3 discussions about microstates and macrostates in thermodynamics

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Need help for 3 Discussion posts about flollowing items. Each 150 words

1- Basic probability and combinatorics:

discussion of any questions and problems you have with the mathematics and conceptual understanding of basic probability theory and combinatorics. Are you comfortable using factorials? In real life, how would you verify that a coin is unbiased? What does it mean for two rolls of a dice to be independent of each other?

3- The paramagnet and the Einstein solid:

discussing the physical meaning of the two model systems we encounter this week. What is an example of a paramagnet, and what are its physical properties? What, physically, does it mean for a paramagnet to be a two state system? What is the meaning of Magnetization and other quantities that were briefly introduced? What, physically, do the oscillators in an Einstein solid correspond to? How does the model of an Einstein solid link to the phenomenon of phonons?

4- Microstates, macrostates, multiplicity, probability and the fundamental postulate of statistical mechanics:

This thread is to discuss you understanding of microstates and macrostates, and how multiplicity links to probability. Think of physical systems, or even just games, and give examples of their micro and macrostates. Also, discuss the fundamental postulate of statistical mechanics – that each micro state is equally likely. Should we expect this to be generally true for physical systems? Try some examples. E.g. the ideal gas: what are the microstates of the ideal gas? Should we expect them to be equally likely? why?

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