Thermodynamics: Entropy Conclusion

Transcription

1 Thermodynamics: Entropy Conclusion

2 From Warmup I would like to see an overview of all the chapters covered, and if possible some of the key concepts. I would appreciate a second opinion to make sure that I have a great study paper. Review session tonight, 6pm in C266 ESC

3 From Warmup Lots of questions about the equation: ds = dq/t The integral of ds=qr/t seemed a ton more applicable. I find confusing that ds=0 through a Carnot engine. I think the problem is I'm not seeing how Qr is 0. Q is not zero for a Carnot cycle! Qh > Qc, but Qc is at a lower temperature. I don't understand how entropy is supposed to "tie everything together". I'm a little unclear on how they did the derivation for it (it seemed to me that they had some expression that they wasn't equated to anything and they decided to take the natural log of it and multiply it by k simply so it looked like something else and that seemed somewhat sneaky and a little bit like cheating)... The key insight is that taking the natural log and mulitplying it by k gives you an expression that looks like something you ve seen before.

4 Clicker Poll Is the Second Law of Thermodynamics a Fundamental Law of Physics? a) Yes b) No As we discuss this, be prepared to defend what you mean by Fundamental Law of Physics.

5 Clicker Poll Is Boltzmann s constant a Fundamental Physical Constant? a) Yes b) No What do we mean by a Fundamental Physical Constant?

6 Some Philosophical Questions Thermodynamics is driven by Entropy. Entropy depends on the definition of the macrostates. Who, or what, determines the macrostate? Is it entirely subjective? A matter of perspective? Could we choose different macrostates and get a different theory of thermodynamics? Defining different macrostates for the same system: Dice Sum of the numbers Difference of the numbers Number of 1 s Etc.

7 Maxwell s Demon o Maxwell imagined a microscopic demon that could violate the 2 nd law o Imagine a gas in a container with a partition and a door. o The demon lets fast moving molecules into the right half and vice versa. o Therefore (Maxwell concludes), the 2 nd law is a statistical consequence of our being big (macroscopic)

8 Quantifying Information A bit of information is an answer to a question with two possible responses (e.g., Yes or No) One bit distinguishes between two possibilities. How many possibilities can be resolved by 4 bits? a) 4 b) 8 c) 16 d) 32

9 Other units of information trit: dit nat

10 Entropy as information o Entropy is the amount of information needed to give a complete microscopic description of a physical system o The second law of thermodynamics means that information about the microscopic state is always being lost.

11 Maxwell s Demon Revisited o Maxwell s demon must process information about the speeds of approaching molecules o What does it do with this information? Record it? Erase it? o It can t record information indefinitely eventually it must erase some of its information. o Erasing information increases the entropy! o The increase in entropy caused by erasing the information is always more than the entropy decrease caused by sorting the molecules o Maxwell s demon cannot violate the second law!

12 Relevance to current physics: From Science (last November): When we observe systems on different scales (different macrostates), there is a loss of information (entropy) about microscopic details. This is a big part of what makes science possible: If we needed to know string theory to do Newtonian physics, Newton would never have discovered his laws. The same principles hold in other branches of science.

13 Macro/Micro theories in Science Science is hierarchical Branches of science related as macro/micro theories Understanding the relation between macro/micro theories remains one of the fundamental problems in science. Microtheory Kinetic/Atomic Theory String Theory Quantum Mechanics Chemistry Biology Microeconomics Weather Macrotheory Thermodynamics Quantum Field Theory Chemistry Biology Psychology Macroeconomics Climate

14 Outlook We have covered (4 weeks): 1. Fluids 2. Thermodynamics Up Next: 1. Waves (3-4 weeks, Exam 2) 2. Optics (electromagnetic waves, 3-4 weeks, Exam 3) 3. Special Relativity (2 weeks) Cumulative Final Exam