[hamdani yusuf (OP)]

When were the term energy defined in scientific community?

The concept of "energy" has evolved over centuries, but its formal definition in the scientific community began to take shape in the 17th and 18th centuries during the development of classical mechanics.

Key Milestones:

1. Aristotle (4th century BCE): The idea of "energeia," meaning "activity" or "actuality," was introduced in philosophy but was not a scientific concept.


2. Gottfried Wilhelm Leibniz (1676?1689): Introduced the concept of vis viva (living force), an early precursor to kinetic energy, defining it as proportional to the mass and the square of the velocity.


3. Isaac Newton (1687): His work in Principia Mathematica developed foundational principles of motion and introduced concepts that contributed to the later understanding of energy.


4. Thomas Young (1807): First used the term "energy" in its modern sense in a lecture, relating it to the capacity to perform work.


5. William Rankine and James Prescott Joule (19th century): Formalized the concept of energy as a measurable quantity and connected it to the principle of conservation of energy.

Joule's experiments (1840s) demonstrated the equivalence of mechanical energy and heat, a cornerstone of the first law of thermodynamics.




By the mid-19th century, energy was universally recognized in science as the capacity to perform work, with multiple forms like kinetic, potential, thermal, and chemical energy systematically classified.

[hamdani yusuf (OP)]

What does thermal energy mean?

Thermal energy refers to the total internal energy of a system due to the random motion of its particles, such as atoms and molecules. It is associated with the temperature of the system and arises from the kinetic and potential energies of these particles.

Key Points:

1. Particle Motion:

In solids: Particles vibrate around fixed positions.

In liquids: Particles move more freely but still interact strongly.

In gases: Particles move rapidly and independently.



2. Relation to Temperature:

Temperature is a measure of the average kinetic energy of particles in a system.

Thermal energy depends on both temperature and the number of particles in the system.



3. Forms of Thermal Energy:

Kinetic energy of particles: Due to their movement.

Potential energy of particles: Due to intermolecular forces.



4. Units: Thermal energy is measured in joules (J) in the SI system.


5. Not Heat: Thermal energy is not the same as heat.

Thermal energy is the energy contained within a system.

Heat is the transfer of thermal energy from one body to another due to a temperature difference.




Examples:

Boiling water has high thermal energy due to the rapid motion of water molecules.

A heated metal rod has more thermal energy than a cold one because its atoms vibrate more intensely.

[hamdani yusuf (OP)]

When were the term entropy defined in scientific community?

The term entropy was first defined in the scientific community in the mid-19th century as a concept related to the second law of thermodynamics. Its development is primarily credited to Rudolf Clausius, a German physicist.

Key Milestones:

1. Rudolf Clausius (1850s-1865):

In 1850, Clausius formulated the second law of thermodynamics, introducing the idea that energy transformations involve a loss of usable energy.

In 1865, Clausius coined the term entropy from the Greek word trope (transformation) to describe the measure of energy unavailable for work during a thermodynamic process.

He mathematically defined entropy () and introduced the famous relation:




dS =  dQ / T

2. Ludwig Boltzmann (1870s):

Boltzmann provided a statistical interpretation of entropy, linking it to the microscopic properties of systems.

He introduced the equation:




S = k_B ln W

3. Josiah Willard Gibbs (1870s):

Extended the concept of entropy to chemical thermodynamics and equilibrium, laying the groundwork for its broader applications in physics and chemistry.




Summary:

1865: Clausius defines entropy in thermodynamics.

1870s: Boltzmann and Gibbs refine and expand the concept to statistical mechanics.


Entropy is now recognized as a central concept in thermodynamics, statistical mechanics, and information theory.

[Bored chemist]

OK, so we can start with water being boiled. That, by definition, is the temperature at which the liquid and gas phases are at equilibrium at the local external pressure.
It really is at equilibrium.

At equilibrium with what?

The water at the bottom is not boiling.
It is, therefore irrelevant to any discussion of "boiling water".
Why did you mention it?

[Bored chemist]

ChatGPT's answer to my question

Why are you still asking ChatGPT and wasting bandwidth with it?

[hamdani yusuf (OP)]

OK, so we can start with water being boiled. That, by definition, is the temperature at which the liquid and gas phases are at equilibrium at the local external pressure.
It really is at equilibrium.

At equilibrium with what?

The water at the bottom is not boiling.
It is, therefore irrelevant to any discussion of "boiling water".
Why did you mention it?

The system is not in equilibrium. But the temperature can still be defined and measured.

[alancalverd]

But the temperature can still be defined and measured.

The temperature of what, where? Obviously the ice is at 273K or less, and the water at anything between ambient and 373K depending on where you measure it. The outside of  the test tube may be close to 273K at the bottom and anything up to 1500K in the flame.

[alancalverd]

What kind of thermometer is the most accurate to measure the real temperature?

An ideal gas thermometer defines kelvin over the range of its gas phase, but (a) it is clumsy and (b) it only exists in textbooks. For most applications a platinum resistance thermometer gives a very good approximation to ideal linear performance but a calibrated thermistor or radiation pyrometer is usually more practical over a short range.

[paul cotter]

Indeed, the pt100 is a great device, up to ~500degree c(?).

[Bored chemist]

The system is not in equilibrium. But the temperature can still be defined and measured.

You can't sensibly talk about that tube full of water having "A temperature".
It has at least three. The water at the top is near 100C The water at the bottom is near 0C and there's a range in between.
So, it has many "temperatures".
A thermal camera would make that obvious.

[hamdani yusuf (OP)]

But the temperature can still be defined and measured.

The temperature of what, where? Obviously the ice is at 273K or less, and the water at anything between ambient and 373K depending on where you measure it. The outside of  the test tube may be close to 273K at the bottom and anything up to 1500K in the flame.

You've answered your own question. Every small part of the system have defined and measurable temperature.
But how small the subsystem can be while still having defined temperature when isolated?

[alancalverd]

If you define temperature as the mean kinetic energy of a confined ensemble, then one molecule in a box can have a temperature. Though that does raise the question: what is the box made of?   

[Bored chemist]

But how small the subsystem can be while still having defined temperature when isolated?

If you isolate some matter and then wait, the equipartition principle will shuffle the energy around until you have an equilibrium.
I dare say Alan knows more about relaxation times than I do.

[hamdani yusuf (OP)]

If you define temperature as the mean kinetic energy of a confined ensemble, then one molecule in a box can have a temperature. Though that does raise the question: what is the box made of?   

The definition in dictionary is

the degree or intensity of heat present in a substance or object, especially as expressed according to a comparative scale and shown by a thermometer or perceived by touch.

While Wikipedia says

Temperature is a physical quantity that quantitatively expresses the attribute of hotness or coldness. Temperature is measured with a thermometer. It reflects the average kinetic energy of the vibrating and colliding atoms making up a substance.

The last sentence put a constraint to objects made up of atoms. Hence temperature of a collection of free electrons or positrons, or vacuum of space can't be defined.
The word "reflect" there implies that there are other factor(s) not mentioned yet in the sentence.

The Wikipedia article contains definition of temperature as Intensive variability.

Intensive variability
In thermodynamic terms, temperature is an intensive variable because it is equal to a differential coefficient of one extensive variable with respect to another, for a given body. It thus has the dimensions of a ratio of two extensive variables. In thermodynamics, two bodies are often considered as connected by contact with a common wall, which has some specific permeability properties. Such specific permeability can be referred to a specific intensive variable. An example is a diathermic wall that is permeable only to heat; the intensive variable for this case is temperature. When the two bodies have been connected through the specifically permeable wall for a very long time, and have settled to a permanent steady state, the relevant intensive variables are equal in the two bodies; for a diathermal wall, this statement is sometimes called the zeroth law of thermodynamics.

In particular, when the body is described by stating its internal energy U, an extensive variable, as a function of its entropy S, also an extensive variable, and other state variables V, N, with U = U (S, V, N), then the temperature is equal to the partial derivative of the internal energy with respect to the entropy:
T = (dU/dS) _{V, N}

Local thermodynamic equilibrium
Real-world bodies are often not in thermodynamic equilibrium and not homogeneous. For the study by methods of classical irreversible thermodynamics, a body is usually spatially and temporally divided conceptually into 'cells' of small size. If classical thermodynamic equilibrium conditions for matter are fulfilled to good approximation in such a 'cell', then it is homogeneous and a temperature exists for it. If this is so for every 'cell' of the body, then local thermodynamic equilibrium is said to prevail throughout the body.

[hamdani yusuf (OP)]

This is another attempt to explain temperature related to radiation.

How Hot is Light? How Lasers Bend the Rules of Heat Transfer

made a video before explaining that lasers can heat things to any positive temperature due to the fact that they have a population inversion which gives them a negative absolute temperature which is hotter than any positive temperature. But the problem with that explanation is that a temperature can only be defined in a system that is in thermal equilibrium. So technically you can't assign a laser a negative absolute temperature. Only a "psuedo" negative temperature. But it turns out that explanation isn't necessary since magnetrons can do it and they don't have a negative temperature. Really the best explanation of why a laser can heat things hotter than itself is that you are inputting energy into the system and that energy turns into heat as I explained in this video. All of the mystery fades away when you think of it this way.

[Bored chemist]

Rather than posting lots of definitions of temperature, perhaps you should read and understand them.

All of the mystery fades away when you think of it this way.

What mystery?

[Eternal Student]

Hi.

    This bit worried me:

If you define temperature as the mean kinetic energy of a confined ensemble, then one molecule in a box can have a temperature.

     I might be missing the context, is this a hypotehtical retort to some older post perhaps?

   Anyway, I would have asked    "Can you really do this?"

    Typically the bulk translational motion of an object is excluded as a mode of energy that might be called "thermal energy" or contribute to the temperature we can assign to the object.  It's still an important form of energy that the object can have -  but just not one which contributes to its temperature or "hotness".

    Simple example:   Heat a metal rod to 100 deg. C while at rest in the lab frame.   Now set the rod moving at 100 mph (or 1000,  or 10 000 mph) relative to the lab frame.   Has that changed the temperature of the rod?    Does a thermometer used on the moving rod record a temperature of 100 deg C,  or slightly more than 100 deg C now that the rod has some more translational k.e. ?    If you put some good lubricating (0 friction) but also heat conducting gel between the moving rod and a thermometer you keep static in the lab frame, surely the thermometer still reports the temperature as being 100 deg C exactly?    Or... do you not think so?
    As mentioned earlier,  the bulk translational motion of the metal rod is an important form of energy that the object does have and there are certainly ways you could convert this into extra heat delivered to some other object  (e.g. forget about using the lubricating gel) but the point is that we don't have to and there is no reason why this form of energy would be considered to contribute to the temperature of the object.   As a more extreme example, we don't consider the mass of an object to contribute to its temperature.    You could annhilate the mass in the rod and generate a whole lot more heat energy if you wanted but that isn't anything that is counted as making a contribution to the temperature or hotness of the object.

    In your example, the entire object under consideration is just one molecule and you'd want to exclude the bulk translational motion of that object when assigning a temperature to it.    Or... do you not think so?
    For additional consideration please keep in mind that there's no reason why the bulk translational k.e. of an object would have to be in equilibrium with other modes of storing energy within that object (your object is one molecule so modes of storing energy which will contribute to temperature can include the vibration of atoms within the molecule).

Best Wishes.

[alancalverd]

Perhaps I should have said "of particles within a confined space" but I guess that's still not absolutely explicit.

The atoms within your rod have no idea how fast the rod is travelling in space if the speed is constant, but they do know what happens when they bash into each other. If you decelerate the rod by crashing into a brick wall, the energy transferred to the wall will be the  0.5mv² component of the rod plus its heat content, but we are no longer talking about the original bounded ensemble.

[Eternal Student]

Hi.

    Thanks for your comments @alancalverd .    I think I can see what you're saying.
Although there isn't anything resembling an ensemble of particles inside your box, there is only one particle in the box, we can theoretically treat it as a confined ensemble of particles.    That theoretical ensemble of particles could have a temperature much as you described.
     
      I don't often sympathise with a lot of stuff that @hamdani yusuf  talks about.   However, temperature isn't the simple or completely objective thing that we may have thought it was after sutdying some school level science and there's not much wrong with discussing this in a science forum like this.   It can be fun to re-examine some of the stuff that you (we) thought we knew and understood.    All the words you may have heard at school like "we are only presenting some models and as you study more, you'll find that many of these models will be replaced with something else or possibly that the model is just wrong and fails to explain some things but there's no better model available at the moment" are actually true but the problem is that people do actually leave school and then there's no school reunion event to actually follow up with the discussion about this.   A forum like this one can usefully provide a place for such discussion.

      If you (we) end up teaching some young people then we'd better make sure we teach the syllabus but at least we can say those words in red   (.... we are only presenting some models..... ) with some genuine conviction.

      One of the things about "temperature" or "hotness" of an object that I don't think has been mentioned much so far is that it can depend on the place where the object is put.   I hope @hamdani yusuf  won't mind too much if I spend a moment discussing something about this here.

Let's start here:
        Temperature is a measure of a quality of a state of a material. The quality may be regarded as a more abstract entity than any particular temperature scale that measures it, and is called "hotness" by some writers.   The quality of hotness refers to the state of material only in a particular locality, and in general, apart from bodies held in a steady state of thermodynamic equilibrium, hotness varies from place to place....
     [Taken from Wikipedia under "Basic Theory" for temperature.   https://en.wikipedia.org/wiki/Temperature#Basic_theory  ]
     
What does it mean?    Well it could mean that some things, like a long rod, have a temperature of 100 deg C at one end and a temperature of 80 deg C at the other end -   temperature can be locally defined and vary from place to place.   However, that is almost certainly NOT what was meant.   They probably meant that even if the whole rod had a temperature of 100 deg C while it's measured in one place then if we pick the whole rod up and just put it in a different place, it's quality of hotness or temperature can change.

    An example:    The Zeeman effect describes how the energy levels occupied by electrons can split in the presecence of a magnetic field.
     We consider a theoretical object, a sink for all thermal energy, that we identify as being at 0 Kelvin (absolute zero).   If we put a test object into thermal contact with this sink then energy will flow from our test object to the sink   if and only if   the test object has a temperature above 0 kelvin.  So we have a way to know if our test object is at absolute zero.
    Now we have a test object that is a bit like a group I metal, with a single valence electron in its outer shell.  We'll have this test object in its lowest possible energy state.   In a place with no magnetic field, the electrons have no lower energy level they can fall to, we can make thermal contact with out idealised thermal sink and no energy will flow to that sink.   Our test object seems to have a temperature of 0 kelvin.
    If we move our test object to a region with a uniform but non-zero magnetic field, without deliberately adding or removing any energy to the test object, then the electrons wave functions become a superposition of the two energy levels available from the splitting by the Zeeman effect.   Alternatively, if you prefer to think of the electrons individually and more classically then you could say half of the electrons go into the lower energy level, half go into the higher energy level and overall the energy of the test object remains the same.    Either way you wish to consider it, there are some electrons capable of falling into a lower energy state.  So when we make thermal contact with the sink, some energy can flow into the sink and out of our test object.   It seems that the test object has a temperature above 0 kelvin now that it's in a place with a non-zero magnetic field.

   There's quite a few things about temperature that are strange and not as clear cut as we may have thought.   In General Relativity we don't often consider temperature as an important thing, it may not be fundamental or objective enough.   For example, the temperature of an ideal fluid doesn't appear in the stress-energy tensor but the pressure of that fluid does.   Similarly, cosmological "equations of state" relate energy density to pressure and don't involve temperature unlike the typical "equatons of state" that you may encounter in thermodynamics.   Pressure may be a bit more fundamental, objective, or useful as a property that an object can have rather than temperature.    I don't know.... it's all just a model but maybe a model where we recognise temperature as just an approximate and emergent property is a small step closer to the underlying nature of things.

    In that respect, I would differ from @hamdani yusuf 's  line of attack:   I'm not sure there is a lot of point trying to make a better or more precise definition for temperature.   It's just an approximation that is useful sometimes.

Best Wishes.

[hamdani yusuf (OP)]

Typically the bulk translational motion of an object is excluded as a mode of energy that might be called "thermal energy" or contribute to the temperature we can assign to the object.  It's still an important form of energy that the object can have -  but just not one which contributes to its temperature or "hotness".

Bulk rotational motion is also usually excluded as a mode of thermal energy.
But a freely spinning magnet inside a vacuum glass container can transfer it's energy to a nearby metal block and raise its temperature. Then the next question is what is thermal energy?