[Bored chemist]

The question is, what distinguishes thermal energy from kinetic energy?

The motion having some sort of structure, rather than being random. Essentially, it's an effect of entropy.

What distinguishes thermal radiation from other electromagnetic radiation?

In the case of your experiment, the spectrum.

[hamdani yusuf (OP)]

The question is, what distinguishes thermal energy from kinetic energy?

The motion having some sort of structure, rather than being random. Essentially, it's an effect of entropy.

What distinguishes thermal radiation from other electromagnetic radiation?

In the case of your experiment, the spectrum.

Afaik, thermal energy has highest entropy among other kinds of energy, which makes it the most random form.

Black body radiation is the simplest spectral distribution of thermal electromagnetic radiation. The object's temperature can be calculated from the peak frequency. But most objects are not black body. Spectrum of low pressure gas has much different shape than black body radiation.

[hamdani yusuf (OP)]

I bring Alan's post here because I think it's more appropriate to continue the discussion about temperature.

For there to be an exchange of heat, the mean internal kinetic energy of one object must decrease and that of the other object must increase. We measure mean kinetic energy as temperature. If two objects are at the same temperature, their temperatures will not change by putting them in contact with one another. That's how temperature is derived from the zeroth law.

https://en.wikipedia.org/wiki/Gravity_assist involves exchange of kinetic energy.
Quickly rotating magnets or electrets in a box have large kinetic energy, although they have ambient temperature.
We also have problems like https://en.wikipedia.org/wiki/Stellar_corona#Coronal_heating_problem.
And how https://en.wikipedia.org/wiki/Parker_Solar_Probe can survive high temperature environment.

[hamdani yusuf (OP)]

I bring this here for the same reason.

What seems more relevant is just to jump straight to a higher level answer:
"Temperature",  "thermal contact" and "heat"  are all very difficult things to define.  At least, they are difficult to define or explain at any microscopic scale (where you're trying to take a reductionist approach and break things down to the smallest indivisible units like particles with well defined properties).   However, they can be easily defined (or really just decalred to exist) on a macroscopic scale.  This is the usual development of the subject matter that is called "thermodynamics".

Do you have any idea why it's hard to define?

[Bored chemist]

Do you have any idea why it's hard to define?

As he said; there's a difference between the macroscopic and microscopic pictures.
You also need to be aware of this
https://en.wikipedia.org/wiki/Equipartition_theorem
And this

https://en.wikipedia.org/wiki/Virial_theorem

[hamdani yusuf (OP)]

For example, if you try to take a microscopic definition for "heat" then it is not supposed to include a transfer of matter from one system to another  BUT  a transfer of photons such as infra-red radiation is something we would very much like to include in the definition of heat.   What makes a photon different to some other particle with energy?   If an electron and positron cross a barrier then that would seem to be a transfer of matter across the barrier and would not be considered as a heat transfer.  However, if they annhilate on one side of the barrier, only some photons cross the barrier and then the photons interact with some nucleus on the other side of the barrier to reform particles and anti-particles  -  that would seem to be just fine.

Is there any exclusion from following methods of heating water?
- Radio wave heating
- Microwave heating
- Infrared heating
- Visible Laser heating
- Induction heating
- Ohmic heating

[hamdani yusuf (OP)]

Do you have any idea why it's hard to define?

As he said; there's a difference between the macroscopic and microscopic pictures.
You also need to be aware of this
https://en.wikipedia.org/wiki/Equipartition_theorem
And this

https://en.wikipedia.org/wiki/Virial_theorem

What makes it easier to define in macroscopic picture?

https://en.wikipedia.org/wiki/Equipartition_theorem
In classical statistical mechanics, the equipartition theorem relates the temperature of a system to its average energies. The equipartition theorem is also known as the law of equipartition, equipartition of energy, or simply equipartition. The original idea of equipartition was that, in thermal equilibrium, energy is shared equally among all of its various forms; for example, the average kinetic energy per degree of freedom in translational motion of a molecule should equal that in rotational motion.

For large molecules, it seems to be easier to vibrate than translate or rotate, especially when the shape is long like a needle, and the intermolecular space is limited.

[alancalverd]

Temperature is a statistic of a very large ensemble so it is only defined macroscopically.

[alancalverd]

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!

[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!

The magnets are inside a box.
IMO water molecules can be modeled as microscopic electrets.

[hamdani yusuf (OP)]

Temperature is a statistic of a very large ensemble so it is only defined macroscopically.

How many molecules is the minimum limit for a system to have a defined temperature?

[Bored chemist]

Temperature is a statistic of a very large ensemble so it is only defined macroscopically.

How many molecules is the minimum limit for a system to have a defined temperature?

Enough for the QM effects to be relatively small compared to the total energy.

[Bored chemist]

seems

If you are using that word in science, be very careful.
What "seems" to happen isn't reliably what does happen.

[Bored chemist]

For large molecules, it seems to be easier to vibrate than translate or rotate,

How far do you think it has to translate or rotate?

[Eternal Student]

Hi.

What makes it (temperature) easier to define in macroscopic picture?

As @alancalverd stated:

Temperature is a statistic of a very large ensemble so it is only defined macroscopically.

   Although I would have used a few more words and said something like this:

    It has been observed that macroscopic systems seem to follow certain behaviours.   Developing models that assume the system has quantities called state variables and there is a connection between those state variables called the equation(s) of state was extremely successful.   This is thermodynamics.  Different systems can have different state variables.  Temperature and Pressure are just some common examples of state variables that some systems have and the ideal gas equation  PV = kT is a good example of an equation of state that might apply.
     So,  "temperature"  is just a state variable that some systems will have.   This is an acceptable definition of temperature for thermodynamics.   There is no requirement to attempt to explain temperature at any microscopic scale.  It is simply a property that some systems will have.

    You (Hamdani) might feel that a definition should really be an explanation for why something exists or what it is on some small scale.  Most of us are biased and believe that a reductionist approach should be applied to science,  i.e. that everything should be pulled apart and examined on the smallest and possibly most fundamental level.   However, there may not be a more fundamental level for temperature.  It does seem to be an emergent property that a whole system might have but not something that any small component like a particle in that system must have.

    There are some objects and some systems that do not have a well defined temperature.
    Simple examples:   A small container of gas that has been left for days can be assumed to have a well defined temperature.     A container of gas that has just had some high velocity gas particles added to one side of it does not have a well defined temperature until enough time has passed and an equilibrium and equi-partition of energy has been established.

    Now, for some systems we can make additional assumptions.   We can assume properties and relationships will hold above and beyond just having some state variables for the system and an equation of state.   For example, an ideal gas can be assumed to consist of particles with properties you expect of particles like velocity and mass.  We can then assume one state variable, Pressure, can be determined at the walls of the container as being the consequence of collisions and all the usual principles apply.   (Note that it's not assumed pressure only exists at the walls, just that it is easily determined at the walls).   Anyway, from these assumptions you can determine that the state variable "temperature" would be proportional to the average kinetic energy of the particles.    This is a bonus, for some systems it does seem that temperature could have a microscopic explanation.  It's a hint that there might be a good microscopic explanation for every real-world system but that's all - it's not a guarantee or an absolute requirement.   It's sufficient that temperature is just a state variable of a system.

Best Wishes.

[Eternal Student]

Hi again.   There seem to be some more questions I didn't answer:

Is there any exclusion from following methods of heating water?
- Radio wave heating
- Microwave heating
- Infrared heating
- Visible Laser heating
- Induction heating
- Ohmic heating

    I'm not the definitive rule maker.  These seem to be conventional forms of radiation and are very much the sort of energy transfer that you would want to consider as heat when you apply the existing and conventional concepts and models from thermodynamics to the problem you're considering.  Ohmic heating is different but that is included in most definitions of heat.  (See earlier posts and Wikipedia's definition of permitted heat transfer mechanisms).
    You seem to be under the impression that there will always be one universally agreed upon definition of heat but I don't think there has to be one.  Different systems only support a few mechanisms of heat transfer, they do not have to support them all.

    It is optimistic to assume that if we keep taking a large enough picture, everything can be considered as a thermodynamic system and we would always be able to identify state variables like temperature for that system.  It may actually be true but it's not required.  Instead it's better to consider that thermodynamics is a simplification and idealisation, there are many systems to which thermodynamics can be applied.  In each system there are different things that will be considered as a heat flow.

Best Wishes.

[hamdani yusuf (OP)]

Different systems can have different state variables.  Temperature and Pressure are just some common examples of state variables that some systems have and the ideal gas equation  PV = kT is a good example of an equation of state that might apply.

I think this ideal gas definition is the simplest way (mathematically) to describe temperature. Practical methods to measure temperature, such as used in mercury and alcohol thermometer, bimetal, thermocouple, RTD, and infrared thermometer are less reliable, involve non-linearity, and have narrower range and use case. 

[hamdani yusuf (OP)]

There are some objects and some systems that do not have a well defined temperature.
    Simple examples:   A small container of gas that has been left for days can be assumed to have a well defined temperature.     A container of gas that has just had some high velocity gas particles added to one side of it does not have a well defined temperature until enough time has passed and an equilibrium and equi-partition of energy has been established.

Perhaps I can add another example. The air inside a running microwave oven, radio wave oven, induction cooker, laser oven, may show different temperature measurement value, depending on the thermometer type used.

[Eternal Student]

Hi.

I think this ideal gas definition is the simplest way (mathematically) to describe temperature.

   
Yes.  I like a bit of theory.
   In fairness, we should mention that it's a bit of shame that not everything is an ideal gas.  People will still assign a temperature to these things and you can be pretty sure they will have used a hybrid of methods or approaches to defining temperature.

Best Wishes.

[hamdani yusuf (OP)]

Hi.

I think this ideal gas definition is the simplest way (mathematically) to describe temperature.

   
Yes.  I like a bit of theory.
   In fairness, we should mention that it's a bit of shame that not everything is an ideal gas.  People will still assign a temperature to these things and you can be pretty sure they will have used a hybrid of methods or approaches to defining temperature.

Best Wishes.

For objects that are not ideal gas, their temperature can be defined as the same as the ideal gas which don't exchange energy with them when they are in contact, which is indicated by preservation of the ideal gas temperature where the pressure and volume are maintained. Of course, it's easier said than done. But at least, with a robust definition, the practical difficulties can be addressed and solved using engineering methods.