Lecture 11,12,13

# Lecture 11,12,13 - "Entropy and the Second Law of...

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“Entropy and the Second Law of Thermodynamics” Prof. GianluigiVeglia

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So far, we have described: The zero th law of thermodynamics: two bodies that are in thermal equilibrium with a third body are in thermal equilibrium with each other. The first law”: the total energy of an isolated system is constant. That is what we use to predict the position of the thermal equilibrium. What we do not have is an explanation for why systems evolve toward the thermal equilibrium.
Why is it that two metal pieces of dissimilar temperature always evolve toward the same temperature when they are put in physical contact? Why don’t thermal gradients spontaneously form? Why do gases spontaneously intermix? Etc.

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There are many ways of formulating the second law of thermodynamics, all of them equivalent, although they may not seem so at first glance: 1. No cyclic process is possible in which the sole result is the absorption of heat from a reservoir and the complete conversion into work (ENGINEERS VERSION!) 2. There is a state function S (the entropy) which is defined so that: T q dS rev δ =
Or in terms of cyclic integral (in a conservative field): However for any transformation: This expression is called macroscopic view of entropy . 0 = = T q dS rev δ

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3. There is a state function S (the entropy) which is defined so that: Where (k=R/N A ), Ω is the number of ways a system can achieve a specified configuration. We will use each of the formulation of the second law, depending on the phenomenon we wish to elucidate. = ln k S particle
Let’s imagine that we subject a system to a reversible transformation from state A to state B: What about the surroundings? Since the heat transfer is reversible, there can be no temperature discontinuities at the system/surroundings boundary. In other words, T sys =T surr . Also, if dq rev is the heat flow from the system to the surroundings, then dq rev is also the heat flow from the surroundings to the system.

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By definition the variation of entropy of the system must be equal to the negative of the entropy variation for the surroundings. Note that this is valid for a reversible transformation. surr sys S S = 0 = + = surr sys univ S S S
What about an irreversible transformation? We know that for any cyclic transformation: where the “equal” sign is referred to reversible transformations. Now, let’s imagine that a subject the system to some cyclic transformation, from state A to state B and back again. 0 T q any δ

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We can describe this transformation: Then we can write: This is equivalent to say < + = B A A B rev irr T q T q T q 0 δ < B A B A rev irr T q T q < B A B A irr dS T q
Rewriting: In an isolated system undergoing irreversible change, (since the system is isolated), therefore dS 0 .

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Lecture 11,12,13 - "Entropy and the Second Law of...

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