MSE306Chap7Vacancies

# MSE306Chap7Vacancies - Chapter 7 Chemical Thermodynamics...

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Chapter 7: Chemical Thermodynamics, Statistical Mechanics We will only do a BRIEF overview of these topics as they each constitute courses in themselves. However, our understanding of “high temperature” phenomena, such as annealing (Chapter 8) would be completely inadequate without some definitions. The text offers a concise treatment of these topics that even I can comprehend! (not false humility)

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Broad Definitions Thermodynamics – is an empirical discipline concerned with macroscopic (not atomistic) phenomena related to temperature, pressure, volume, entropy, internal energy, and enthalpy . Thermo - useful for accurate calculations, such as the familiar state equation (PV = nRT) and driving forces , though it does not provide “why” Kinetic Theory – seeks to derive those equations using atomistic and/or molecular level processes. Kinetics – uniquely suited for describing nonequilibrium and determining the time dependence of reactions. (We will see examples during discussions of diffusion .) Statistical Mechanics – applies probability theory bridge the gap between atomic level processes and macroscopic phenomena, which involve vast numbers of atoms. Stat. Mech. – will be used to introduce entropy .
Thermodynamics Internal Energy U = sum of total kinetic and potential energy Recall Debye theory, teaching that atoms within a crystal vibrate with three d.o.f. Further, the intensity of those vibrations increases with T. Entropy – a measure of disorder Consider the phase transformation from water to ice and vice versa . At the melting point (273K) water and ice coexist in equilibrium with one another (the reaction is reversible). – If T is lowered below T m , water spontaneously freezes and therefore the reaction is irreversible. Gibbs Free Energy – a measure of driving force G = U + PV – TS = H – TS ΔG = ΔH – TΔS (since constant T reaction) T dQ dS T dQ S S S reversible B A A B = = - = or T dQ dS T dQ S S S le irreversib B A A B - = or

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Gibbs Free Energy (cont.) First Law – conservation of energy Change in internal energy equivalent to sum of work done on system and heat added to system dU = dW + dQ dH = dU + PdV + VdP ~ dU ~ ΔQ Driving Force for Reversible Reaction ΔG = ΔH – TΔS ΔG = ΔQ – T(ΔQ/T) = 0 Driving Force for Irreversible Reaction ΔS > ΔQ/T or TΔS > ΔQ ΔG = ΔQ– TΔS < 0 (i.e. ΔG is negative) System can lower its free energy by proceeding to the equilibrium condition
Entropy New example: two gases initially separated and then allowed to mix at contstant temperature and pressure. First Law – conservation of energy dU = dH = dW + dQ = 0 Driving Force for Reversible Reaction dG = dH – TdS = – TdS Entropy of mixing – provides the driving force We will need this later to discuss diffusion The probability that all the blue atoms will stay on the right side and all the red atoms on the left is nill. The probability that they will randomly mix (purple) is certain.

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## This note was uploaded on 11/24/2009 for the course MSE 306 taught by Professor Smith during the Spring '09 term at UVA.

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MSE306Chap7Vacancies - Chapter 7 Chemical Thermodynamics...

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