# Average kinetic energy of the molecules in a cold liquid less?

DrClaude
Mentor
http://hyperphysics.phy-astr.gsu.edu/hbase/thermo/temper.html
which shows some complications using only kinetic energy as the only desigated definition of temperature for heat ransfer.
This is correctly written, but one has to pay attention to all the words:
Clearly, temperature has to do with the kinetic energy of the molecules, and if the molecules act like independent point masses, then we could define temperature in terms of the average translational kinetic energy of the molecules, the so-called "kinetic temperature". The average kinetic energy of the molecules of an object is an important part of the concept of temperature and provides some useful intuition about what temperature is. If all matter just consisted of independently moving point masses that just experienced elastic collisions with each other, that would be an adequate picture of temperature.

I guess the difference in the definition is only dependent on whether you choose to describe the system on a microscopic or macroscopic state, and whether the particles in the system exhibit ideal behavior or not.

jtbell
Mentor
calculating entropy in the first place requires the temperature to be known?
No. See the equation on Ludwig Boltzmann's gravestone:

(Nowadays I think most textbooks use the symbol Ω instead of W.)

Added: Ugh, I didn't notice the thread has a second page which already gives the equation. Oh well, it's a cool picture anyway.

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OmCheeto
sophiecentaur
Gold Member
This is correctly written, but one has to pay attention to all the words:

But that's the basis of the Kinetic theory that we all start with. It's only fair tp acknowledge that (albeit with a caveat or two). We discuss Newton's Laws of motion on PF, despite the fact that we know about Relativity.

russ_watters
Mentor
But that's the basis of the Kinetic theory that we all start with. It's only fair tp acknowledge that (albeit with a caveat or two). We discuss Newton's Laws of motion on PF, despite the fact that we know about Relativity.
Agreed. DrClaude, what struck me as odd was your initial incredulity on the issue - as if you'd never heard of the connection.

Anyway, i don't see a problem with using kinetic energy as an admittedly limited starting point. Then, you pull out the caveats as needed. To me, it is a lot better than using an empty/circular definition.

DrClaude
Mentor
Agreed. DrClaude, what struck me as odd was your initial incredulity on the issue - as if you'd never heard of the connection.
What probably got me started was the use of the the word defined, with emphasis, in PWiz' original reply (and please don't take this personally, PWiz). Temperature has never been defined as such.

But that's the basis of the Kinetic theory that we all start with. It's only fair tp acknowledge that (albeit with a caveat or two). We discuss Newton's Laws of motion on PF, despite the fact that we know about Relativity.
I disagree with your analogy in that historically, temperature was never based on kinetic theory. All of classical thermodynamics and even parts of statistical physics were developed with scientists not even agreeing on the existence of molecules.

Anyway, i don't see a problem with using kinetic energy as an admittedly limited starting point. Then, you pull out the caveats as needed. To me, it is a lot better than using an empty/circular definition.
This entire thread has made me think a lot about how the concept of temperature is taught. I have myself used the simplification that temperature is motion, but I think that at the moment one reaches university level on the subject, this should be abandoned, as my feeling is that it leads to a wrong way of thinking. I have even revisited threads on PF, in particular Can a single atom have a temperature? I agree with Vanadium's answer and more or less disagree with Baluncore answer.

Anyway, my intentions were purely pedagogical, so I hope at least one person reading my posts will have learned something. I hope this didn't go over the head of the OP, and maybe it would be time to close the thread as we have most probably veered off course from the original question.

PWiz and OmCheeto
OmCheeto
Gold Member
We had a minor run-in with "temperature" over on the latest "Ceres" thread. It was quite enlightening.

This might be a counterexample to sophiecentaur's quote; "The enemy of understanding is classification."
Temperature in the ISM may need a different classification.
I learned long ago that temperature was defined as; "The average internal translational kinetic energy", or something like that.
For solids, liquids, and gasses, this kind of makes sense to me.
It's the average jigglinesss.
I think it started, with a comment about the temperature of outer space, which led me to an interesting thread: Coldness of Space

Where I found that Marcus had described "temperature" as a bunch of photons in a box.

Which, I'm quite sure, is true, also.

so I hope at least one person reading my posts will have learned something.
I did. Thanks for sharing the knowledge!
and please don't take this personally, PWiz).
There is no "I" in objectivity; hopefully, I'll never take these things personally in the future too, because the day I do, I'll stop learning.