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Unformatted text preview: Lecture 25 Entropy and Temperature 1 Review from Last Time • “State” of a system – macrostate - described by macroscopic parameters like temperature, internal energy, etc. – microstate - detailed specific state describing how energy is distributed among in- dividual particles (or oscillators) in a system. – There can be many different microstates for a given macrostate. • Two systems in thermal contact: – We model each system as a collection of oscillators. Energy can be distributed among the different oscillators in each system in many ways. – The most probable state that we will find the system in is the state that has the largest number of microstates. (REMIND: coin tosses). – Review example from book: show plot and explain in detail why the total number of states is the product Ω 1 Ω 2 • Entropy – If Ω is the number of microstates, then entropy is defined as: S = kln Ω – Conceptually: entropy is the natural log of the number of microstates. – We can also think of entropy as a measure of the disorder of a sytem – Entropies add: notice that the entropy of the two block system is S total = kln Ω 1 Ω 2 = kln Ω 1 + kln Ω 2 = S 1 + S 2 – This makes sense. When we put more energy into a system by bringing it into thermal contact with another system, the number of ways to arrange the energy grows. – When we bring the two blocks into thermal contact, we found before that the energy gets distributed in the most probable way, meaning the macrostate of the system that is most likely is the one with the largest number of microstates. This it the state with the largest entropy!...
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