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This is an excerpt from Fundamentals of Heat Transfer

The internal energy consists of a sensible component, which accounts for the translational, rotational, and/or vibrational motion of the atoms/molecules comprising the matter; a latent component, which relates to intermolecular forces influencing phase change between solid, liquid, and vapor states; a chemical component, which accounts for energy stored in the chemical bonds between atoms; and a nuclear component, which accounts for the binding forces in the nucleus

(This paragraph from the textbook is also the reason why I asked this question)

The internal energy $U$ of a system (say water vapor),

$$U = KE_{micro} + PE_{micro}$$

$KE_{micro}$ is the sensible energy of the system. The potential energy component has many sub-components

$$PE_{micro} = PE_{molecular \, interaction} + PE_{atomic \,interaction} + PE_{nuclear \,interaction} + PE_{others}$$

The book calls $PE_{molecular \, interaction}$ as the latent component. I'm having some issues with calling entire $PE_{molecular \, interaction}$ as the latent energy.

The $PE_{molecular \, interaction}$ for water vapor will be equal to the sum of latent energy that was added to liquid water to convert it to vapor and Potential energy possessed due to molecular interaction in the liquid state. i.e.

$$PE_{molecular \, interaction, vapor} = Latent \, energy + PE_{molecular \, interaction \, ,liquid}$$

By the above argument isn't latent energy only a part of $PE_{molecular \, interaction}$? But the book says that entire $PE_{molecular \, interaction}$ is the latent energy.

So,

Is latent energy a part of molecular interaction potential energy, or the entire molecular interaction potential energy is latent energy?

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I think the book's authors would have better avoided introducing conceptual confusion by mixing microscopic and macroscopic concepts without a good reference to statistical mechanics.

First of all, latent heat is much a better concept than latent energy. Latent heat has a thermodynamic definition independent of any microscopic separation of different contributions to the energy. Moreover, the definition of latent heat as the energy released or absorbed by a thermodynamic system during a constant-temperature process — usually a first-order phase transition, makes clear that the relevant quantity to focus on is the variation of the energy under the external conditions for the transition.

Even more clear, if we look at the Clausius-Clapeyron equation $$ \frac{{\rm d}p}{{\rm d}T}=\frac{\Delta s}{\Delta v}=\frac{L}{T\Delta v} $$ we see that the latent heat $L$ is directly connected to the entropy change at the transition. Entropy depends, of course, on the interactions, but indirectly.

The intuitive idea that the presence of latent heat, i.e., the case of no temperature variation when energy is added to the system, is connected to the breaking of chemical bonds does not survive a careful analysis based on statistical mechanics: purely repulsive interacting systems still show an entropy jump and then latent heat at the liquid-solid transition.

In summary, the intermolecular interactions are responsible for the whole thermodynamic behavior of a system (provided that the intramolecular degrees of freedom are frozen). However, it is impossible to equate latent heat with the intermolecular potential energy average. It is possible to define latent energy as the average intermolecular potential energy, but such a quantity is not directly related to latent heat.

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  • $\begingroup$ So, it's much better if I just understand Latent energy to be the energy required to change the phase of a substance at a given temp. and pressure. I should avoid the approach where I'm trying to call a part of microscopic molecular interaction potential energy as latent energy. Did I infer that right? $\endgroup$ Commented Jun 15, 2022 at 9:10
  • $\begingroup$ 'latent heat is much a better concept than latent energy'. But isn't what actually is getting transferred during a phase change is energy? Heat as I've learned is just a means of transferring energy. Or am I interpreting your statement a bit out of context? $\endgroup$ Commented Jun 15, 2022 at 9:13
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    $\begingroup$ @HarshitRajput Certainly, some energy is transferred into or from the system during a phase transition. However, while latent heat has a definite operative meaning (no change of temperature accompanying the energy transfer), partitioning the potential energy in a "latent energy" plus something else has neither an operational nor a theoretical foundation. $\endgroup$ Commented Jun 15, 2022 at 12:40

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