Temperature

studiot

Joined Nov 9, 2007
4,998
Specific heats, as derived by Bill's equation, only work for monatomic molecules. this is because the only place for monatomic molecules to 'put' their energy is into the kinetic energy of motion.

As soon as we have a polyatomic molecule energy can be distributed into other modes such as stretching, vibration and rotation of the bonds.

Unfortunately things get more complicated than this because the dear old Quantum Theory rears its head at this point and requires that the specific heats of polyatomic molecules ivary with temperature, whereas in a purely mechanical model they remain constant.

Some real world values for Cv are


Monatomic helium..............12.48 ; 12.48

Diatomic oxygen................21.05 ; 21.79

Triatomic hydrogen dioxide...25.25 ; 25.93

Triatomic carbon dioxide.......28.81 ; 33.00

all figures in joules per degree K per mole. the first at 298°K and the second at 400°K in each case.
 

studiot

Joined Nov 9, 2007
4,998
OK Bill, so let me expand upon my iceberg for you to comment further.

On the iceberg there are three igloos.
I have filled each igloo with carbon dioxide and sealed the entrance.

If I told you that the average speed of the carbon dioxide molecule in igloo A is 362.5 metres per second how would you use that information to calculate which way the heat flowed, from the carbon dioxide to the ice or from the ice to the carbon dioxide. The corresponding average speed for a water molecule is 566.5 m/sc.

Personally I would prefer to be told that the gas in igloo A is at 273°K ( the temp of ice) to say that they are in equilibrium and no heat flows either way.

Similarly I would prefer to know that
The gas in igloo B is at 263°K so the heat flows from the igloo to the gas
and
The gas in igloo C is at 283°K so the heat flows from the gas to the igloo.
 

BillO

Joined Nov 24, 2008
999
I can only comment that I agree with everything you said in your last two posts. I hope I've not given the impression that I don't.

I still stand by the notion that temperature is a measure of average thermal energy at the microscopic scale and I agree that life would be very difficult if we did use it in that form for our calculations.

Being able to represent things in a different and more useful way is one of the wonderful things about nature in the greatest sense.

Representing and using temperature the way we do rather than using some gawdawful expression for it is not exactly like but somewhat analogous to replacing C with 1 in relativistic calculations.

I'm fuly sold on the merit of both.
 

studiot

Joined Nov 9, 2007
4,998
Bill,

Are you aware of the Lubeck conference of 1895?

I find it fascinating that you are using the equations of one side (the atomists) to put forward the arguments of the other (energetics).

How also do you square the assigning of a temperature, other than absolute zero, to free space where there are no molecules? And what about the pyrometric measurement of the temperature of a black cavity, where again there are no molecules.


Surely the great triumph is, as I said earlier, the fact that science has been able to demonstrate the equivalence of this entity temperature in different branches (mechanical, thermodynamic, quantum etc) and produce a single consistent scale.

Nor is it unique to employ scales based upon comparison. Hardness scales are such. Although these are based on surface energy, there are other factors in play so that SE alone does not determine hardness.
 

BillO

Joined Nov 24, 2008
999
Are you aware of the Lubeck conference of 1895?

You mean the one where the 'Energetics' got a sound thrashing from Boltzman? I’m aware of it but not versed in the proceedings.

I find it fascinating that you are using the equations of one side (the atomists) to put forward the arguments of the other (energetics).

Unintentional I assure you. My choice of equations was for brevity and my argument is to show that temperature is a measure (of sorts) of average energy.

How also do you square the assigning of a temperature, other than absolute zero, to free space where there are no molecules? And what about the pyrometric measurement of the temperature of a black cavity, where again there are no molecules.

Well, I wasn’t going to attempt these, but isn’t T related to the average photon energy in these cases? Or, if you prefer, the intensity of the wavelength distribution?

Surely the great triumph is, as I said earlier, the fact that science has been able to demonstrate the equivalence of this entity temperature in different branches (mechanical, thermodynamic, quantum etc) and produce a single consistent scale.

Nor is it unique to employ scales based upon comparison. Hardness scales are such. Although these are based on surface energy, there are other factors in play so that SE alone does not determine hardness.




Fully agreed on these.

On another point studiot, how have you been affected by the recent heavy snowfalls?
 

studiot

Joined Nov 9, 2007
4,998
The 'Atomists' believed in the existance of fundamental particles which really had mass, momentum etc. They (Boltzmann) were able to derive the relationship you posted, between the average kinetic energy of these particles and the gas law temperature for an ideal gas.

'Energeticists', however saw the world as based entirely upon transformations and flows of energy. The atomic model was regarded as a useful mathematical model that got some right answers, but no more.

I suspect you can't have one without the other.

Let us suppose I want to do away with mass as a fundamental quantity. Could I derive an 'average mass' (in principle) by taking the sume of all the mass in the universe and dividing by the number of particles?

As regards to snow,
What snow?

15 years ago I did a spell as Winter Maintenace Engineer for the Motorway net in this area and we never had such nonsense, though we did have some snow. It never happened on my watch brother.
 

BillO

Joined Nov 24, 2008
999
Let us suppose I want to do away with mass as a fundamental quantity. Could I derive an 'average mass' (in principle) by taking the sume of all the mass in the universe and dividing by the number of particles?
I suppose you could, but even I would doubt the application and validity of such a number. You'd need to adjust for the 'empty' space and all the energy not already bound in mass. You'd get a number....

As regards to snow, What snow?
I had heard, just after getting up on my roof for the third time this winter to clear off a metre of the stuff, that parts of England were experiencing record snowfalls. I was born in Ireland. We never got more than a few cm in Bray, and then it only lasted a day to two.
 

studiot

Joined Nov 9, 2007
4,998
We had a lovely holiday in Ireland last year, principally in the Burren.

Yes we've had a few flurries and some isolated places are snowed up in the hills, as happens most years. But there has also been significant over reaction, egged on by over excited media.

Since we are shooting the breeze consider these propositions.

Temperature is clearly connected with energy. To increase temperature you have to add energy (heat it up).

Now enter the atomic theory, then considered as small, but finite, hard balls.

It was quite an inspired leap to attribute the energy uptake to the KE of these balls and the pressure to the momentum tranfer due to impact.

For instance if we heat something material up we know it expands. We can equate the take up of heat energy to the increase in strain energy.

So it would not have been unreasonable to propose that at an 'atomic' level the heat added should be equated to an expansion of each individual ball, not increased speed and therfore KE.

And if they had wanted to consider energy of motion, why not propose that the balls are spinning and just spin faster?
 

thingmaker3

Joined May 16, 2005
5,083
Getting back to the notion of "Joules per mole," would we have to use separate numbers for separate substances at the same Kelvin temperature?
 

BillO

Joined Nov 24, 2008
999
We had a lovely holiday in Ireland last year, principally in the Burren.
Beautiful landscape up in county Clare. If you liked that you would love Newfoundland. All along the coast, especailly in the Twillingate area, just spectacular.


Temperature is clearly connected with energy. To increase temperature you have to add energy (heat it up).

Now enter the atomic theory, then considered as small, but finite, hard balls.

It was quite an inspired leap to attribute the energy uptake to the KE of these balls and the pressure to the momentum tranfer due to impact.

For instance if we heat something material up we know it expands. We can equate the take up of heat energy to the increase in strain energy.

So it would not have been unreasonable to propose that at an 'atomic' level the heat added should be equated to an expansion of each individual ball, not increased speed and therfore KE.

And if they had wanted to consider energy of motion, why not propose that the balls are spinning and just spin faster?
I'd suggest the observation of Brownian motion would have lead to the thinking on translational KE quite naturally. This motion is not consistent with expansion or spin.

Plus, the matter of how heat is transferred. It's easy to see how one moving object transfers energy to another, but it would not be so easy to explain this in terms of expansion, or, to some extent, spin.
 

BillO

Joined Nov 24, 2008
999
Getting back to the notion of "Joules per mole," would we have to use separate numbers for separate substances at the same Kelvin temperature?
If taken as ideal gases, substances with different masses just move at different velocites to acheive the same average KE.

If we are taking about real substances, yes, we would need different numbers.

edit: I guess it would be better to say multiple terms with different units. However, with work they should all be reduced to MLT units, added, then changed back to whatever you want. Joules/mole might not be meaningful for solids or liquids.
 
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studiot

Joined Nov 9, 2007
4,998
To talk further about the energy idea, how do you deal with (chemical) phase changes?

For example two samples of a substance, at the same temperature, only differing by their latent heats.

They clearly have different average energies per molecule at the same temperature, but the temperature will positively define which way heat flows to a third body.
 

BillO

Joined Nov 24, 2008
999
Physical phase changes are also interesting. Some more than others.

Take water for instance. It expands below a certain temperature as it arranges itself into rings. Then, as with many other substances, remains at a fixed temperature as considerable heat is removed.

Certainly no simple task to do the bookkeeping in all these cases.
 

studiot

Joined Nov 9, 2007
4,998
Of course phase changes are the classic textbook examples of entropy changes, at constant temperature.

ΔH = TΔS

How would this equation work without the T?
 

BillO

Joined Nov 24, 2008
999
Indeed, I suspect that this is the equation (in essence) that gave rise to the equation boks originated the thred with.
 
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