# What is Heat Content?

Frequently, I have seen enthalpy defined as the measure of Heat Content. However, it is unclear what this actually means.

Heat can be defined as the energy transferred between two bodies when there is a difference in temperature. So, could Heat Content measure how much heat is theoretically available to transfer between two bodies? Could it be the sum of all particles' individual kinetic energies? The term does not appear to be clearly defined online, so what does it actually mean?

It's somewhat "incorrect" use of words in physics, because heat is not a state variable, there is no unique number we can assign to any system that would tell us how much heat it contains in some objective universal sense. This is because heat is a mode of energy transfer, and the same energy can go in via heat, or work. After the energy is in the system, there is no way to find out, from state variables of the system, whether it came in through heat, or work.

"Heat content" refers to and applies to a restricted set of situations, where we put in some energy only via heat, not via work, during this transfer the system changes its state (typically it expands and does work on the atmosphere), while the external pressure $$p$$ remains constant (usually, due to atmosphere). Later we can reverse all of this and extract that same amount of heat and put it elsewhere. During heat absorption/heat release, the system is allowed to do work or accept work from atmosphere.

Enthalpy comes up because in this kind of process with constant external pressure, its change equals the heat accepted:

$$\Delta H = Q.\tag{*}$$

So if 2.2MJ of heat is accepted by the system, then its enthalpy has increased by 2.2MJ. In this context, telling the value of enthalpy (and the minimum enthalpy the system had before we put heat in it) tells us how much heat we can recover back from the system.

Why does enthalpy behave this way? Internal energy $$U$$ doesn't; this is because part of the energy income is going out via work on the outside atmosphere. But enthalpy is defined as

$$H = U + pV$$ to get a quantity that does not decrease due to volume work. We can see this easily: we have

$$\Delta H =\Delta U + \Delta(p V) = \Delta U + p \Delta V$$ and since the 1st law of thermodynamics for volume work implies $$\Delta U = Q - p\Delta V$$ combining these two equations, we obtain (*).

There is no such thing as a body “containing heat.” The closest thing you could argue is vibrational/rotational energy, but even this can easily change form and does not need to be transferred as heat between bodies. Any energetic transfer that could be manifested as heat could just as well be transferred as work. This is why the first law is written in the form $$\Delta E= q+w$$, and there is no $$\Delta$$ associated to the heat or work. The amount you get out strictly depends on the mechanism of energy transfer, I.e. the path you take matters. Now, you can talk about the enthalpy change $$\Delta H$$ for a process that occurs at constant pressure. By expanding out the total differential using the fundamental thermodynamic relation, we find that $$\Delta H=q$$ for a constant pressure process with all particle numbers conserved. It is only in this sense that enthalpy and heat are related to one another. Anywhere you see the language of something “containing heat,” the author is either mistaken or is abusing terminology.

• There is nothing wrong with saying that in the Gibbs formula for internal energy $U=TS-pV+\mu_1 N_1 + \mu_2 N_2+...$ the term $TS$ represents the contained thermal energy or even the contained "heat", so much so that whenever is claimed that "heat" is being transferred some amount of entropy is indeed being transferred at some given temperature. I am yet to hear of an example where this view is contradictory to experiment or understanding. Aug 27 at 21:42
• I think there is something deeply wrong with that statement. There is no sense in which the contribution $TS$ is thermal energy. It is just energy. It is energy that might possibly be transferred as heat, but it might also be transferred as work. There is no meaningful distinction as far as the energy is concerned. Think about the quantum states of a small molecule. The vibrational energy is often associated with “heat” due to thermal transfer, but as far as the molecule knows it just has some amount of energy. The transfer process dictates how we “count” it. Aug 27 at 23:35
• (1) If $gh$ is gravitational potential and $m$ is mass then what you call $mgh$ if not the gravitational energy? (2) "There is no meaningful distinction as far as the energy is concerned." Of course there is meaningful distinction: energy conservation is not energy conversion, it matters in U what the relative distribution of $TS, pV, \mu N$, etc., is. (3) But most importantly, what does your concept of "heat" have that is not encoded in the product of the transported entropy and its temperature? The most important lesson in ThDy is that heat at $T_1$ is not the same as at another $T_2$. Aug 28 at 0:42
• The problem is that, by your thinking, $PV$ would be the “work content” of a body. This is obviously utterly absurd, as the body does not contain work. It just has the capacity to do work based on the amount of internal energy it has. Likewise, $TS$ is not the heat, it is just a contribution of the internal energy from temperature and entropy. In an ideal reversible process $TdS$ is the heat differential exactly, but in no other case can that identification be made explicit. Aug 28 at 1:14
• I think all the arguments around this mostly liniguistic issue could be resolved if we introduce and use two words: "zesti" for $TS$ and "ergasia" for $U-TS=\sum_k Y_k X_k$ both stolen from Greek ($\zeta\epsilon\sigma\tau\eta$ and $\epsilon\rho\gamma\alpha\sigma\iota\alpha$). Using only these fine English words we are now safe to declare that both zesti (not "heat") and ergasia (not "work") can be contained, stored and transported, and thereby end the linguistic debate while keeping everybody happy and just fight over physics. Aug 28 at 16:30

Often we see enthalpy defined as the measure of "Heat Content".

Per the Wikipedia article on enthalpy, the term "heat content" originating in the 19th century is a now an obsolete term, though still used. That's because, as you apparently already know, heat is energy transfer due solely to temperature difference. Heat is not something "stored" in a system. The proper term for that is internal energy.

So, could "Heat Content" Be a measure of how much heat is theoretically available to transfer between two bodies.

It is not "heat content" that is theoretically available to transfer between two bodies. It is internal energy that is theoretically available to transfer between two bodies, either by the mechanism of heat or work. From the first law for a closed (no mass transfer) system

$$\Delta U=Q-W$$

If $$W$$=0 then the only mechanism to transfer energy is heat, $$Q$$. It is in this case, where heat is the only mechanism available to transfer energy, where one of the reasons the misnomer "heat content" arises.

Could it be the sum of all particles individual kinetic energies?

Again, substances do not contain heat. Substances contain internal energy, which is the sum of the kinetic and potential energy of all the particles of the substance at the microscopic level.

Hope this helps.