l13 - 20.110J / 2.772J / 5.601J Thermodynamics of...

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Lecture 13 5.60/ 20 .110/2.772 1 What is Statistical Mechanics? Brief Review of probability and combinatorics S=k ln and S = -k Σ p i ln p i What is Statistical Mechanics? Spontaneous processes: under certain conditions, know what system would like to maximize/minimize: () i i i i n P T G n P S H n V T A n V S U , , , , , , , , 0 0 0 0 , , , , , , , , i i i i n P T n P S n V T n V S dG dH dA dU These tell you which way a reaction will go, and when it will stop or reach equilibrium. Want these thermodynamic properties, now in terms of molecular level picture . E p Before: ignore molecular properties Now want to account for it: molecule exists in states, has energy levels (recall 5.111) If have large number of molecules (N A = 6 × 10 23 ), it is nearly impossible to track all of the states. Mind boggling! How? : use probability to describe molecule instead of tracking each one p i = probability that molecule will be in i th state. The link between microscopic and macroscopic: 20.110J / 2.772J / 5.601J Thermodynamics of Biomolecular Systems Instructors: Linda G. Griffith, Kimberly Hamad-Schifferli, Moungi G. Bawendi, Robert W. Field
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Lecture 13 5.60/ 20 .110/2.772 2 = multiplicity k=Boltzmann constant, = 1.38 × 10 -23 J/K Another form: p i = probability that molecule will be in i th state t = number of states Probabilistic description of entropy! Then relate these microscopic properties to macroscopic ones: U, S, etc. (Driving forces). Explain: unfolded protein Æ folded protein Do not need to know exactly how many molecules are in a state, just the probability that it is. Ludwig Boltzmann (1844-1906) Approach : make model to represent problem describe the states a system can be in use statistics and probability to average relate to a thermodynamic property (U, S, etc) DEMYSTIFYING S = ln k S i t i i p p k S ln 1 ¦ = = 20.110J / 2.772J / 5.601J Thermodynamics of Biomolecular Systems Instructors: Linda G. Griffith, Kimberly Hamad-Schifferli, Moungi G. Bawendi, Robert W. Field Image removed due to copyright reasons.
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This note was uploaded on 11/11/2011 for the course BIO 20.010j taught by Professor Lindagriffith during the Spring '06 term at MIT.

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l13 - 20.110J / 2.772J / 5.601J Thermodynamics of...

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