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String Trimmer Batteries - same weight charged and empty

Adding you can add enrgy to a system without adding mass. Wind up trhe spring of a mechanical clock and you have added energy to the system but no mass.

I hold a baseball in hand. It has potential, kinetic, and nuclear energy. Total energy E = PE + KE + mc^2.
.

I throw the ball in the air adding PE and KE. Total energy is still PE + KE + mc^2. Energy comes and goes mc^2 does not change.


You've got two responses disagreeing with this post. I'm not sure why.

There are other forms of energy than mass. If you heat up the box with the ashes in it, it will have more energy (in the form of heat) without having more mass. If you throw the box of ashes, you'll give it kinetic energy without increasing its mass.

This doesn't change the fact that chemical reactions involve tiny conversions from mass to other forms of energy, or from other forms of energy to mass.

Suppose a hydrogen atom absorbs a photon, thus raising an electron to a higher orbit. Does the atom then weigh more? I'm guessing that it does. The other form of energy is gone, and mass is what remains, so the mass of the atom should be increased by one photon's worth. I don't know this for a fact. I haven't read it anywhere. I'm just thinking it makes sense.

Energy is conserved. If energy comes out of your glass box when the paper burns, then the box contents will have reduced mass. This must be true unless the exiting energy comes from something other than mass. Your hypothetical doesn't mention any other energy source, and we know that burning paper is exothermic.

So the answer is that the chemicals in the box get lighter in proportion to the amount of energy escaping from the box.

You can't give something additional kinetic energy without increasing its mass.


That's a viewpoint thing, right, having to do with who the observer is? That paradigm change doesn't help Steve with his problem. In fact, it gives him an out. It lets him think that we're resorting to relativistic mysticism, while, in the real world, chemical reactions don't involve changes in weight.

I think it's better, in this circumstance, just to stick to the fact that chemical reactions do involve converting mass to other forms of energy (or vice versa).

It's a fact that--regardless of how fast observers travel--chemical reactions change mass. And it is this fact that Steve is struggling with.
 
You can't give something additional kinetic energy without increasing its mass.


That's a viewpoint thing, right, having to do with who the observer is? That paradigm change doesn't help Steve with his problem. In fact, it gives him an out. It lets him think that we're resorting to relativistic mysticism, while, in the real world, chemical reactions don't involve changes in weight.

I think it's better, in this circumstance, just to stick to the fact that chemical reactions do involve converting mass to other forms of energy (or vice versa).

It's a fact that--regardless of how fast observers travel--chemical reactions change mass. And it is this fact that Steve is struggling with.

It's a fact that the equals sign in Einstein's famous equation is not a "conditionally equals", or an "equals for certain types of energy", or an "equals for atomic nuclei" sign; It's a universal equivalence that applies to any and all forms of energy.

Saying "no exceptions; No, not even that one; No, not that one either; No, really, there are not ANY exceptions to this fact" isn't adding complexity or making it harder to understand - it's the exact opposite. All changes in energy imply proportional changes in mass. ALL of them. And the constant of proportionality in EVERY case is the square of the speed of light.
 
Adding you can add enrgy to a system without adding mass. Wind up trhe spring of a mechanical clock and you have added energy to the system but no mass.

I hold a baseball in hand. It has potential, kinetic, and nuclear energy. Total energy E = PE + KE + mc^2.
.

I throw the ball in the air adding PE and KE. Total energy is still PE + KE + mc^2. Energy comes and goes mc^2 does not change.


You've got two responses disagreeing with this post. I'm not sure why.

There are other forms of energy than mass. If you heat up the box with the ashes in it, it will have more energy (in the form of heat) without having more mass. If you throw the box of ashes, you'll give it kinetic energy without increasing its mass.

This doesn't change the fact that chemical reactions involve tiny conversions from mass to other forms of energy, or from other forms of energy to mass.

Suppose a hydrogen atom absorbs a photon, thus raising an electron to a higher orbit. Does the atom then weigh more? I'm guessing that it does. The other form of energy is gone, and mass is what remains, so the mass of the atom should be increased by one photon's worth. I don't know this for a fact. I haven't read it anywhere. I'm just thinking it makes sense.

Energy is conserved. If energy comes out of your glass box when the paper burns, then the box contents will have reduced mass. This must be true unless the exiting energy comes from something other than mass. Your hypothetical doesn't mention any other energy source, and we know that burning paper is exothermic.

So the answer is that the chemicals in the box get lighter in proportion to the amount of energy escaping from the box.

I do not care. I do not claim to be infallible and an expert in anything. However over time responding to posts from people who really have no foundation is a waste of time. Some are on ignore.

What I do have is a lot of experience applying general mostly undergrad physics.

Energy is defined as the capacity to do work. Anything that can do work by definition is energy.

Back in the early days of radio and transmission lines there was debate over whether reflected energy due to an impedance mismatch on transmission lines was real. An rf amplifier drives a coax cable to an antenna. If the amp output impedance, cable impedance, and antenna impedance are not equal not all of the energy is transferred to the antenna. Some is reflected back to the amp.

The question was resolved by using what is called a directional couplet. Return energy reflected from say an antenna is diverted to a port with a resistor across it. A temperature rise was measured on the resistor indicating the energy was indeed real.

There can be theoretical energy. To prove something has energy you have to be able to do work with it. If Zero Point Energy is real then it can do work. A simple demo is creating heat.

Some people who post here are influenced by scifi where the word energy is used liberal as a plot device. To them energy has some kind of independent reality. I can get a bucket of coal that has energy in Joules, I can not get a bucket of energy.

The way I say it is energy is work derived from relate states of matter. A waterfall. Add kinetic enrgy to a baseball and it can do work breaking a window.

I do not have the nuclear physics to say what energy bound in an atom released by fission represents. I assume i is the energy in fields holding particles together, like a wound up spring that is released.

When I started out over 30 years ago I struggled with it until I realized it is all just consistent models based on SI with no special meaning. Asking what energy is becomes one of those endless metaphysical debate on reality.
Those who want to ague that can talk to a wall.

Energy is the capacity to work. In system all energy must add up.

As to photon emission and absorption in a photo emitter the energy balance is defined in eV. I do not have my books any more to go deeper.
 
wiploc

In a photo emitter quantum efficiency photons per electron. In a photo detector it is reverse.

If there is a mass change then heating a metal bar increasing thermal radiation means the bar weighs less. If that is true then as the bar is cooled back to equilibrium it regains weight?

I believe current theory is electrons as an amorphous cloud instead of discrete orbits.

Just thinking out loud. Heat a metal bar and thermal BB radiation increases. Heat goes to a higher excitation of an atom leading to a photon. A causal chain of energy conversion. Energy of a photon derived from heat energy. No need for a change in mass.

In E=mc^2 I do not see that it means because a photon has energy mass of the atom goes down. In these kinds of problems I rend to fall back on LOT and conservation. Mass can not come from or go to nothing. It would seem that a reduction in mass in the atom would have to reflected as mass somewhere else. The only alternative is to argue that E = mc^2 implies creation and destruction of mass.

We are always exchanging photons with the background locally. The energy for that is heat. A bar of metal at equilibrium in a room is emitting BB tradition proportional to temperature. I used to work with IR sensors and video systems.

It comes down to what a photon is. It is just a model that works experimentally. In the model it can not have mass but has momentum that can be used lift a metal plate on a cable with a laser. For me there are plenty of questions, but the models work.

In an AC current moving electrons yield photons.
 
You can't give something additional kinetic energy without increasing its mass.


That's a viewpoint thing, right, having to do with who the observer is? That paradigm change doesn't help Steve with his problem. In fact, it gives him an out. It lets him think that we're resorting to relativistic mysticism, while, in the real world, chemical reactions don't involve changes in weight.

I think it's better, in this circumstance, just to stick to the fact that chemical reactions do involve converting mass to other forms of energy (or vice versa).

It's a fact that--regardless of how fast observers travel--chemical reactions change mass. And it is this fact that Steve is struggling with.

It's a fact that the equals sign in Einstein's famous equation is not a "conditionally equals", or an "equals for certain types of energy", or an "equals for atomic nuclei" sign; It's a universal equivalence that applies to any and all forms of energy.

Saying "no exceptions; No, not even that one; No, not that one either; No, really, there are not ANY exceptions to this fact" isn't adding complexity or making it harder to understand - it's the exact opposite.
Exactly
All changes in energy imply proportional changes in mass. ALL of them. And the constant of proportionality in EVERY case is the square of the speed of light.
Well, it's not really correct. Someone alrerady mentioned "relativistic" mass which changes with object velocity. This concept was and still is popular in popular laymen explanations of SR. It allows to use classical physics for illustrating SR but it is absent in more-less serious textbooks. Mass is a center of mass energy, so it does not depend of frame of reference.
classical E=p2/(2*m) corresponds to SR E2=m2c4+p2*c2
 
I do not care. I do not claim to be infallible and an expert in anything. However over time responding to posts from people who really have no foundation is a waste of time. Some are on ignore.
I guess PhD (Partice Physics of all) is no foundation anymore :)
What I do have is a lot of experience applying general mostly undergrad physics.
You apply it incorrectly.
 
I do not care.

I'd have accepted that, and abandoned this conversation, but for the fact that you go on as if you do care.




I do not claim to be infallible and an expert in anything. However over time responding to posts from people who really have no foundation is a waste of time. Some are on ignore.

Well, I wouldn't want to misrepresent my foundation. When I was in grade school or junior high, they showed us an educational film directed at grade school or junior high school students. That film is my authority for saying that H plus H plus O has a different atomic weight than H20.




What I do have is a lot of experience applying general mostly undergrad physics.

My experience is definitely undergrad. I quizzed out of Man's Physical World.




In system all energy must add up.

Bingo. If heat and light come out of your box when the paper burns, then some form of energy in the box must be reduced. In this case, the lost energy was in the form of mass.




I believe current theory is electrons as an amorphous cloud instead of discrete orbits.

Originally they were a gimmick, a shortcut. If we pretended that electrons existed, and that two of them would fit in an innermost shell, etcetera, then we would be able to calculate valence and predict which kinds of atoms would fit together to produce molecules.

Then they were little planets in actual orbits.



Bertrand Russel argued that if we assumed an electron was a particle in the middle of a field, then we might eventually be wrong, but if we assumed that the field itself was the electron, then we couldn't be wrong even if the particle later proved to be real.

At some point, they became statistical smudges.

Now various models seem to peacefully coexist. People use whichever model simplifies their current conversation.

It's the same with gravity. Some people talk about gravitons, others about gravity waves, and others yet about curved space. These various models don't seem to be taken as contradicting each other.
 
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I'd have accepted that, and abandoned this conversation, but for the fact that you go on as if you do care.






Well, I wouldn't want to misrepresent my foundation. When I was in grade school or junior high, they showed us an educational film directed at grade school or junior high school students. That film is my authority for saying that H plus H plus O has a different atomic weight than H20.




What I do have is a lot of experience applying general mostly undergrad physics.

My experience is definitely undergrad. I quizzed out of Man's Physical World.




In system all energy must add up.

Bingo. If heat and light come out of your box when the paper burns, then some form of energy in the box must be reduced. In this case, the lost energy was in the form of mass.




I believe current theory is electrons as an amorphous cloud instead of discrete orbits.

Originally they were a gimmick, a shortcut. If we pretended that electrons existed, and that two of them would fit in an innermost shell, etcetera, then we would be able to calculate valence and predict which kinds of atoms would fit together to produce molecules.

Then they were little planets in actual orbits.

Bertrand Russel argued that if we assumed an electron was a particle in the middle of a field, then we might eventually be wrong, but if we assumed that the field itself was the electron, then we couldn't be wrong even if the particle later proved to be real.

At some point, they became statistical smudges.

Now various models seem to peacefully coexist. People use whichever model simplifies their current conversation.

It's the same with gravity. Some people talk about gravitons, others about gravity waves, and others yet about curved space. These various models don't seem to be taken as contradicting each other.

"Shut up and calculate!" - David Mermin, on interpretations of Quantum Mechanics (specifically the Copenhagen Interpretation).
 
If there is a mass change then heating a metal bar increasing thermal radiation means the bar weighs less.

Why would it weigh less? You put energy (heat) in, and you got energy out. Presumably you got out the same amount that you put in.



If that is true then as the bar is cooled back to equilibrium it regains weight?

In an earlier post, I posited that an atom might gain mass when its electron jumps to a higher shell. If that's true, then we can look at it like this:


  • First, you hold your Bic lighter under your box, heating the contents.

    Second, the heat from the lighter is detected/captured by the bar in the box when it causes an electron in the bar to jump to a higher shell. This increases the mass of one atom in the bar. So chemical energy has become heat energy, which has now become increased mass.

    Third, the electron drops back to a lower shell, and the atom emits a photon which leaves the box. Thus, the mass of the bar is reduced by the "rest mass" of the photon.

At no time does the mass of the bar drop below it's original mass. If it drops at all, it is only because heating increased it's mass, so it sheds mass as it cools back to ambient temperature.



Just thinking out loud. Heat a metal bar and thermal BB radiation increases. Heat goes to a higher excitation of an atom leading to a photon. A causal chain of energy conversion. Energy of a photon derived from heat energy. No need for a change in mass.

Right. Energy into the box equals energy out, so the contents end with the mass they started with.

If there was a change of mass, that was because excited electrons temporarily increase the mass of their atoms.

But does that really happen? I don't know. I made it up. It's just a thought that I had while we were having this conversation. I mentioned it as a possibility. I never urged it as a truth.




Mass can not come from or go to nothing.

Agreed. If energy quits being mass, then it has to take some other form. Sometimes it becomes electromagnetic radiation.



It would seem that a reduction in mass in the atom would have to reflected as mass somewhere else.

Is it that you think there is a law of conservation of mass? Science stopped believing in that when Einstein gave us relativity. Now we have conservation of energy, and mass is recognized as one form of energy.



The only alternative is to argue that E = mc^2 implies creation and destruction of mass.

Water has three states, solid, liquid, gas. Nothing is created or destroyed when water changes state.

Energy has multiple states too, with matter being one of them. Other forms of energy can be converted to mass; mass can be converted to other forms of energy.

We don't say that bread and cheese are "destroyed" when they are converted into a grilled cheese sandwich. Neither do I think it is appropriate to say that matter is destroyed when it converts into electromagnetic energy.



We are always exchanging photons with the background locally.

Agreed, yes.



The energy for that is heat.

Some of it, yes.



A bar of metal at equilibrium in a room is emitting BB tradition proportional to temperature.

Agreed, though I don't know why you stipulate that the bar is at room temperature.
 
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Why would it weigh less? You put energy (heat) in, and you got energy out. Presumably you got out the same amount that you put in.





In an earlier post, I posited that an atom might gain mass when its electron jumps to a higher shell. If that's true, then we can look at it like this:


  • First, you hold your Bic lighter under your box, heating the contents.

    Second, the heat from the lighter is detected/captured by the bar in the box when it causes an electron in the bar to jump to a higher shell. This increases the mass of one atom in the bar. So chemical energy has become heat energy, which has now become increased mass.

    Third, the electron drops back to a lower shell, and the atom emits a photon which leaves the box. Thus, the mass of the bar is reduced by the "rest mass" of the photon.


At no time does the mass of the bar drop below it's original mass. If it drops at all, it is only because heating increased it's mass, so it sheds mass as it cools back to ambient temperature.



Just thinking out loud. Heat a metal bar and thermal BB radiation increases. Heat goes to a higher excitation of an atom leading to a photon. A causal chain of energy conversion. Energy of a photon derived from heat energy. No need for a change in mass.

Right. Energy into the box equals energy out, so the contents end with the mass they started with.

If there was a change of mass, that was because excited electrons temporarily increase the mass of their atoms.

But does that really happen? I don't know. I made it up. It's just a thought that I had while we were having this conversation. I do not urge it as a truth.




Mass can not come from or go to nothing.

Agreed. If energy quits being mass, then it has to take some other form. Sometimes it becomes electromagnetic radiation.



It would seem that a reduction in mass in the atom would have to reflected as mass somewhere else.

Is it that you think there is a law of conservation of mass? We believed in that until Einstein gave us relativity. Now we have conservation of energy. Mass is recognized as one form of energy.



The only alternative is to argue that E = mc^2 implies creation and destruction of mass.

Water has three states, solid, liquid, gas. Nothing is created or destroyed when water changes state.

Energy has multiple states too, with matter being one of them. Other forms of energy can be converted to mass; mass can be converted to other forms of energy.

We don't say that bread and cheese are "destroyed" when they are converted into a grilled cheese sandwich. Neither do I think it is appropriate to say that matter is destroyed when it converts into electromagnetic energy.



We are always exchanging photons with the background locally.

Agreed, yes.



The energy for that is heat.

Some of it, yes.



A bar of metal at equilibrium in a room is emitting BB tradition proportional to temperature.

Agreed, though I don't know why you stipulate that the bar is at room temperature.

I think what he is trying to get at is that according to his understanding, if what we say is right, the bar should be constantly losing mass as it emits energy.

What he is missing of of course is thay the bar is at equilibrium according to his own scenario - meaning it absorbs exactly as much energy as it emits.
 
wiploc

In a photo emitter quantum efficiency photons per electron. In a photo detector it is reverse.

If there is a mass change then heating a metal bar increasing thermal radiation means the bar weighs less. If that is true then as the bar is cooled back to equilibrium it regains weight?

You have it ass-backwards.

When you heat up that bar you are adding energy--the atoms are moving faster, m' = m / (1 - v2/c2). The mass goes up. As the energy radiates away it cools, the atoms slow, the weight goes down.
 
wiploc

In a photo emitter quantum efficiency photons per electron. In a photo detector it is reverse.

If there is a mass change then heating a metal bar increasing thermal radiation means the bar weighs less. If that is true then as the bar is cooled back to equilibrium it regains weight?

You have it ass-backwards.

When you heat up that bar you are adding energy--the atoms are moving faster, m' = m / (1 - v2/c2). The mass goes up. As the energy radiates away it cools, the atoms slow, the weight goes down.

That's always been my understanding, that a hot iron is more massive than a cold iron.

It makes sense from a relativistic perspective as well. Mass is motion, more motion equates with more mass. Heat is motion, as are all forms of energy. If things are moving faster, as they are with a hot iron, you will have more mass.
 
wiploc

You are making my case. Heat is the energy that powers the photon.

Energy in energy out with losses in the energy conversion.

In an incandescent bulb the heat is supplied by resistive heating, i^2*R.

In an LED that is not the case. I'd have to look it up.

Photons are EM radiation, the wave particle duality. In free space the propagation is orthogonal electric and magnetic oscillating fields. Photons are the energy carriers. For a given EMR power in watts there are a specific number of photons.

Clarifying, I do care. I do not care to exchange with those who argue from scifi and when called on it resort to ad homs.

You and I are having a reasonable conversation.
 
wiploc

You are making my case. Heat is the energy that powers the photon.

Energy in energy out with losses in the energy conversion.

In an incandescent bulb the heat is supplied by resistive heating, i^2*R.

In an LED that is not the case. I'd have to look it up.

Photons are EM radiation, the wave particle duality. In free space the propagation is orthogonal electric and magnetic oscillating fields. Photons are the energy carriers. For a given EMR power in watts there are a specific number of photons.

Clarifying, I do care. I do not care to exchange with those who argue from scifi and when called on it resort to ad homs.

You and I are having a reasonable conversation.

E=mc2 isn't scifi.
 
You are making my case.

On the contrary.



Heat is the energy that powers the photon.

Facepalm? Absent context, that seems an outrageous claim. :)



Energy in energy out with losses in the energy conversion.

Again, I suspect that I'm failing to understand due to lack of context.

Take your burning paper in a sealed glass box. Energy comes out without being matched by energy going in.



In an incandescent bulb the heat is supplied by resistive heating, i^2*R.

In an LED that is not the case. I'd have to look it up.

Photons are EM radiation, the wave particle duality. In free space the propagation is orthogonal electric and magnetic oscillating fields. Photons are the energy carriers. For a given EMR power in watts there are a specific number of photons.

This part is above my pay grade.



Clarifying, I do care. I do not care to exchange with those who argue from scifi and when called on it resort to ad homs.

You and I are having a reasonable conversation.

Cool, thanks.
 
https://phys.org/news/2017-06-atomic-mass-photon-momentum-paradox.html

It looks like the question of a photon having momentum but no mass is an active problem.

If I read the link right in the theory part of the mass travels with the photon. That I can accept. The queswtion I would have for say a laser diode operating continuously the mass loss would be continuous with no restoration.

Beyond that the theory beyond my depth.
 
https://phys.org/news/2017-06-atomic-mass-photon-momentum-paradox.html

It looks like the question of a photon having momentum but no mass is an active problem.

If I read the link right in the theory part of the mass travels with the photon. That I can accept. The queswtion I would have for say a laser diode operating continuously the mass loss would be continuous with no restoration.

Beyond that the theory beyond my depth.

The energy in the laser beam comes from the electrical power applied not from the mass of the diode. - - electrical energy converted to light energy.

Burning paper involves a very different process though it is still energy converting to a different form. There is no electrical energy applied to the burning paper. The energy (heat and light) that radiates from burning paper comes from chemical energy which involves the energy difference (mass difference) between free atoms and those atoms when combined into a molecule.
 
https://phys.org/news/2017-06-atomic-mass-photon-momentum-paradox.html

It looks like the question of a photon having momentum but no mass is an active problem.

If I read the link right in the theory part of the mass travels with the photon. That I can accept. The queswtion I would have for say a laser diode operating continuously the mass loss would be continuous with no restoration.

Beyond that the theory beyond my depth.

The energy in the laser beam comes from the electrical power applied not from the mass of the diode. - - electrical energy converted to light energy.

Burning paper involves a very different process though it is still energy converting to a different form. There is no electrical energy applied to the burning paper. The energy (heat and light) that radiates from burning paper comes from chemical energy which involves the energy difference (mass difference) between free atoms and those atoms when combined into a molecule.

Sure, but electricity is just an intermediary in that case - the chemical energy comes from the fuel burned in the power plant that generates the electricity (typically carbon [coal], methane [gas], or higher alkanes [oil]).

Most electricity worldwide is still made by burning coal, with gas catching up fast. Nuclear power is only a few percent, and the intermittent renewables (wind and solar) are a drop in the ocean. The renewables sector is still dominated by hydropower, with biofuels second, wind a distant third, and solar barely registering.
 
https://phys.org/news/2017-06-atomic-mass-photon-momentum-paradox.html

It looks like the question of a photon having momentum but no mass is an active problem.

If I read the link right in the theory part of the mass travels with the photon. That I can accept. The queswtion I would have for say a laser diode operating continuously the mass loss would be continuous with no restoration.

Beyond that the theory beyond my depth.

The energy in the laser beam comes from the electrical power applied not from the mass of the diode. - - electrical energy converted to light energy.

Burning paper involves a very different process though it is still energy converting to a different form. There is no electrical energy applied to the burning paper. The energy (heat and light) that radiates from burning paper comes from chemical energy which involves the energy difference (mass difference) between free atoms and those atoms when combined into a molecule.

Agree energy comes from the mains. Conservation of energy holds. The problem is current theory says a photon has a measurable momentum but no mass. I objected to a solution involving direct energy mass conversion in the atom. The link indicates a possible solution with mass being somehow attached to the photon. I do not have the physics to talk to it off the top of my head.
 
https://phys.org/news/2017-06-atomic-mass-photon-momentum-paradox.html

It looks like the question of a photon having momentum but no mass is an active problem.

If I read the link right in the theory part of the mass travels with the photon. That I can accept. The queswtion I would have for say a laser diode operating continuously the mass loss would be continuous with no restoration.

Beyond that the theory beyond my depth.

The energy in the laser beam comes from the electrical power applied not from the mass of the diode. - - electrical energy converted to light energy.

Burning paper involves a very different process though it is still energy converting to a different form. There is no electrical energy applied to the burning paper. The energy (heat and light) that radiates from burning paper comes from chemical energy which involves the energy difference (mass difference) between free atoms and those atoms when combined into a molecule.

Agree energy comes from the mains. Conservation of energy holds. The problem is current theory says a photon has a measurable momentum but no mass. I objected to a solution involving direct energy mass conversion in the atom. The link indicates a possible solution with mass being somehow attached to the photon. I do not have the physics to talk to it off the top of my head.
I think the problem is that you are trying to resolve it as a Newtonian process. Newton was damn good and came damned close but, after 300 years, science moved on and found a few cracks in his physics. But, even at that, Newton was close enough that, for every-day human-scale, his physics is still reliable enough to send rovers to Mars and land them safely.

A few things Newton had problems with are;
... He had no idea what gravity was even though the understood its effect well enough to give us his universal law of gravitation.
... He knew nothing of atoms, electrons, protons, binding energy, energy levels of electrons in atoms, etc.
... He assumed space was a Euclidean backdrop unaffected by matter or events.
... He assumed that time was a universal, completely independent of space and events.
... He assumed that mass and energy were completely separate and independent phenomena.

It is the last one that you are having problems with. Physics now knows and understands that there is an equivalence between mass and energy or that mass is just another form of energy. So much so that mass is expressed as an energy level in particle physics.

I don't recall reading that Newton ever tried to model where the energy released by fire came from. If he did then it must have been like his attempt to understand what gravity was... he just left it as god's mystery.

This seems to be where you are, not seeing where the energy released by fire comes from since mass is immutable and there was no source of energy. However, physics has understood since the very early 1900s that mass is not immutable but can be released as energy. Balancing mass or balancing energy is no longer sufficient... now we must balance mass/energy (which makes the answer to the question of the energy of fire obvious).
 
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