Is it only thermal energy that contributes to entropy of a system, or it is also chemical one and others?

Question

(Here, by ”thermal energy” I mean the energy associated with chaotic motion of molecules.)

Preface

In a textbook “Principles & Practice of Physics” by Eric Mazur, I came across two things, which make me ask this question.

First, on the picture below the author lists possible energy conversion processes.

By $E_s$ the author means so-called “source energy”, here what he means:

Broadly speaking, there are four kinds of source energy: chemical energy; nuclear energy; solar energy delivered by radia tion from the Sun; and stored solar energy in the form of wind and hydroelectric energy.

Second, when the concept of entropy is discussed, the author relates entropy change of an ideal gas with change of its thermal energy distribution and change particles’ position.

Looking at the picture I was wonder whether there are other possible energy transformations (e.g. thermal energy into chemical energy) and how one can explain them in terms of entropy.

The main part

For a single ideal gas as a system, we can say that its entropy change can be caused by changes of its thermal energy, volume, and number of particles.

(Now, let us consider the following systems as closed ones, i.e. ones that cannot exchange energy and particles with surroundings.)

Let’s consider more complicated systems, like (1) a single real gas that is experiencing a free expansion, and (2) two substances that are contacting and experiencing chemical reaction.

Question 1.

In the first case, there is energy transformation between thermal energy and energy of molecular interaction.

Let the real gas be cooling while it is expanding. Then we can say that its entropy is decreasing due to cooling, but at the same time it is increasing due to expanding. The total entropy should be increasing, because it’s irreversible process in closed system.

Is it correct reasoning? Should be change of energy of molecular interaction considered as a direct factor of entropy change (like change of thermal energy)?

Question 2.

In the second case, there is energy transformation between thermal energy and chemical energy.

Let the substances be cooling during the chemical reaction, so we have an endothermic reaction. We can say here that the system’s entropy is decreasing due to cooling, but at the same time it is increasing due to mixing of atoms (atoms of one substance mix with atoms of the other substance, forming new molecules). The total entropy again should be increasing, because it’s irreversible process in closed system.

The same question: Is it correct reasoning? Should be change of chemical energy considered as a direct factor of entropy change (again, like change of thermal energy)?

Answer 1

You seem very confused, and it is not that complicated. For a closed system, the focus is what the process does to the system which determines the entropy change.

The Clausius relation tells you all you need to know to ascertain what causes entropy of a closed system to change: $$\Delta S=\int{\frac{dQ}{T_B}}+\sigma$$where dQ is the differential heat flow across the boundary between the system and its surroundings during the process, $T_B$ is the temperature of the boundary through which this heat flow occurs, and $\sigma$ is the amount of entropy generated within the system during the process due to process irreversibility. According to this equation, there are only two mechanisms by which entropy of a closed system changes during a process:

1. Heat flow across the boundary interface between the system and surrounding at the temperature $T_B$. This mechanism is present during both reversible and irreversible processes.

2. Entropy generation $\sigma$ within the system as a result of process irreversibilities. This mechanism is present only in irreversible processes. Irreversibilities here include transport processes occurring within the system at finite rates and chemical reactions occurring within the system at finite rates:

(a) internal conductive heat transfer under finite temperature gradients

(b) internal viscous dissipation of mechanical energy to internal energy at finite deformation rates

(c) internal diffusion of chemical species at finite concentration gradients (including mixing)

(d) chemical reaction at finite reaction rates (either forward reaction or reverse reaction)

Answer 2

Latent heat is thermal energy, for sure.

So this Joule-Thomson effect then, that is the generation of latent heat from sensible heat.

So the amount of thermal energy stays the same in Joule-Thomson effect. But temperature of thermal energy goes down. So entropy of thermal energy increases, because S=Q/T.

Your question 2 is also about generation of latent heat from sensible heat. Because sensible heat decreased, it had to turn into latent heat, what else could it turn to?

Answer 3

Entropy is generated any time energy moves down an intensive-variable gradient (e.g., temperature, force, pressure, stress, electric field, magnetic field, surface tension); in the process, the corresponding conjugate extensive variable shifts (here, entropy, displacement, volume, volumetric strain, polarization, magnetization, surface area).

Such energy flow can be driven only by a nonzero gradient, so all real processes are irreversible, although we can approach reversibility arbitrarily closely by moving slowly and by suppressing diffusive phenomena (e.g., lubricating a mechanical mechanism to reduce stiction/friction).

Let the real gas be cooling while it is expanding. Then we can say that its entropy is decreasing due to cooling, but at the same time it is increasing due to expanding. The total entropy should be increasing, because it’s irreversible process in closed system. Is it correct reasoning?

Yes; the entropy increase due to expansion always outweighs any entropy decrease due to cooling of a real gas.

Let the substances be cooling during the chemical reaction, so we have an endothermic reaction. We can say here that the system’s entropy is decreasing due to cooling, but at the same time it is increasing due to mixing of atoms (atoms of one substance mix with atoms of the other substance, forming new molecules). The total entropy again should be increasing, because it’s irreversible process in closed system. The same question: Is it correct reasoning?

Broadly; the dominating entropy increase could also be due to gas creation and expansion, for example, rather than mixing. Reducing an oxide to a base metal is endothermic but spontaneous (and irreversible in practice) for sufficiently high temperatures because the gas production produces entropy, more than enough to counter any cooling. (A high temperature is needed because the Gibbs free energy change $\Delta G=\Delta H-T\Delta S$ must be negative, and the $\Delta S$ term contains $T$ as a coefficient. One consequence to this is that the higher-temperature equilibrium phase/product is always the higher-entropy substance.)

Answer 4

Let the real gas be cooling while it is expanding. Then we can say that its entropy is decreasing due to cooling, but at the same time it is increasing due to expanding. The total entropy should be increasing, because it’s irreversible process in closed system.

Gas expansion can be either reversible or irreversible process. If it is a reversible process, then obviously the entropy does not change. I presume however that the specific question that the OP has in mind is free expansion of gas into vacuum - in this case the expansion is adiabatic, i.e., there is no internal energy change and hence no temperature change (i.e., no cooling), but the process is irreversible, due to the expansion.

Let the substances be cooling during the chemical reaction, so we have an endothermic reaction. We can say here that the system’s entropy is decreasing due to cooling, but at the same time it is increasing due to mixing of atoms (atoms of one substance mix with atoms of the other substance, forming new molecules). The total entropy again should be increasing, because it’s irreversible process in closed system.

Again, chemical reactions can be reversible and irreversible, see, e.g., Difference between Reversible and Irreversible processes in Physics vs. Chemistry and Can we call rusting of iron a combustion reaction?.

Statistical physics texts usually start their discussion with explicitly omitting chemical reactions from consideration (paragraphs without formulas in the beginning), but then usually allow for chemical transformations when discussing the grand canonical ensemble, where the chemical reactions can be seen in terms of chemical potentials - adding one type of molecules and removing the other type (see Gibbs-Duhem equation.)

Whether the entropy is generated in a process of reaction again depends on the path that the system takes from the initial to the final state. A situation very close to the gas expansion into vacuum would be starting with, say, two-atomic molecules, $AB$ that can dissociate into atoms upon absorbing some energy, $AB+E_b\leftrightarrow A+B$ (see How does an exothermic reaction release energy?). If we start with only one type of molecules ($AB$) then the system would evolve to a higher entropy state where we have all three types of entities, and the rate at which atoms $A,B$ combine to form molecules is equal to the rate at which molecules $AB$ dissociate. The transformation from a "pure" state to the state where all there species are present is irreversible, and the temperature does change, because we have conversion of the internal energy into kinetic one, but the irreversibility is again due to the higher probability of a state with mixed species present.