Exploring Entropy Production in Chemical Processes

[nonequilibrium]

Hello,

So presume we have a system in which a chemical process A + B -> X + Y is happening. We allow it to be a non-equilibrium process (so there will be an entropy production inside the system) but for ease we presume the system is characterized by the usual variables E, V, N_A, ..., N_Y (and the homogenous T, P, \mu_i), i.e. no local densities.

In a book I found that $\mathrm d S = \frac{1}{T} \left( \mathrm d Q - \sum \mu_i \mathrm d N_i \right)$ where they regard the first term as an entropy flux, i.e. an equilibrium process (I presume Q is simply the energy the system gets from an environment in equilibrium). Hence they explicitly draw the distinction $\mathrm d_e S = \frac{\mathrm d Q}{T}$ which is the entropy flux from the environment, and $\mathrm d_i S = - \frac{1}{T} \sum \mu_i \mathrm d N_i$, which is the entropy produced internally, by the chemical process (remember: non-equilibrium).

But I was wondering: are they then neglecting energy production from the chemical reaction? Or am I overlooking something? For example, is it allowed, in a more general case, for there to be a ``$\mathrm d_i Q$'' which would stand for the energy produced in the chemical reaction? Hence in that case $d_e S$ would go unchanged and we would have $\mathrm d_i S = \frac{1}{T} \mathrm d_i Q - \frac{1}{T} \sum \mu_i \mathrm d N_i$.

Hence if we write $\mathrm d_i S = \sum_j X_j J_j$ (= entropy production in terms of thermodynamic forces X_j and currents J_j) we would have that the heat production would have the thermodynamic force $\frac{1}{T}$ (which is notably different from the thermodynamic force for heat conduction, being $\nabla \frac{1}{T}$ or sometimes written as $\sim \nabla T$ (Fourier's law!))

The thing I'm also wondering about: I'm saying "the energy created by the chemical reaction" but of course there is no real energy created: the energy was there all along. So does it make sense to say that thermodynamically energy was created, but fundamentally there was not?

 

[DrDu]

Obviously there is no energy "created" in course of the reaction. The internal energy change at fixed V and S (i.e. the energy change due to chemical reaction) is Sum mu_i dN_i, but it is energy being released which was stored in the chemical compounds.

 

[nonequilibrium]

I didn't say though there was energy created, did I? But thermodynamically, we act as if new energy is entering the system, right? I'm a bit confused about this dichotomy. If E stands for internal energy, then I would expect it to be constant even in a thermodynamic sense, but apparently...

The internal energy change at fixed V and S (i.e. the energy change due to chemical reaction) is Sum mu_i dN_i, but it is energy being released which was stored in the chemical compounds.

So you say that the energy $\mathrm d_i Q$ (the heat released in a chemical reaction) that I describe in my OP is actually the $\sum \mu_i \mathrm d N_i$ term? For example, saying a reaction is exothermic, means $\sum \mu_i \mathrm d N_i > 0$?

 

[DrDu]

I fear I still don't understand exactly your question.

 

[sardar]

Hello,

Thank you for sharing your thoughts on exploring entropy production in chemical processes. It is clear that you have a good understanding of the thermodynamic principles involved in this topic.

To answer your question, yes, it is possible for there to be energy production from a chemical reaction. In fact, this is a key aspect of many chemical processes, as the conversion of one form of energy to another is often the driving force behind these reactions. However, in the context of thermodynamics, we do not consider this energy production as a separate term in the equation for entropy production. This is because, as you mentioned, the energy was already present in the system and is simply being converted from one form to another.

In terms of your notation, it is important to keep in mind that the thermodynamic force \frac{1}{T} (or \frac{1}{T} \mathrm d Q) is not the same as the thermodynamic force for heat conduction, which is \nabla \frac{1}{T}. The former represents a change in entropy due to heat transfer, while the latter represents a change in temperature due to heat transfer. They are related, but not the same.

In summary, while there may be energy production from a chemical reaction, it is not explicitly included in the equation for entropy production in thermodynamics. Instead, it is accounted for in the terms for heat transfer and chemical potential. I hope this helps clarify your doubts. Keep exploring and asking questions!