Ch6_Entropy_T_FreeEnergy

# Ch6_Entropy_T_FreeEnergy - Ch.6 Entropy, T, and Free Energy...

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1 Ch.6 Entropy, T, and Free Energy Friction ; dissipative process ; erase order The 2nd law of thermodynamics Concept of free energy Whenever we release an internal constraint on an isolated macroscopic system in equilibrium, eventually the system comes to a new equilibrium whose entropy is at least as great as before.

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2 ¾ Biological Question : If energy is always conserved, how can some devices be more efficient than others? ¾ Physical Ideas : Order controls when energy can do useful work, and it’s not conserved.
3 Roadmap 6.1 How to measure disorder 6.2 Entropy 6.3 Temperature 6.4 The 2nd law 6.5 Open systems 6.6 Microscopic systems 6.7 Excursion:”RNA folding as a 2-state system”

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4 6.1 HOW TO MEASURE DISORDER High order Low disorder Low information needed to describe the system Low order High disorder High information needed to describe the system The disorder reflects its predictability. ln I total # of all possible messages (quantum states)
5 6.2 ENTROPY 볼수있는것과볼수없는것 PE KE Heat Heat 흡수 Entropy controls the direction of Energy Flow.

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6 6.2.1 The Statistical Postulate When an isolated system is left alone long enough, it evolves to thermal equilibrium. Equilibrium is not one particular microstate. Rather, it’s that probability distribution of microstates having the greatest possible disorder allowed by the physical constraints on the system.
7 6.2.2 Entropy is a constant times the maximal value of disorder Thermodynamical () AB AB Q S AB T Δ = R ln B Sk = Statistical : dQ dS T = quasi-static & infinitesimal B AB A dQ S T Δ = ln Br r r P P =− for a microcanonical ensemble for a canonical ensemble r r r E P e Z β ⎛⎞ = ⎝⎠ : Shannon’s formula AB AB Q S T Δ >→

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8 Ideal gas of monatomic molecules, 3 2 2 11 1 22 NN ii E Kp p mm == = = ∑∑ α JJG 33 3 3 3 1 () ! ! EE N E N N N E E dr d p Nh V dp + + = = G JG δ δ 3 111 222 3 ( ) ( ) ( ) ( ) N NNN N x y zx y N y Nz N d r dx dy dz dx dy dz dx dy dz d p dp dp dp dp dp dp dp dp dp G " " volume of 3N dimensional spherical shell 3/ 2 2 3 (2 ) !( 3 / 2 1 ) ! N N V mE N = π 2 2 35 ln Sackur-Tetrode Equation B BB mkT V Sk N k π ⎛⎞ ⎢⎥ + + ⎝⎠
9 6.3 TEMPERATURE 6.3.1 Heat flows to maximize disorder 6.3.2 Temperature is a statistical properties of a system in equilibrium 1 S T E ⎛⎞ = ⎜⎟ ⎝⎠ Fundamental definition of temperature Two boxes of gases in thermal equilibrium are most likely to divide their energy in a way that equalizes their temperature.

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## This note was uploaded on 07/08/2009 for the course KIM 0150-5 taught by Professor Dong during the Spring '09 term at Ewha Womans University.

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Ch6_Entropy_T_FreeEnergy - Ch.6 Entropy, T, and Free Energy...

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