Note 3 - Note 3. Entropy I: Entropy in terms of heat 3.1...

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1 Note 3. Entropy I: Entropy in terms of heat 3.1 Reversibility and equilibrium: a recapitulation Let’s briefly recap some important concepts we’ve learned in the previous chapter: 1. Conservation of energy: If the internal energy U changes, this change in energy will take the form of work w and/or heat q ( Δ U = q + w ) 2. Reversible reactions: we can perform a transformation reversibly if we make the transformation in many small steps and let the system reach equilibrium at each step. 3. dw rev < dw irrev : In the reversible process, work done by the system is a maximum (i.e. work done on the system is a minimum). 4. dq rev > dq irrev : In the reversible process, heat absorbed in the system is maximized (i.e. heat transferred to the heat bath is minimized). These observations will be important in our understanding of entropy and the second law of thermodynamics. 3.2 The second law of thermodynamics The second law relates to equilibrium and reversibility: Spontaneous changes are those which can be made to do work. If carried out reversibly , they yield a maximum amount of work. In natural processes, the maximum work is never obtained (since complete reversibility is an idealization). This essentially is just a summary of what we have been talking about: reversible systems can do a maximum amount of work, but this is never truly realizable. Another way to think about this is in terms of two bodies which have different temperatures. This temperature imbalance is like a state with potential energy (although we will see that U itself is not the important concept here). The system will relax back to equilibrium when the heat goes from the hotter body to the colder one. Heat will never spontaneously go in the other direction. This reformulation of the second law in terms of heat flow is the more common way in which it is stated, although it has the same fundamental roots as the previous formulation. In the end, the important concept to understand here is that this law of thermodynamics relates to the fact that some events can occur without doing any (additional) work to cause them (the so-called “spontaneous events”), i.e. we can just let them go and they will occur. Some examples are gas fleeing a balloon or a drop of dye spreading in a bucket. There are some events which we would call “non-spontaneous” since they do not happen without doing work. Once spread out, the dye never spontaneously comes to its initial drop.
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2 It’s also intriguing to ask where in physics it says that this shouldn’t happen. Certainly Newton’s equation doesn’t talk about this. In fact, Newton’s equations work perfectly well, either forward or backward in time. There must be something else that we’re missing. 3.3 Entropy
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Note 3 - Note 3. Entropy I: Entropy in terms of heat 3.1...

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