Thermodynamics: Entropy
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1 Thermodynamics: Entropy
2 From Warmup I still do not understand the benefit of using a reversible process to calculate data when it is not possible to achieve. What makes a reversible process so useful? Why do we use Qr instead of just Q? Practically speaking, no "reversible" processes exist. Why then do we use one in the computation? Some of these questions didn't make a lot of sense... This is awesomely fun! It may be 2 am, and I'm tired and have a whole bunch of work to do, but this is fun! Haha. A poll: is it worth going to see the Frozen sing-a-long in theaters even though I've seen the movie five times and have the songs memorized?
3 Up to now We have introduced many concepts: State Variables Energy, Temperature, Pressure, Volume, Transfer Variables Heat, Work, Processes Reversible Irreversible Forbidden processes These are combined with a hodgepodge of equations. Can we unify them into a single theory? The next two lectures are heavy on math and theory (light on demos)
4 Entropy Some processes are reversible, others are irreversible, and still others are forbidden. Speculate: there must be another variable, S DS = 0 for reversible processes DS > 0 for irreversible processes DS < 0 for forbidden processes That is, S never gets smaller, it only grows. Can we say anything else about S?
5 Consider Heat Flow Q T1 T2 S Q T1 T2 Q T1 Q T2 Since heat flows from hot to cold: S increases when T1 > T2 S decreases when T1 < T2 Therefore: S vs Q is flat when T1 = T2.
6 What is temperature? Q T1 T2 Temperature is something that is equal when two objects are in thermal equilibrium. Not quite.. Actually:
7 What is temperature? Why not define temperature as a measure of microscopic kinetic energy? This requires we know atomic and kinetic theory. The definition would be different for different materials/objects. Historically, kinetic theory was not universally accepted when thermodynamics was developed. Thermodynamics, as a theory, does not require kinetic theory to be true. Thermodynamics is applicable to other systems without knowing the microscopic dynamics, e.g. black holes
8 What is entropy? Entropy helps us relate the macroscopic world to the microscopic world. Macrostate: a state defined on the macroscopic level (e.g. Pressure, Volume, Energy) Microstate: a state defined on the microscopic level (e.g. position, momentum of all particles in a gas) Entropy describes how many microstates are consistent with a macrostate
9 From Warmup 8 random choices on an 8x8 grid: Rank these 5 outcomes in order of likelihood These are each microstates. They have the same probability. All are equally probable, because no matter where certain spaces are occupied, it will be the same probability to get each space to be a certain way.
10 Microstates vs Macrostates You know, the most amazing thing happened to me tonight. I was coming here, on the way to the lecture, and I came in through the parking lot. And you won't believe what happened. I saw a car with the license plate ARW 357. Can you imagine? Of all the millions of license plates in the state, what was the chance that I would see that particular one tonight? Amazing! --Richard Feynman
11 Disordered This is an adjective for macrostates, not for microstates! Macrostates have a multiplicity, microstates don t. Macrostates don t fully specify the system. Multiplicity is the number of microstates consistent with the macrostate. Disordered macrostates have large multiplicity
12 Distinguishing Macrostates and Microstates You have a shoebox containing 35 pennies. The pennies are numbered 1 thru 35. You shake the box. Peering inside you find that the sequence is: HTTTHHHTTTHTHTTHHTHTTTHTTHHTTTTHTTT True (A) or False (B): The specific sequence is a microstate. Can you describe this macrostate?
13 More on Macrostates You have a shoebox containing 35 pennies. The pennies are numbered 1 thru 35. You shake the box. Peering inside, what are you most likely to see?
14 Combinations, Permutations, and entropy
15 Combinations, Permutations, and entropy
16 Combinations, Permutations, and entropy
17 Entropy increases during heat flow: Example
18 Entropy increases during heat flow: Example After lots of random exchanges.
19 Entropy increases during heat flow: Example Intuitively, which of these two cases is the most disordered?
20 Entropy increases during heat flow: Example How many arrangement are there having 20 cards of one color and 6 cards of the other in one half of the deck? How many arrangements are there having 13 cards of one color and 13 cards of the other in one half of the deck?
21 Entropy increases during heat flow: Example What is the relative probability of these two macrostates?
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