[alancalverd]

so it will surely

You may be sure, but the rest of us aren't.
Eventually, it all ends up moving fast enough to overcome the gravitational attraction- it's above escape velocity- so it becomes more and more diffuse.

Stephen Hawking thought pretty much the same as JL and myself, in "Black holes and baby universes". Not sure whether he ever recanted.

[Bored chemist]

so it will surely coalesce back to a new primordial lump.

On the way to doing that it would form black holes- which would evaporate into photons  (at least, that's what Hawking said) and those photons will diffuse away.

[alancalverd]

Isn't the essence of a black hole, that photons cannot leave it? Hence black, and hole.

[Bored chemist]

Isn't the essence of a black hole, that photons cannot leave it? Hence black, and hole.

It depends on whether Hawking was right or not.
https://en.wikipedia.org/wiki/Hawking_radiation

[paul cotter]

Hawking radiation is a very slow form of black hole ablation. With the rate of the universe's expansion apparently increasing and "all the time in the world " available it looks like the density will approach near infinite dilution regardless of what black holes do. ( why am I posting again in "new theories" ?, I must be suffering from mental aberrations !)

[alancalverd]

Has it ever been changed or replaced?

Yes. The usual reason is that someone finds a process that is more precisely or more easily reproducible. Problem with temperature is that you need two accessible points to define a temperature scale. Whilst 0K is a calculable point it isn't actually accessible, thermometers that work well at low temperatures don't always work at high ones, and the linearity of any practical thermometer is limited so you really need several reference points.

We tend to use the platinum resistance thermometer to provide a standard scale up to a few hundred K, accepting that it is not inherently linear but sufficiently consistent. The triple point of water is a simple reference for most industrial purposes but as we have discussed, it is a very difficult substance to use with precision, whereas gallium is rather "better behaved" around its triple point. Most people would agree that temperature measurement above about 700K  is very difficult to establish to better than ±0.1K but it is a matter of little practical consequence.

[alancalverd]

Hawking radiation is a very slow form of black hole ablation.

And you have to coalesce a lot of stuff to make the black hole in the first place.

[Bored chemist]

Hawking radiation is a very slow form of black hole ablation.

[Bored chemist]

Of course, it's not only black holes that "evaporate".
Everything does.
So, let's try to calculate how long it would take the earth to evaporate in a universe at 1K.

Data on  volatility of planets is a bit hard to come by.
So I will choose tungsten as a model substance. Not, as you might imagine, because I have taken leave of my senses.

(1) To a very good approximation, everything is more volatile than tungsten, so it's a "worst case"
(2) The data on evaporation rates is available for solid tungsten, because it's important to the people who make light bulbs and such.
I found it in my copy of this.
https://www.wob.com/en-gb/books/fred-rosebury/handbook-of-electron-tube-and-vacuum-techniques
(I like to keep up with cutting edge technology).


W evaporn.jpg (89.65 kB . 320x485 - viewed 1551 times)
The first column is the temperature (Kelvin) and the second is the rate of evaporation in g/ cm2 / sec
Those of you who ever studied physical chemistry will recognise the significance of the other two columns. It's a a magic trick called a Van't Hoff plot which allows you to linearise rates of things as a function of temperature.
https://en.wikipedia.org/wiki/Van_%27t_Hoff_equation

And that allows me to interpolate the data down to a lower temperature.
OK over 3 orders of magnitude looks like I'm pushing it but...
Here's the graph

W evap graph.jpg (46.65 kB . 627x504 - viewed 1506 times)
and it looks linear enough to me.
That extrapolation tells me the the rate of evaporation is of the order of 10^-50,000 g/cm^2 per second.

And this puts us in an interesting world of extrapolation where I can ignore the fact that the mass of the world is more than 1 gram.
Because that would only add  something like 27 orders of magnitude to the answer.
And I can ignore the fact that the earth has an area bigger than 1 square centimetre because that would only contribute about a couple of dozen orders of magnitude, and I can ignore the fact that I want an answer in years , rather than seconds because that only makes about 7 or 8 orders of magnitude difference.

My estimate for the time taken for an earth sized lump of tungsten the size of the earth to evaporate at 1K is about 10^50000 years.
Quite a while...
But infinitely shorter than "forever".

[alancalverd]

Because that would only add  something like 27 orders of magnitude to the answer.

Possibly apocryphal but I heard it from one of his research associates:

Fred Hoyle: "Sorry, I've made an error somewhere. There's a missing factor of 10⁴⁵."

Student: "Plus or minus 45?"

Hoyle: "It doesn't make much difference".

[hamdani yusuf (OP)]

Has it ever been changed or replaced?

Yes. The usual reason is that someone finds a process that is more precisely or more easily reproducible. Problem with temperature is that you need two accessible points to define a temperature scale. Whilst 0K is a calculable point it isn't actually accessible, thermometers that work well at low temperatures don't always work at high ones, and the linearity of any practical thermometer is limited so you really need several reference points.

We tend to use the platinum resistance thermometer to provide a standard scale up to a few hundred K, accepting that it is not inherently linear but sufficiently consistent. The triple point of water is a simple reference for most industrial purposes but as we have discussed, it is a very difficult substance to use with precision, whereas gallium is rather "better behaved" around its triple point. Most people would agree that temperature measurement above about 700K  is very difficult to establish to better than ±0.1K but it is a matter of little practical consequence.

What I'm looking for is the fundamental definition of temperature, and how it relates to other physical concepts.
So far, the closest thing I get is by comparison to the kinetic energy of ideal gas in thermal equilibrium with the object we want to measure.

[Georginajackson]

Isn't the essence of a black hole, that photons cannot leave it? Hence black, and hole.

Yes, but besides this there are other reasons why this would not be so.

[hamdani yusuf (OP)]

Quickly rotating magnets or electrets in a box have large kinetic energy,

You ignored the word "internal" in my quote. It isn't there for padding!

Rotating magnets or electrets in a box have low entropy. The rotation can be described by small amount of information.
Vibrating tuning forks also have low entropy, because it can be described by small amount of information..

Now, yes the heat is also a mechanical energy, but he say it himself... it is a statistical mechanical energy.

What's the difference between statistical mechanical energy and non-statistical mechanical energy?
How would it compare to temperature?
Is there a statistical mechanical energy which is not kinetic? What would it be called?

These can be seen as rhetorical questions. But since no one is interested to answer them, I'll give it a try, starting with this video.

Entropy is a fundamental concept in Data Science because it shows up all over the place - from Decision Trees, to similarity metrics, to state of the art dimension reduction algorithms. It's also surprisingly simple, but often poorly explained. Traditionally the equation is presented with the expectation that you memorize it without thoroughly understanding what it means and where it came from. This video takes a very different approach by showing you, step-by-step, where this simple equation comes from, making it easy to remember (and derive), understand and explain to your friends at parties.

My conclusion so far, is that temperature of an object is proportional to its kinetic energy, as well as its entropy. I'm still open to suggestion that there might be some other factors involved.

[alancalverd]

The temperature of an object is indeed proportional to its internal kinetic energy, as several people stated on Page 1 and all the textbooks. The constant of proportionality is called the temperature scale, and most scientists use the Kelvin scale starting at absolute zero and incrementing by Celsius degrees.

There is little point in arguing about the meaning of words in physics - the important ones are all defined, mostly English (or Latin/Greek/German incorporated into English), and fully understood by those who use them daily.

[Bored chemist]

My conclusion so far, is that temperature of an object is proportional to its kinetic energy, as well as its entropy.

Then your conclusion is wrong.
Temperature is sometimes proportional to the energy in some simple cases.
But the heat capacity is not actually a constant, so your idea is not actually correct.
It's not proportional to the entropy.

[hamdani yusuf (OP)]

The temperature of an object is indeed proportional to its internal kinetic energy, as several people stated on Page 1 and all the textbooks. The constant of proportionality is called the temperature scale, and most scientists use the Kelvin scale starting at absolute zero and incrementing by Celsius degrees.

There is little point in arguing about the meaning of words in physics - the important ones are all defined, mostly English (or Latin/Greek/German incorporated into English), and fully understood by those who use them daily.

The proportionality between temperature and kinetic energy is well established for ideal gases. But for other things, the kinetic energy is also manifested in other things which are not measurable by thermometers. The point of this thread is to identify and quantify these other things. You've identified one of those as "gross" motion. The next questions are how to quantify it, and how to separate it from the types of motion which contribute to temperature measurement.

Here is a more complete table of molar heat capacity I compiled from NIST website.

Temp (K)      Hydrogen   Deuterium   Helium   Argon   Radon
300               28.85        29.19           20.79    20.79    20.79
1000             30.20        31.64           20.79    20.79    20.79
3000             37.09        38.16           20.79    20.79    20.79
6000             41.97        42.25           20.79    20.79    20.79

From the table we can conclude that increase of temperature also increases the portion of rotational and vibrational movements in kinetic energy of diatomic gases. In noble gases, those types of motion are virtually non-existent.

[hamdani yusuf (OP)]

My conclusion so far, is that temperature of an object is proportional to its kinetic energy, as well as its entropy.

Then your conclusion is wrong.
Temperature is sometimes proportional to the energy in some simple cases.
But the heat capacity is not actually a constant, so your idea is not actually correct.
It's not proportional to the entropy.

What's your conclusion?

[Bored chemist]

What's your conclusion?

Temperature is sometimes proportional to the energy in some simple cases.
But the heat capacity is not actually a constant, so your idea is not actually correct.
It's not proportional to the entropy.

The proportionality between temperature and kinetic energy is well established for ideal gases.

There are no ideal gases.

The next questions are how to quantify it, and how to separate it from the types of motion which contribute to temperature measurement.

If all the modes in which energy can be present have (on average) the same amount of energy then you have a temperature and you can calculate it based on any of those modes.
If they aren't the same, you don't have a defined temperature.

[paul cotter]

I was going to query how such a simple question could expand to 38 pages and still appear to be alive. However having scanned a number of pages I do see education at work, albeit at a snail's pace. I have one small addition from the early pages: the op referenced Jean Piere Robitaille, this guy is a notorious crank and not a scientist. He is a medic of some description, an anaesthetist as far as I remember.

[hamdani yusuf (OP)]

But the heat capacity is not actually a constant

What makes it change?