How does entropy production occur in non-equilibrium 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.