would be offset by an equally probable collision during a
vibrational compression or rotational backward motion, which should decrease the impact of the
collision. So probability would dictate that the overall effect of the population of collisions is to
transfer energy (on average) by an amount proportional to the translational Ek only.
I'm sure there is more to this, but this seems to me like a reasonable starting place, and is
accessible to HS understanding (and this HS chemistry teacher).
-------------------Date: Mon, 13 Mar 2006
From: Larry Dukerich, Dobson High School, Arizona State University
The question on the worksheet: "Does the concept of temperature apply to a single
molecule? " was supposed to set up the discussion of the concept that temperature is a measure
of the average kinetic energy of a collection of molecules. This leads to the distribution of
kinetic energies of molecules at a given temperature.
------------------Date: Tue, 14 Mar 2006
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What temperature means
From:
Karrie Anderson, Chemistry Instructor, Kiel High School
My students had an excellent discussion of what temperature really is. We set up a "bob"
with a really long arrow of speed and decided what would happen if he hit a thermometer. As a
class (twice) decided that "bob"'s long arrow would need to be divided up equally among all of
the thermometer molecules. The temperature increase from this small increase in the
thermometer molecules would be extremely small and that it would not be representative of
"bob"'s actual speed.
I thought that they nailed it. They then brought up the fact that you must let a
thermometer sit in something for a bit for the temperature to be representative of what it is in.
Needless to say, I was impressed. I never understood temperature this well in school. Hurray for
modeling!!!!
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