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So I read that processes where there is no thermal gradients in the system are internally reversible, but for other cases, do we have to consider the temperature of boundary to calculate entropy change? What does this model of using boundary temperature do? Does it account for heat generation inside the system or does it consider it thrown outside?

So how does temp gradient in the system relate to irreversibility quantitatively? And to calculate entropy generation as a whole, do we need to consider whole universe or only system and surrounding separately, I mean for heat transfer between 2 thermal reservoirs with large heat capacities ( infinite) at finite temp difference, the system heat gen is zero but in universe, entropy is generated. So how do we spatially account for entropy generation in any general case, or can we only find entropy generation in universe as a whole? I am quite confused about this.

So basically two questions: How to map entropy generation in a general case? Why does considering boundary temperature help in determining overall entropy generation inside the system(in case of non uniform temperature inside the system)?

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    $\begingroup$ This question includes multiple questions in one, it needs more focus and should be re-written or closed. Spell checking would also not hurt. $\endgroup$
    – hft
    Commented Oct 20, 2021 at 7:47

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There are two ways by which the entropy of a closed system (no mass flow in or out) can change:

  1. Entropy transfer across the boundary interface between the system and its surroundings. This is equal to the integral of $dQ/T_B$, where dQ is the amount of heat flowing across the system boundary from the surroundings and $T_B$ is the temperature of the portion of the boundary through which dQ flows. For a reversible process, this is the only mechanism for entropy change and, in this case, $T_B$ is equal to the system temperature (which is uniform throughout the system, including at the boundary).

  2. Entropy generation within the system as a result of process irreversibility. This entropy generation is caused by (a) finite heat conduction within the system as a consequence of finite temperature gradients, (b) viscous dissipation of mechanical energy to internal energy within the system as a consequence of finite velocity gradients, (c) molecular diffusion within the system as a consequence of finite concentration gradients, and (d) changes is chemical composition within the system as a consequence of finite chemical reaction rates.

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  • $\begingroup$ Many thanks, but I have a problem in attributing the entropy generation to space, is all entropy generation attributable spatially, i.e, can we map all entropy generation to a particular region in space , If not in what cases? $\endgroup$ Commented Oct 20, 2021 at 14:29
  • $\begingroup$ As in cases where there is heat transfer with finite temperature difference but negligible thermal gradients as in case of phase transformation or case of infinite heat capacity or thermal conductivity, where do we account for entropy generation spatially? $\endgroup$ Commented Oct 20, 2021 at 14:43
  • $\begingroup$ If I understand correctly, you are asking where the entropy generation is occurring when we have transfer of heat between two ideal constant temperature reservoirs at different temperatures. Is that it? $\endgroup$ Commented Oct 20, 2021 at 18:09
  • $\begingroup$ If you want to have a better understanding of entropy generation and how it is distributed spatially within a fluid system undergoing an irreversible change, see Transport Phenomena by Bird, Stewart, and Lightfoot, Chapter 11, Problem 11.D.1, Equation of change for entropy. This was a real awakening for me. $\endgroup$ Commented Oct 20, 2021 at 18:13
  • $\begingroup$ Yes, in all such cases where the entropy generation is not apparent where to ascribe those to? And how is taking the value of $$\delta s =\delta q/T_{b}+ s_{gen}$$ is a definition of entropy transfer accounting for all the entropy change occuring inside the system including entropy generation. $\endgroup$ Commented Oct 20, 2021 at 18:17

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