Lecture03-02.1.Entropy_and_Temperature

# Lecture03-02.1.Entropy_and_Temperature - 1 Statistical...

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Unformatted text preview: 1 Statistical Physics How to connect the microscopic properties -- lots of changes to the macroscopic properties -- not changing much. We will care about: N = # atoms T = temperature V = volume U = total energy Deep philosophical issue : Microscopic: physical laws are reversible in time Macroscopic: They’re not always reversible! Reversibility Movie taken and modified from: www.theclam.com/Video/JumpingIndex.asp 2 The Fundamental Assumptions of Statistical Physics 1. Quantum States are either accessible or inaccessible to the system “The System” IN OUT 2. The System is equally likely to be in any accessible state . Last Time- Sharpness of Multiplicity Function Stirling’s Approximation Gaussian Distribution- Binary (two state) model multiplicity function approaches Gaussian at large N:- RMS fluctuations ~- Weighted averages ( ) 1 2 ! 2 N N N N N e π- & 3 Today Fundamental assumption Closed System Probability and Ensembles Two systems in thermal contact Entropy Temperature Laws of thermodynamics Chapter 2 Entropy and Temperature Closed system is equally likely to be in any accessible state Fundamental Assumption Closed system: clueless of outside world constant energy ( δ U / U << 1) constant number of particles ( δ N /N << 1) constant volume Accessible state: compatible with “macrostate” i.e. at the right energy, number of particles, volume Note : some states can be inaccessible due to time constraints. Diamond and graphite – can one spontaneously convert into the other? 4 Probability System is equally likely to be in any accessible state. Multiplicity = g = number of accessible states ~ 10 23 Probability of any one state: All microstates are equally likely. s = general state label. Always Normalize: Ensemble Multiplicity = g = number of accessible states There are g states in the ensemble. To do math, replace “The System” with “The Ensemble” ( ↑ 1 + ↓ 1 ) ( ↑ 2 + ↓ 2 ) = ↑ 1 ↑ 2 + ↑ 1 ↓ 2 + ↓ 1 ↑ 2 + ↓ 1 ↓ 2 System can be in any accessible state Ensemble – a set of systems that are all alike....
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## This note was uploaded on 12/14/2010 for the course PHYSICS 416 taught by Professor Savikhin during the Spring '10 term at Purdue.

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Lecture03-02.1.Entropy_and_Temperature - 1 Statistical...

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