(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)?
Best Answer
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:
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.
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)