Why is thermal energy treated differently than other kinds of energy?

[nataliaeggers]

If “E=mc²”, where “E” is energy, if “W=delta-E”, if a change in gravitational potential energy produces work transforming into kinetic energy, if a change in kinetic energy produces work, if a difference in electrical potential is converted into a change in energy or work, if, in the end, different “E” (i.e., energies) is always a ‘theoretical’ (i.e., didactic, because energy is energy) transition of a fundamental manifestation — energy —, if every action produces a reaction (Newton's third law), then why is thermal energy the only different one? Why can thermal energy be used in science to generate work (e.g., combustion of petroleum derivatives), but cannot be used to explain the change in kinetic energy and the work done by the boiling motion of water inside my pan? Why, only in what is tangible to any human being in the world, does energy transformation cease to be a vector force like all the others and become a mathematical tautology?

 

[mfb]

I have no idea how to parse this run-on sentence. What is your question?

if every action produces a reaction (Newton's third law)

That's a statement about forces, not energy.

Then why is thermal energy the only different one?

Different from what?
The difference in unordered kinetic energy of water molcules is the gain in thermal energy if you heat water.

E = mc^2 is the energy of an object at rest.

 

[haruspex]

if every action produces a reaction (Newton's third law), then why is thermal energy the only different one?

Not sure what Newton III has to do with energy. Please elaborate.

Why can thermal energy be used in science to generate work (e.g., combustion of petroleum derivatives), but cannot be used to explain the change in kinetic energy and the work done by the boiling motion of water inside my pan?

Thermal energy is just disordered kinetic energy. Can you be more specific about what can't be explained by thermal energy but can be explained by other forms?

Why, only in what is tangible to any human being in the world, does energy transformation cease to be a vector force like all the others and become a mathematical tautology?

No idea what you mean by a mathematical tautology in this context.
You seem to be saying that energy transformation involves a force except where thermal energy is one of the two forms. The real difference is that transfer of heat energy involves countless forces in random directions (disordered) whereas kinetic, potential, elastic… involve one or a few forces in observable directions.

[old Australian cartoon (Patrick Cook), depicted Newton, observing an apple fall, declaring "It fell down". Title: "Newton discovers tautology".]

 

[kuruman]

Why can thermal energy be used in science to generate work (e.g., combustion of petroleum derivatives), but cannot be used to explain the change in kinetic energy and the work done by the boiling motion of water inside my pan?

I don't know about the water in your pan, but I know that I can use thermal energy to explain the change in kinetic energy of a book on my table that receives a sudden kick and slides across the table top until it stops. I can write total energy conservation from the moment the book starts moving until it stops as $$\Delta E_{\text{total}}=\Delta E_{\text{thermal}}+\Delta K=0.$$The equation explains what's happening. The kinetic energy change is negative whilst the thermal energy of the book and the table increases to keep the total energy constant.

In a more complex situation, muscles use biochemical energy stored in ATP molecules. You can view the muscle as a heat engine that takes in biochemical heat energy $\Delta Q_{\text{in}}$ and produces mechanical energy $\Delta E_{\text{mech.}}$ while rejecting heat $\Delta Q_{\text{out}}$ which is manifested as change in the thermal energy of the muscle (the muscle warms-up.) The total energy conservation equation is $$\Delta E_{\text{total}}=\Delta E_{\text{biochem.}}+\Delta E_{\text{mech.}}+\Delta E_{\text{thermal}}=0.$$The first change is always negative and the third is always positive. The second change can be either, positive if I use my muscles to lift an object up or negative if I lower an object to the ground.

My point here is that thermal energy is treated just like any other form of energy.

 

[berkeman]

(Thread discussion level changed from Graduate to Undergraduate, based on the OP's background.)

 

[cianfa72]

The total energy conservation equation is $$\Delta E_{\text{total}}=\Delta E_{\text{biochem.}}+\Delta E_{\text{mech.}}+\Delta E_{\text{thermal}}=0.$$The first change is always negative and the third is always positive. The second change can be either, positive if I use my muscles to lift an object up or negative if I lower an object to the ground.

My point here is that thermal energy is treated just like any other form of energy.

I'd like to point out that the increase in mechanical energy associated with lifting an object up, goes into the potential energy of the "Earth + object" system. In other words potential energy is a property of a system, not of an object (book) alone.

 

[Herman Trivilino]

Why can thermal energy be used in science to generate work (e.g., combustion of petroleum derivatives), but cannot be used to explain the change in kinetic energy and the work done by the boiling motion of water inside my pan?

In the 19th century researchers unified two different different types of phenomena, mechanical interactions and thermal interactions, using the concept of energy. Thus was created the grand principle of conservation of energy known as the First Law of Thermodynamics, and is taught to all children using the phrase "energy can neither be created nor destroyed, only converted from one form to another".

The Work-Kinetic Energy theorem applies only to mechanical interactions. For example, you will find that the work done is not, in general, equal to the change in kinetic energy. This is because some of the work done is used to generate an increase in thermal energy (or more correctly, internal energy). Thus, one has to account for both mechanical and thermal interactions if one expects energy to be conserved.

The reason thermal interactions and mechanical interactions are treated differently in physics is because it is necessary to do so to create a valid description of the way Nature behaves.

So your question can be replaced with another: Why does Nature behave in such a way that mechanical interactions are different from thermal interactions? And the answer can generate another "Why?" question, ad infinitum.

 

[kuruman]

I'd like to point out that the increase in mechanical energy associated with lifting an object up, goes into the potential energy of the "Earth + object" system. In other words potential energy is a property of a system, not of an object (book) alone.

Sure, but note that mechanical energy is the sum of kinetic plus potential energy. Therefore, in my expression, it is implied that $$\Delta E_{\text{mech.}}=\Delta K+ \Delta U$$no matter what you consider as the system.

 

[cianfa72]

Sure, but note that mechanical energy is the sum of kinetic plus potential energy. Therefore, in my expression, it is implied that $$\Delta E_{\text{mech.}}=\Delta K+ \Delta U$$no matter what you consider as the system.

Yes, for instance in the rest frame of the "Earth + object" system's Center-of-Mass, the kinetic energy is basically associated to the rising object, i.e. we can neglect the kinetic energy term associated to the Earth.

 

[nataliaeggers]

Not sure what Newton III has to do with energy. Please elaborate.

Thermal energy is just disordered kinetic energy. Can you be more specific about what can't be explained by thermal energy but can be explained by other forms?

No idea what you mean by a mathematical tautology in this context.
You seem to be saying that energy transformation involves a force except where thermal energy is one of the two forms. The real difference is that transfer of heat energy involves countless forces in random directions (disordered) whereas kinetic, potential, elastic… involve one or a few forces in observable directions.

[old Australian cartoon (Patrick Cook), depicted Newton, observing an apple fall, declaring "It fell down". Title: "Newton discovers tautology".]

Mathematical tautology means that the 2nd law of Thermodynamics can accommodate anything through post hoc rationalization i.e., it doesn’t prohibit any outcome (i.e., anything is impossible, anything can only be unlikely), so it can’t be falsified (by Popper’s terms), so it’s pseudoscience…

 

[nataliaeggers]

I don't know about the water in your pan, but I know that I can use thermal energy to explain the change in kinetic energy of a book on my table that receives a sudden kick and slides across the table top until it stops. I can write total energy conservation from the moment the book starts moving until it stops as $$\Delta E_{\text{total}}=\Delta E_{\text{thermal}}+\Delta K=0.$$The equation explains what's happening. The kinetic energy change is negative whilst the thermal energy of the book and the table increases to keep the total energy constant.

In a more complex situation, muscles use biochemical energy stored in ATP molecules. You can view the muscle as a heat engine that takes in biochemical heat energy $\Delta Q_{\text{in}}$ and produces mechanical energy $\Delta E_{\text{mech.}}$ while rejecting heat $\Delta Q_{\text{out}}$ which is manifested as change in the thermal energy of the muscle (the muscle warms-up.) The total energy conservation equation is $$\Delta E_{\text{total}}=\Delta E_{\text{biochem.}}+\Delta E_{\text{mech.}}+\Delta E_{\text{thermal}}=0.$$The first change is always negative and the third is always positive. The second change can be either, positive if I use my muscles to lift an object up or negative if I lower an object to the ground.

My point here is that thermal energy is treated just like any other form of energy.

I appreciate everyone taking the time to respond, but I think there’s a fundamental misunderstanding about what I’m asking. When mfb says “not sure what Newton III has to do with energy,” this reveals exactly the conceptual gap I’m trying to address.

Newton’s third law isn’t just about forces in isolation. It’s about the relationship between action and reaction in physical interactions, and this is directly tied to energy and work. The entire foundation of classical mechanics rests on understanding that work equals force times distance, and work equals the change in energy. So we have w=f.d and w=delta-e, which means delta-e=f.d. Force, work, and energy are not separate concepts that we can discuss independently. They’re intrinsically linked in the mathematical structure Newton gave us.

When I push a book across a table, my hand exerts a force, the book moves a distance, work is done, and the kinetic energy of the book changes. The book simultaneously exerts an equal and opposite force on my hand. This is Newton’s third law in action, and it’s inseparable from the energy transformation occurring. Every mechanical process we describe involves this interplay between forces, work, and energy changes.

Now here’s my actual question: why does thermal energy get treated as a special case where this relationship breaks down? Kuruman says thermal energy involves countless forces in random directions while other forms involve forces in observable directions. But this is exactly what I’m questioning. When water boils in my pan, I can observe the direction. The water moves upward, vapor forms and rises, convection currents flow in specific patterns. These aren’t random motions without direction. They’re organized, observable movements that clearly involve forces acting in particular ways.

The standard answer is that at the molecular level it’s all random collisions, and we use statistics because we can’t track individual molecules. Fine. But my question is more fundamental: why can we use thermal energy to explain work in an engine, where we happily connect heat to mechanical motion through expansion and pressure, but we cannot use thermal energy to explain the mechanical motion of boiling water using the same energy-force-work relationship? It’s the same energy, the same type of molecular motion, yet in one context we maintain the connection to directional forces and work, and in the other we say it’s just disordered and statistical.

I’m not claiming energy is a force. I’m asking why the transformation of thermal energy into kinetic energy and work suddenly requires us to abandon the force-work-energy framework that applies everywhere else in physics. When gravitational potential energy converts to kinetic energy, we describe it through forces and work. When elastic potential energy converts to kinetic energy, we describe it through forces and work. When electrical potential energy converts to kinetic energy, we describe it through forces and work. Why does thermal energy conversion require a completely different explanatory framework based on statistical disorder rather than physical causality?

The equation delta-E-total = delta-E-thermal + delta-K = 0 that kuruman provided describes conservation, which I’m not disputing. But conservation equations tell us that energy is accounted for, not how it physically transforms. The “how” question is what I’m asking. In every other energy transformation, we have physical mechanisms involving directional forces. In thermal processes, we replace mechanism with statistics and call it fundamental randomness.

I’m genuinely trying to understand why this one form of energy gets ontologically different treatment. If the answer is “because that’s how statistical mechanics works,” then I’m asking why we built statistical mechanics that way rather than seeking the same kind of causal, directional force explanations we demand everywhere else in physics. That’s not an undergraduate confusion about definitions. It’s a question about why our theoretical framework treats thermal phenomena as fundamentally different from all other physical phenomena.

 

[jbriggs444]

Newton’s third law isn’t just about forces in isolation. It’s about the relationship between action and reaction in physical interactions, and this is directly tied to energy and work.

Newton's third law is all about momentum. It amounts to a statement that momentum is conserved.

Newton's third law has less to do with energy. However, let us proceed to your next paragraphs...

The entire foundation of classical mechanics rests on understanding that work equals force times distance, and work equals the change in energy. So we have w=f.d and w=delta-e, which means delta-e=f.d. Force, work, and energy are not separate concepts that we can discuss independently. They’re intrinsically linked in the mathematical structure Newton gave us.

When I push a book across a table, my hand exerts a force, the book moves a distance, work is done, and the kinetic energy of the book changes. The book simultaneously exerts an equal and opposite force on my hand. This is Newton’s third law in action, and it’s inseparable from the energy transformation occurring.

Let us chase this down. The force of your hand on the book is equal and opposite to the force done by the book on your hand. That is Newton's third law in action, just as you say.

The displacement of the book at the interface with your hand is equal to the displacement of your hand at the interface with the book. This is a characteristic of non-slipping mechanical interactions.

As a result we can conclude that the work done by hand on book is equal and opposite to the work done by book on hand.

But let us examine the situation where the book slides to a stop on the top of the table.

Again, the force of book on table is equal and opposite to the force of table on book. But this time the displacement of the book during the interaction is not equal to the displacement of the table during the interaction. The book moves. The table does not.

Now the work done by book on table is zero while the work done by table on book is non-zero (and negative). The net work done during the interaction is non-zero and negative. Mechanical energy has been lost.

If we measure the temperature of the book and of the table, we can find the missing energy. It is impractical to model this energy in terms of a large but finite sum of a myriad of microscopic interactions involving not-perfectly-rigid ridges, not-perfectly-rigid valleys and Van Der Waal's interactions between molecules that are not on geodesic trajectories. Instead we just wave our hands and call it "thermal energy".

Every mechanical process we describe involves this interplay between forces, work, and energy changes.

Certainly.

Now here’s my actual question: why does thermal energy get treated as a special case where this relationship breaks down?

Because it is impractical to model the interaction between book and hand as the interaction of $6.02 \times 10^{23}$ point-like book molecules with $6.02 \times 10^{23}$ point-like table molecules.

Or, to state it differently, because we can measure mechanical energy with platform balances, rulers and stopwatches. But we usually measure thermal energy with thermometers (and platform balances and graduated cylinders).

We can model some systematic non-rigid motions in ways that are tractable. For instance, Hooke's law. For other random motion, we throw up our hands and retain only bulk statistical measures such as temperature, density, pressure (or stress), flow velocity and thermal energy per unit mass.

 

[cianfa72]

But let us examine the situation where the book slides to a stop on the top of the table.

Again, the force of book on table is equal and opposite to the force of table on book. But this time the displacement of the book during the interaction is not equal to the displacement of the table during the interaction. The book moves. The table does not.

You mean the table doesn't move w.r.t. the rest frame of "book + table" system's Center-of-Mass.

 

[jbriggs444]

You mean the table doesn't move w.r.t. the rest frame of "book + table" system's Center-of-Mass.

No, that is not the frame that I implicitly chose. The table does move with respect to the table+book COM frame.

The frame that I had in mind is the lab frame where the table is continuously at rest. One can tell that this is the choice I made based on the fact that I spoke of the table having zero displacement.

Other inertial frames could have been chosen. In every one of them, the total work done (table on book plus book on table) would be identical and negative. This is a somewhat useful fact. In Newtonian mechanics, the mechanical work performed in an interaction (total of A on B and B on A) is an invariant. It does not depend on the choice of [inertial] reference frame. This squares neatly with the fact that the thermal energy increase resulting from an interaction is also an invariant.

[If one shifts to the realm of special relativity, I believe that @Dale worked out once that the total work done is still an invariant. But memory fades and I am not sure about the details that would support such a claim]

The center of mass frame is of no particular interest. A typical table rests motionless (relative to the ground) on the floor rather than sliding on some hypothetical frictionless surface.

 

[cianfa72]

No, that is not the frame that I implicitly chose. The table does move with respect to the table+book COM frame.

The frame that I had in mind is the lab frame where the table is continuously at rest. One can tell that this is the choice I made based on the fact that I spoke of the table having zero displacement.

Ok, you are assuming the inertial rest frame of the table. By Newton 3rd law, the book acts with a force on the table, so there must be a force from the floor (friction) acting to the table to get zero net force on it. The table stays continuously at rest in that inertial frame, so no mechanical work is done by those two forces on it (zero displacement). Therefore the kinetic energy from the book that "disappers" goes in thermal energy within both.

 

[Herman Trivilino]

Ok, you are assuming the inertial rest frame of the table. By Newton 3rd law, the book acts with a force on the table, so there must be a force from the floor (friction) acting to the table to get zero net force on it.

The table doesn't move relative to the floor in any frame.

 

[Dale]

I think there’s a fundamental misunderstanding about what I’m asking

That isn’t surprising given how poorly written your original post was. This one was much better

So we have w=f.d and w=delta-e, which means delta-e=f.d.

These equations are incorrect. The correct equations are

$$W_{\mathrm{mech}}=\int \vec f \cdot d\vec s$$$$W=W_{\mathrm{mech}} + W_{\mathrm{non-mech}}$$$$\Delta E = Q - W$$ so it is not generally true that $\Delta E = \vec f \cdot \vec d$. In particular, there are many forms of work that are not mechanical work.

why does thermal energy get treated as a special case where this relationship breaks down?

Because it is useful to do so. If I could wave a magic wand I would not define heat as something different from work. I would call it "thermal work". But the terminology evolved historically, so it is what it is. The important thing is not consistency of terminology, but the consistency with experimental results.

Newton’s third law isn’t just about forces in isolation. It’s about the relationship between action and reaction in physical interactions, and this is directly tied to energy and work.

Newton's third law is directly tied to momentum and impulse, not energy and work. Force is the rate of transfer of momentum, it is not generally a transfer of energy.

Why does thermal energy conversion require a completely different explanatory framework based on statistical disorder rather than physical causality?

It is not that thermal energy requires a different framework, it is that it allows a different framework. Yes, in principle we could write down many quintillions of force equations for each individual particle at a causal level. But we don't need to.

Statistical mechanics shows that if you have a huge number of degrees of freedom then the details of the microscopic causal mechanisms don't matter. We can have electromagnetic interactions, mechanical collision interactions, torsion or bending interactions, each of which are governed by different causal mechanisms with their own individual equations. The aggregate properties described by heat, entropy, etc. follow the statistical laws of thermodynamics regardless of the details at the microscopic causal level.

This is very useful because we can describe a lot of what happens without requiring us to look into the huge number of degrees of freedom that would otherwise be required.

 

[kuruman]

To @nataliaeggers:
Let me elaborate a bit more along the lines presented by @jbriggs444. Suppose you have a collection of $10^{24}$ gas atoms in a metal container. These atoms are all moving in random directions colliding with each other and with the walls of the container. Furthermore, let's assume that the collisions are perfectly elastic and there is no energy loss anywhere. In this model, application of Newton's laws predicts that

1. When gas atom collides with the wall, the component of the atom's velocity that is perpendicular to the wall changes direction whilst the component of the velocity parallel to the wall remains the same. This is otherwise known as "specular refection".
2. When gas atom collides with another gas atom, the component of the atom's velocity that is perpendicular to the line joining the two atoms remains unchanged whilst the component of the velocity parallel to that line is swapped, i.e. in the direction joining the two atoms, $~V_{\text{final, 1}}=V_{\text{initial, 2}}~$ and $~V_{\text{final, 2}}=V_{\text{initial, 1}}~.$

If I stick a thermometer in the container I will read a certain temperature. If I use a blow torch on the container, I see that the temperature of the gas rise. How is the temperature rise related to the heat energy that was added? The kinetic theory of gases provides the link between the macroscopic ideas of pressure, volume and temperature and the $10^{24}$ microscopic idea of gas molecules. The idea is simple: Adding energy to the container increases the kinetic energy of each molecule but, because there so many of them and they exchange energy with each other through collisions, we cannot keep track of all of them but consider instead the average energy of a gas atom. The kinetic theory of gases uses Newtonian mechanics to deduce that temperature $T$ appearing in the ideal gas law $pV=NkT$ is proportional to the average kinetic energy of an atom. Higher/lower temperatures mean faster/slower moving atoms on average.

So how is energy from the blowtorch transferred to the gas atoms? Here is a possible mechanism. The heat energy in the flame comes from the combination of carbon in the fuel with oxygen to form carbon dioxide. $$\text{C}+\text{O}_2\rightarrow \text{CO}_2.$$ Now the CO₂ molecule is a bound system that has a lot of kinetic energy as required by total energy conservation. Think of it this way: energy is required to separate the carbon atom from the oxygen molecule and have them at rest in front of you. Conversely, if the two are in front of you at rest and combine to form a CO₂ molecule, to conserve energy the molecule has to have kinetic energy matching the binding energy of its constituents.

So now you have the ingredients to figure out how the flame increases the kinetic energy of the gas atoms inside the container. The fast moving combustion products (CO₂ molecules if you wish) collide with the molecules forming the exterior wall of the container. The collisions transfer kinetic energy from the CO₂ molecules to the wall molecules. The more rapidly jiggling exterior wall molecules transfer extra jiggling energy to the molecules forming the interior wall of the container through the forces that bind the molecules of the wall together. Finally, the more rapidly jiggling interior wall molecules transfer, on average, more energy to the gas atoms when the latter collide with the wall. Thus, the temperature of the gas inside the container rises when you put the blowtorch to the container.

As you can see, the transfer of thermal energy involves increases of the kinetic energy through collisions and jiggling (waves through solids) in a medium and is subject to Newton's laws. This covers heat transfer through conduction and convection. A medium is not needed when heat energy is transferred by radiation. The energy is contained in packets (photons) which can travel through vacuum and are absorbed by individual atoms. An example of this is microwave ovens. The frequency of the microwave photons is "tuned" to the rotational frequency of water molecules. This added rotational energy soon becomes added jiggling energy which as we have seen means higher temperature.

I have said much more than I Intended to say, but I hope to have given you a mechanism that is subject to Newton's laws and that you can use to model the process of heating the water in your pan. It's not much different from heating gas atoms in a metal container.

 

[Herman Trivilino]

Newton’s third law isn’t just about forces in isolation. It’s about the relationship between action and reaction in physical interactions, and this is directly tied to energy and work.

When Newton wrote about action and reaction he was referring to forces. It was the 1680's. The concept of energy, if it even existed at that time, was not anything like the fully-formed concept of today.

As I told you before it wasn't until the 1800's that researchers formed the concept of energy as we know it today.

You interpret these terms to mean one thing, but in the standard lexicon of physics they mean something else.

 

[jbriggs444]

When Newton wrote about action and reaction he was referring to forces. It was the 1680's. The concept of energy, if it even existed at that time, was not anything like the fully-formed concept of today.

Agreed. I like to point to Newton's original text from time to time. The second part is the one that really resonates with me.

Actioni contrariam semper et æqualem esse reactionem: sive corporum duorum actiones inse mutuo semper esse æquales et in partes contrarias dirigi.

To every action there is always opposed an equal reaction; or the mutual actions of two bodies upon each other are always equal, and directed to contrary parts.

In modern words: "the force of A on B is equal and opposite to the corresponding force of B on A".

The notions of "action" and "reaction" are often mistakenly understood in terms of cause and effect.

 

[haruspex]

Mathematical tautology means that the 2nd law of Thermodynamics can accommodate anything through post hoc rationalization i.e., it doesn’t prohibit any outcome (i.e., anything is impossible, anything can only be unlikely), so it can’t be falsified (by Popper’s terms), so it’s pseudoscience…

Clearly that is not the case. If you were to place two inert bodies in contact and observe the result that the warmer body grows warmer at the expense of the other you would have falsified the second law. What you mean, I think, is that the law is not strictly true, merely statistically true. That would be a fair criticism, but in any macroscopic circumstance the probability of such a violation is so low that it is unlikely to have happened anywhere in the universe so far.

Wrt why heat energy is 'treated differently', @jbriggs and others have explained that it is simply more practical than dealing with the detailed motions of the molecules. Indeed, there is no hard boundary. Start with a perfectly elastic red ball bouncing around in a fixed box. Now add a yellow ball. We can still deal with the details of their interactions and calculate that their kinetic energies will tend to equalise, but that the tendency is less when their energies are very similar. As we add more balls, we can become more confident of what the distribution of energies will look like, but precisely what energy each has we cannot say.

 

[kuruman]

If you were to place two inert bodies in contact and observe the result that the warmer body grows warmer at the expense of the other you would have falsified the second law.

I will hazard a guess as to where OP's problem lies. Perhaps something like this.

The second law is justified as a law because heat flowing from the low temperature to the high temperature reservoir has never been observed. Fine. However, if this kind of reasoning is valid for establishing a law, we can very well assert that "The Sun always rises to the East" is a law because we have never observed the Sun rise to the West. But this is clearly a tautology because the direction "East" is defined by the rising Sun. So why is the latter a tautology and not the former?

 

[Herman Trivilino]

Conservation of energy was in serious danger of being abandoned when experiments by Curie seemed to show that radium salts were creating thermal energy with no identifiable source. The Einstein mass-energy equivalence came to the rescue.

To the uninitiated this can all seem like a fabrication. Yes, researchers seem to be manufacturing the sources needed to make the principle valid, and that seems a fabrication.

But the fact is, Nature behaves in such a way that this "fabrication" can be formed. So it's a valid description of Nature's behavior, and in the end that is all that physics can ever do for us.

 

[haruspex]

I will hazard a guess as to where OP's problem lies. Perhaps something like this.

The second law is justified as a law because heat flowing from the low temperature to the high temperature reservoir has never been observed. Fine. However, if this kind of reasoning is valid for establishing a law, we can very well assert that "The Sun always rises to the East" is a law because we have never observed the Sun rise to the West. But this is clearly a tautology because the direction "East" is defined by the rising Sun. So why is the latter a tautology and not the former?

I don’t get the analogy.
If East is defined as the side the Sun has always risen in recorded history, where a 'side' is defined by landmarks, saying it will continue to rise that side is not tautology.
Likewise, for heat flow, we need first to have an independent definition of temperature that suffices to ascribe a (signed) metric to temperature difference. Armed with that, we can rephrase the law as "temperatures even out".

 

[russ_watters]

Likewise, for heat flow, we need first to have an independent definition of temperature that suffices to ascribe a (signed) metric to temperature difference. Armed with that, we can rephrase the law as "temperatures even out".

It's also not an arbitrary convention/just a name, like East/West or for that matter, positive and negative charge. You can't swap high and low temperatures in thermodynamics.

And while "it's never been observed to be false" is good evidence that it's true, the second law isn't just created from that observation, it's predictable.