Joule, through his experiments, established 'heat' as the name for energy transfer across a system boundary when there is a temperature difference between a system and its surroundings.

I may be mistaken yet it sounds that you want to identify something called 'internal heat energy' as a discrete, identifiable state function...discrete and identifiable from the other state functions that describe the condition of a system. In thermodynamics these state functions are called by various name, as you know,...thermodynamic properties, thermodynamic coordinates, state variables, et cetera. Heat, to wit: energy transfer, is not a state function in the classic sense, rather is one dynamic quantity, with work (non-thermal energy) describing the internal energy, U, of a system at some instant in time or interval between equilibrium states.

Is there a discrete, identifiable function of state called internal heat energy? In other words, can we analyze, identify and measure the discrete energy units such that internal heat energy is quantifiably isolated from other energies, such as potential and kinetic energies, internal to a system? Introducing the word and concept 'heat', with its specific experimental and theoretical basis in thermodynamics, into internal energy to attempt a discrete isolation from other conditions of state would be similar to introducing 'internal work energy'. The nomenclature becomes rather confusing from a classical point of view.

You may be better served by investigating the mesoscopic or microscopic conditions, then you find yourself at the macroscopic limit and state functions may no longer be determinative. You may also find 'condensed matter physics' (Anderson) a vital approach for isolating what you are calling internal heat energy, though this approach will take you further from classical thermodynamic systems into symmetry breaking, lattice waves at very low temperatures.

"what do you think about the concept of the internal heat energy?" In a classical view, internal heat energy is a variable, heat, of a state function, internal energy U, along with work and other quantities that determine the dynamics of system. To avoid confusion you might consider a different name and then define it according to intensive or extensive properties of a system. This appears a rational approach in view you desire a concept separable from pressure and volume, which approach may require formulating an ideal model from which to work experimentally.

As for the limitation of reversibility by Clausius, one should also remember that Clausius introduced, as early as 1850, the concept of non-compensated heat as a irreversibility measure. His work was extended by De Donder, among others. Studies and experiments in irreveribility continued with Onsager, Casimir, Meixner, and Prigogine, setting up the phenomenological theory of irreversible processes...giving birth to nonequilibrium thermodynamics. You might benefit from the work of de Groot and Mazur in this regard (ch.VII.2, pages 84-92 for state variables).

Dear Saman，

Many thanks for your reply, which is very useful to me. I found some related articles but not found the full text that you suggest.

Some of the views are very interesting by these related articles, such as

Many books on thermodynamics contain vague and strange statements, such as ‘heat flows’, or ‘heat is a form of energy’, or ‘heat is energy in transit’, or it is ‘energy at a boundary’, or it is ‘the process’, or ‘the mechanism by which energy is transferred’. Work is ‘being done’ or is ‘being transformed into heat’. Heat and work, these ‘two illegitimate troublemakers’, in the words of Barrow1, do not provide a proper base on which to build thermodynamics

Heat and work seem to float between the system we deal with and its surroundings. They are not properties of the system we are dealing with, or of any other system. (R.T. Jones)

In these related articles, the authors use enthalpy H to discuss heat, different from my idea. I am trying to introduce a new concept, the internal heat energy into thermodynamics, which is different from enthalpy H, the difference between the two is the coupling term PV.

As an example, for an idea gas,

The internal heat energy q=U, the enthalpy H=U+pV,

The physical content of the internal heat energy q is one independent type of the internal energy U, which make contribution to temperature T and pressure p. But the enthalpy H is not an independent type of the internal energy U, which contains the coupling term PV

The reason why Q is not a state function is that Q is not part of a thermodynamic equilibrium system. Q is flowing, e.g., from a reservoir to the system. The state function that describes the energy content of a system is the internal energy. Now there is indeed a relation between reversibly exchanged heat and entropy where entropy is a state function. Note that we will here always refer to entropy change due to reversible heat exchange. Also, please don't use the wording internal heat energy. Just say internal energy if you refer to the system and heat when you refer to exchanged energy which is flowing from one system to another.

Dear Saman, you cite a good example.

For the equation you mentioned, we have

U = sum_i ( E_i •n_i ).

dU = sum_i ( E_idn_i +n_idE_i ).

Where n_i is the number of particles that each level i is occupied. The first term corresponds to the heat flux dQ, and the second term to the volume work dW(pV).

In this case, there is only one type of the internal energy U, the sum of ( E_i •n_i ), I call this type of the internal energy as the internal heat energy; marked with the symbol q, distinguished from other types of the internal energy for generalized thermodynamic system.

Where sum ( E_idn_i ) and both sum_i ( n_idE_i ) are not exact differential, but the sum of the two is an exact differential. Correspond to thermodynamics, dQ and both the volume work dW(pV) are not exact differential, but dQ+dW(pV) is an exact differential. Thus for an idea gas we get

dU=dq=deq+diq= dQ-dW(pV).

Where deq is the heat flux, and diq =-dW(pV) is the heat conversion between heat and ( free energy ), or the heat production ( imagine a piston compressing a gas ).

For a generalized thermodynamic system

dU=dQ- dW(pV)-dW+sum_j ( mu_jdN_j ).

It follows that

dU=dq+Ydx+sum_j ( mu_jdN_j ).

Where dW are other types of work, does not include the volume work, and Ydx does not include −pdV. Y is the generalized force, dx is the generalized displacement, μ_j is known as the chemical potential of the type-j particles, and N_j is the number of the type-j particles.

Q is not a state function; the reason is that there is another source of the heat energy: the heat production diq. So a state function might be built by

dq=deq+diq=dQ+diq

Next step just have to prove that dq is an exact differential. If it is, we will get a new concept: the internal heat energy of the system, and could build thermodynamics on energy (and ?)-not on heat flux Q and work W.

Dear Christian, I partially agree with your point of view, but you misunderstood my opinion. We all know that Q is not part of a thermodynamic equilibrium system. In this topic, I want to discuss a new concept: the internal heat energy of the system, which is a part of the internal energy, not the heat flux Q. I will add an article link below this topic later, please see the top floor.

Given an isolated system, which with temperature T and pressure p, the divergence between you and me is that

My opinion: The internal energy of the system contains the heat energy, the latter is the internal heat energy.

Your opinion: Q is flowing, please don't use the wording internal heat energy. ….if you refer to the system.

The given system has no heat energy?

I cannot understand cleary the point. Probably, it is a my fault and I am missing something. From the physical point of view, when we talk about heat we are talking about a process and not about a state, Besides this, what do you means by "heat production"? I have to admit that such a concept appears obscure to me.

Dear Francesco, you have not missed something according to current theories. As the current thermodynamics was built on some non-state variables (such as Q and W) + some mixture of the independent state variables (such as H or F) + some independent state variables (such as T, V, μ, N and G). Though the mathematical conclusions of the theories are correct, which still result in some issues: we cannot unfold some important themes on this base.

For a conserved quantity, such as the internal energy U, the changes of which can be represented as the sum of the exchanges between the two different systems that

dU=dQ-dW+sum_j ( μ_jdN_j ).

Where dU is equal to the sum of the fluxes.

But for a non-conserved quantity, such as Gibbs free energy, there will be the two sources of which, different from a conserved quantity. One is Gibbs free energy flux deG, come from the exchanges between the two different systems, the other is Gibbs free energy production diG, come from energy conversion. Where the exchanges between the two different systems correspond to the fluxes; and the conversion corresponds to the production. Thus we have

dG=deG+diG.

Where dG is the sum of the fluxes deG and the productions diG.

The heat production diq is the change of the heat energy, which does not come from dQ, but from energy conversion, such as diq=-diG (chemical reaction or phase transition), friction and damping.

Similar to Gibbs free energy, we should have

dq=deq+diq

Where q is the internal heat energy of the system, which is one part of the internal energy U, deq=dQ is the heat flux (which can also be used to describe heat transfers within the system), and diq is the heat production.

In current theories, we only have the definition of the heat flux Q, but lack the definition of the heat production, and lack a complete concept: internal heat energy, which seems to be lost.

Thanks for the explanantion. But several points remain unclear to me. I will try to find some time for a deeper insight to the problem. At the moment, your explanation of the locution "heat production" increased my confusion. Now you are talking about heat energy. Which is an almost tautologic concept, because heat is a work.. As you correctly says it is the work necessary for redistributing energy among different degree of freedom. Probably, we have some difficulty with words. I will try to follow your formalism (at least, mathematics is universal). It seems to me that you are trying to make some difference between energy fluxes from different systems and from internal degree of freedom of the same system. But in any case we should have heat flux (between two different systems) or internal heat flux in a out of equilibrium system. I cannot understand, at the moment, why one of them should be a "production".

Dear Francesco, I guess that the “unclear” may be related to the equation that

dq=deq+diq=dQ-dW(pV).

Where dW(pV) is the volume work. The physical meaning of the equation is that

dq = heat exchange + heat conversion.

Consider a generalized thermodynamic system. The internal energy equation of the system may be given by “the sum of the exchanges” that

dU=dQ-dW(pV)-dW+sum_j (mu_jdN_j).

Where I distinguished dW(pV) from other dW.

For a reversible process, the equation corresponds to

dU=deq+diq+Ydx+ sum_j (mu_jdN_j).

The first, third and fourth terms only correspond to the exchanges, but the second term is rather special, which correspond to an exchange process, and itself is also a heat energy conversion. For which, the "production" comes from the“conversion” .

For example, consider the two systmes, the system A is an ideal gas, the systme B is a piston. Imagine the ideal gas promoting the piston to do work, it is an energy exchange process, and is also an energy conversion. For system A, the internal heat energy of the system is equal to the internal energy (q=U). In this case, some of the internal heat energy q is converted into the free energy (Ydx) of the piston via the path of the conversion dW(pV), the reduction of the internal heat energy dq is the heat production diq

Thanks Shamit, I have already read it.

I’m looking for a complete thermodynamic approach, which is only built on some independent state variables except for U and S, instead of the mixed-base of current theories that contains some non-state variables (such as Q and W) + some mixture of the independent state variables (such as H or F) + some independent state variables (such as T, V, μ, N and G).

For a gas the internal energy is the sum of kinetic and potential energy (plus a constant). Can you describe how 'internal heat energy' relates to these?

Dear Stefan, Since dynamics and thermodynamics are built on different multivariable system, in general, there is no simple one-to-one correspondence. Thermodynamics contains some themes that related to structure, phase, order, entropy, etc. the theoretical construct of which is different from dynamics.

In dynamics, we have the internal energy U = U ( p_i,q_i ) , where p_i and q_i are the canonical variables /coordinates. In thermodynamics, we have U = U ( T, V, x, N_j ) , where T, V, x and N_j are the independent state variables. T, V, x and N_j cannot correspond to p_i and q_i by one-to-one.

In your case, for a gas we have

U= q+G

Where U is the internal energy, q is the internal heat energy and G is Gibbs free energy.

q = the part of the kinetic energy, which make no contribution to the chemical potential μ_j.

G = potential energy + the part of the kinetic energy, which make contribution to the chemical potential μ_j.

For a monatomic ideal gas, or a photon gas, we have

q = U

q = the kinetic energy of the system.

Where q is the function of the two independent variables T and V.

Joule, through his experiments, established 'heat' as the name for energy transfer across a system boundary when there is a temperature difference between a system and its surroundings.

I may be mistaken yet it sounds that you want to identify something called 'internal heat energy' as a discrete, identifiable state function...discrete and identifiable from the other state functions that describe the condition of a system. In thermodynamics these state functions are called by various name, as you know,...thermodynamic properties, thermodynamic coordinates, state variables, et cetera. Heat, to wit: energy transfer, is not a state function in the classic sense, rather is one dynamic quantity, with work (non-thermal energy) describing the internal energy, U, of a system at some instant in time or interval between equilibrium states.

Is there a discrete, identifiable function of state called internal heat energy? In other words, can we analyze, identify and measure the discrete energy units such that internal heat energy is quantifiably isolated from other energies, such as potential and kinetic energies, internal to a system? Introducing the word and concept 'heat', with its specific experimental and theoretical basis in thermodynamics, into internal energy to attempt a discrete isolation from other conditions of state would be similar to introducing 'internal work energy'. The nomenclature becomes rather confusing from a classical point of view.

You may be better served by investigating the mesoscopic or microscopic conditions, then you find yourself at the macroscopic limit and state functions may no longer be determinative. You may also find 'condensed matter physics' (Anderson) a vital approach for isolating what you are calling internal heat energy, though this approach will take you further from classical thermodynamic systems into symmetry breaking, lattice waves at very low temperatures.

"what do you think about the concept of the internal heat energy?" In a classical view, internal heat energy is a variable, heat, of a state function, internal energy U, along with work and other quantities that determine the dynamics of system. To avoid confusion you might consider a different name and then define it according to intensive or extensive properties of a system. This appears a rational approach in view you desire a concept separable from pressure and volume, which approach may require formulating an ideal model from which to work experimentally.

As for the limitation of reversibility by Clausius, one should also remember that Clausius introduced, as early as 1850, the concept of non-compensated heat as a irreversibility measure. His work was extended by De Donder, among others. Studies and experiments in irreveribility continued with Onsager, Casimir, Meixner, and Prigogine, setting up the phenomenological theory of irreversible processes...giving birth to nonequilibrium thermodynamics. You might benefit from the work of de Groot and Mazur in this regard (ch.VII.2, pages 84-92 for state variables).

Thanks Don, My main interest is physics (thermodynamics and statistical mechanics) and physical chemistry (chemical thermodynamics) , I know that there are some differences in terminology between the two and engineering thermodynamics.

“Is there a discrete, identifiable function of state called internal heat energy?”

Yes, it is.

The internal energy of a system contains some different types of energy, which can be classified into the two types based on their contribution to entropy. The internal heat energy makes contribution to entropy; the others make no contribution to entropy [please see the article link at the top floor, Eq.(48) ]. At the micro-scale, it can be distinguished according to the types of energy and with the aid of the degrees of freedom.

“Since dynamics and thermodynamics are built on different multivariable system, in general, there is no simple one-to-one correspondence.” In thermodynamics, we cannot distinguish the types of the internal energy based only on “potential and kinetic energies, internal to a system”, or else, there will be no structure, no phase, no order, no entropy, etc.

For YxT system, the “internal work energy” has already been defined. In physics, it is the thermodynamic potential Yx; correspond to Landau potential (grand potential) at constant volume. Where Y is the generalized force and dx is the generalized displacement.

I must apologize, Tang Suye, for having responded to your question without first reviewing your article on Internal Heat Energy. My response would have been demonstratively different.

Your article is an excellent presentation of the difficulties involving entropy and the second law, by offering a mathematical and physical path for further study. I always enjoy new approaches. I now believe, I more clearly understand your insistence on internal heat energy, q, as a state function.

Your articles development of the exact differential definition is most revealing and allows us to apply and test your new approach. I was particularly drawn into your inclusion of j-type particles, which seems to me as a 'bridge' between classical thermodynamics and nonequilibrium thermodynamics. Identifying 'bridges' for understanding a continuum thermodynamics has been of particular importance for my research. Possibly your reference to dissipation is a window to vital research.

Also your New Foundation discussion challenges one to reconsider an area left undone, at least in a thermodynamical sense, with the theoretical link between the first and second laws.

Dear Don, It’s my oversight, I should add some introduction in the topic, and sorry the equation should be Eq.(48).

… an interesting article! I think you should call Q not “heat flux” (that implies a time dependence), but “exchanged heat” or something similar. But why have delta Q and and W in your Eq. (1) different signs? The usual convention is energy going out of the system being considered negative.

Could you also explain why you treat pV work differently from other kinds of work?

Dear Ulrich, I agree with your opinion: 1) Q is really “exchanged heat”, besides Q, there is another kind of “heat flux”, the flux within system, and in non-equilibrium thermodynamics, the heat flux within system cannot be described by the non-state variable Q. 2) delta Q and and W in my Eq. (1) have different signs in that I need to consider the reference 10, where W denotes the work done by the system, the two in my original Eq.(1) have the same signs.

The difference between pV work and other kinds of work can be distinguished besed on reversible process. In a reversible process, pV work itself is an exchange process, and is also a heat conversion. Since p root in heat energy, so pV work denotes the work done by heat energy, and always involve a change in heat energy within system. Other kinds of work don’t involve the heat conversion, which are only the (free) energy transport, or the free energies transformed each other.

There are no such things as internal heat content or internal work content. Heat and work are just the names for different ways of changing the internal energy of the system and is expressed by the common form of the first law. The internal energy is a state function, i.e. its value (relative some reference) only depends on the state of the system. For a system at equilibrium it only depends on its "natural" variables, i.e. volume and entropy. Tang; it seems to me that your change in internal heat energy dq is just a different name for TdS. Of course entropy is, as you know a non-conserved quantity but it is still a state function.

Dear John,

No!

We have the common form of the first law

1) dU=δQ+Ydx-pdV+μdN.

The issue of the equation is that dU is not expressed as the sum of the exact differentials, where δQ is not an exact differential.

2) dU=TdS+Ydx-pdV+μdN.

The issue of the equation is that dU is not expressed as the sum of the different types of the energy within the system, where TdS is not an independent type of the internal energy, please see below.

dq isn’t “just a different name for TdS”, because dq≠TdS.

For example, consider an ideal gas, we have

1) TdS= cdT+pdV,

TdS is the sum of the two terms. The physical meaning of TdS includes the two, which is not one independent term (The first term is dq).

2) dU= TdS-pdV.

Using 1) in 2), we get

3) dU= cdT+pdV-pdV=cdT=dq.

For an ideal gas, all of the internal heat energy U is the internal heat energy q. dq isn’t “just a different name for TdS” because dq≠TdS.

On the other hand, the heat energy within the system is one fundamental type of the internal energy, we need to define it in a primary concept, S is not a primary concept but derived by q and some other variables. For a fundamental definition, we can define S by q, but cannot define q by S.

Dear Tang,

As you say we have the common form of the first law

1) dU=δQ+Ydx-pdV+μdN.

The meaning of this is that we can change the internal energy, a state function, by exchanging heat , work or matter between the system and the surroundings. By the way, as you probably know the heat exchange can be defined in different ways when you consider an open system. So at the moment let us consider a closed system, i.e. fixed composition, and drop the last term.

The second law then states for the change in entropy, also a state function, but not conserved, that

2) TdS=δQ+TdSi

where the first term comes from the exchange of heat and can have any sign and the second term is the entropy produced within the system and must be positive for spontatenous procees or vanish when there are no changes, i.e.if the system is at equilibrium (or frozen in).

Anyhow, we can thus combine the first and second law and obtain,

3) dU=TdS+Ydx-pdV-TdSi

In the simplest case we may write the internal entropy production TdSi=Ddz, where D is the "driving force" and is a state function, z is an internal state variable describing an internal process. Ddz can thus vanish if D=0 (equilibrium) or if D is not 0 but dz=0 for kinetic reasons (frozen in).

Instead of eq. 3 we then have

4) dU=TdS+Ydx-pdV-Ddz

This is an exact differential of the internal energy written as a function

5) U(S,x,V,z)

These are thus the natural variables of U. Observe that T and V are not natural varables.

At fixed S,x and V we have

dU=-Ddz =-TdSi

Since the last term is always positive or vanishes at equilibrium the equilibrium value of z represents a minum in internal energy.

By the way, we may now also add the effect of an open system by allowing

U(S,x,V,N,z)

and call the derivative

dU/dN the chemical potential.

Best regards

John

Dear John,

Your equation dU=TdS+Ydx-pdV-TdSi has changed the fundamental equation of thermodynamics (Euler’s equation). It means that the mathematical results of classical and both non-equilibrium thermodynamics are changed. You need to check it by some instances. dU=δQ+Ydx-pdV can only be used for reversible process. for irreversible process, δW≠Ydx-pdV.

Dear Tang,

First of all it is not my equation. I think it is a rather accepted extension of the fundamental equation to cover also irreversible changes.

When you say that δW≠Ydx-pdV for irreversible changes I guess you think about friction which will contribute to the addition of heat and is included in the entropy production.. I am absolutely sure that that the first law holds for all kind of processes, i.e. also for irreversible changes. For reversible changes of course TdS=δQ but in general TdS=δQ +TdSi.

I think this discussion concerns the foundation of thermodynamics and thermodynamics becomes rather difficult to understand if you do not accept the form dU=TdS+Ydx-pdV-TdSi.

Best regards

John

Dear Tang,

Maybe the question has a rather philosophical answer than a mathematical one.

For simplification reasons let's assume a closed system and suppose Ydx is zero.

The "classical" equation of the 1st law is an expression originated from the "external perspective" (i.e. it assumes that the system is a "black box", with no information on how the energy is stored inside it). In this respect the energy levels ('internal energy') can only be noticed from the energy exchange between the "black box" and the surrounding environment, thus δQ(TdS) or δW (-pdV).

Your perspective is of "internal" type, i.e. you provide information on how the exchanged energy is stored (in the form of molecular kinetic energy). In this respect you can merge the two forms of energy exchange in a single type. Your conclusion remains valid as long as the only form of molecular energy inside the system is the kinetic one. If you include molecular energy of spatial nature (electrostatic forces, molecular repulsion e.t.c.), then the merge of the two energies is not valid any more. For that reason I would consider the "external perspective" as the most general one.

Best regards

Dimitris

Dear Dimitris,

Sorry for too late reply, I had not noticed the e-mail.

You are right, “The classical" equation of the 1st law is an expression originated from the "external perspective", but the micromechanism of thermal motion now is clear, so thermodynamic system themselves are not "black box", only the classical equation is (partly) a "black box" theory.

We had known well the micromechanism of thermal motion, and know the expression of the energy of thermal motion in dynamic theory, i.e., the kinetic energy of random motion.

But in thermodynamics, there has no a state function that denotes “the kinetic energy of random motion”. The thermal motion within the system is a system property but the energy of thermal motion, as an explicit function has never been defined.

There is no a state function that denotes “the kinetic energy of random motion”. Why we had no?

In the classical" equation of the 1st law, the "black box" had been partly opened, the mechanical potential energy and Gibbs free energy have been defined, now we only need to make sure the last one, the internal heat energy, the kinetic energy of random motion.

We can open the "black box". “Open” will make thermodynamic analysis much simpler, and thermodynamic images could become clearer.

Best regards

Tang

But is not temperature that thermodynamic funktion? From statistical thermodynamics we know that it is proportional to the average kinetic energy of random motion.

Best regards

John

Dear John,

Temperature is an intensive quantity, to measure the strength of the average kinetic energy of random motion. We need a state function (extensive quantity) to measure the amount of the kinetic energy of random motion.

The amount of the kinetic energy of random motion is is a system property, but there is no a state function that denotes “the kinetic energy of random motion”.

Why we had no? it is the last one that we need to make sure .

Best regards

Tang

Well the, as you know, extensive quantity conjugated to the potential T is entropy. It is difficult to see that anything is missing.

Best regards

John

Dear John,

TdS is not an independent type of the internal energy, and it is easy to verify that TdS itself contains pdV. As example, for an idea gas

dU=TdS-pdV=CdT+pdV-pdV

The internal energy of an idea gas is the energy of thermal motion (dU=dq), but

dU=CdT≠TdS

Another example is photon gas, the internal energy of a photon gas is equal to αT^4V

dU=4αT^3VdT+αT^4dV

TdS=4αT^3VdT+(4/3) αT^4dV

dU≠TdS

So TdS is not equal to the increment in energy of thermal motion.

On the other hand, the energy of thermal motion is a primary concept, cannot be defined by the secondary concept S.

Best regards

It was in 2006, I found that some issues will be easily clarified if introducing an independent state function that denotes the energy of thermal motion within the system. Until only recently, I realized that it is a profound change in the structure of thermodynamics, I have revised my article (arXiv:1201.4284v4), and a separate section is added for “the internal heat energy”, attached is v5.

What happened to enthalpy in this discussion? If we add thermal energy the enthalpy changes by an amount equal to the integral of the specific heat.

Dear Philip,

Enthalpy H=U-Yx+pV=TS+ΣμN.

H is not equal to the kinetic energy of thermal motion within the system, if we add thermal energy to the system, we have δQ=dH, but here dH is not equal to the change in the kinetic energy of thermal motion within the system.

Enthalpy H≠ the kinetic energy of thermal motion within the system.

For example, consider Joule-Kelvin effect, throttling of a gas through a porous plug and cause cooling or heating, it is known as a constant enthalpy process, dH=0, but the change in the kinetic energy of thermal motion within the system is not equal to zero. Then, which one of the state functions can represent the kinetic energy of thermal motion within the system? and can describe this thermal effect?

Translational motion, ie Temperature, is not the only way to store energy in the system, thus transfer of heat energy Q to a closed system may not result in a change of temperature. Enthalpy includes all of this but indeed also includes the work terms.

Dear Philip,

Enthalpy is a coupling function, can not denote the independent types (forms) of the internal energy. For an internal process, one of the important contents is the conversion of the energy forms, but the internal energy, the total energy within the system has not been completely classified into some independent types (forms). You can see that for Joule-Kelvin effect, Enthalpy can not describe the internal thermal effect (the conversion of the energy forms), due to Enthalpy can not describe internal heat production.

If we classify the internal energy into some independent types (forms), it will be easy to describe the internal conversion of the energy forms,