StatThermo

StatThermo - The Statistical Interpretation of Entropy...

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MSE 3050, Phase Diagrams and Kinetics, Leonid Zhigilei The Statistical Interpretation of Entropy Physical meaning of entropy Microstates and macrostates Statistical interpretation of entropy and Boltzmann equation Configurational entropy and thermal entropy Calculation of the equilibrium vacancy concentration Reading: Chapter 4 of Gaskell Optional reading: Chapter 1.5.8 of Porter and Easterling
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MSE 3050, Phase Diagrams and Kinetics, Leonid Zhigilei What is the physical meaning of entropy? Entropy is introduced in phenomenological thermodynamics based on the analysis of possible and impossible processes. We know that heat flows from a hot region to a cold region of a system and that work can be irreversibly transferred into heat. To describe the observations, the entropy, and the 2 nd law stating that entropy is increasing in an isolated system, have been introduced. The problem with phenomenological thermodynamics is that it only tells us how to describe the empirical observations, but does not tell us why the 2 nd law works and what is the physical interpretation of entropy. In statistical thermodynamics entropy is defined as a measure of randomness or disorder . Intuitive consideration: In a crystal atoms are vibrating about their regularly arranged lattice sites, in a liquid atomic arrangement is more random ± S liquid > S solid . Atomic disorder in gaseous state is greater than in a liquid state - S gas > S liquid . Does this agrees with phenomenological thermodynamics? Melting at constant pressure requires absorption of the latent heat of melting, q = ' H m , therefore ' S m = ' H m /T m - the increase in the entropy upon melting correlates with the increase in disorder. SL G
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MSE 3050, Phase Diagrams and Kinetics, Leonid Zhigilei How to quantify “disorder”? Microstates and Macrostates A macroscopic state of a system can be described in terms of a few macroscopic parameters, e.g. P, T, V. The system can be also described in terms of microstates , e.g. for a system of N particles we can specify coordinates and velocities of all atoms. The 2 nd law can be stated as follows: The equilibrium state of an isolated system is the one in which the number of possible microscopic states is the largest. Example for making it intuitive (rolling dice) Macrostate ± the total of the dice. Each die have 6 microstates, the system of 2 dices has 6 u 6=36 microstates, a system of N dice has 6 N microstates. For two dice there are 6 ways/microstates to get macrostate 7, but only one microstate that correspond to 2 or 12. The most likely macrostate is 7. For a big number N of dice, the macrostate for which the number of possible microstates is a maximum is 3.5 u N If you shake a large bag of dice and roll them it is likely that you get the total close to 3.5 u N for which the number of ways to make it from individual dice is maximum.
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This note was uploaded on 03/05/2012 for the course MSE 305 taught by Professor Zhigilei,l during the Spring '08 term at UVA.

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StatThermo - The Statistical Interpretation of Entropy...

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