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Unformatted text preview: Chemistry 2000 Lecture 11: Entropy and the second law of thermodynamics Marc R. Roussel The thermodynamic description of matter I In classical thermodynamics , we describe the state of a system by macroscopic variables which can be measured using ordinary lab equipment. Macroscopic variables include I the number of moles of each chemical component in a system I the temperature I the total pressure I the volume I We typically only need to know a few of the macroscopic variables since they are connected by equations of state . Examples: I PV = nRT for an ideal gas. I V = V ◦ 1 α ( T T ◦ ) + κ ( P P ◦ ) for solids or liquids with ( T , P ) near a reference state ( T ◦ , P ◦ ). The mechanical description of matter I We can also describe matter by its microscopic state . The microscopic state includes I positions of all particles I momenta of all particles ( p = mv ) I occupation of all energy levels of the atoms or molecules I The microscopic state (or just microstate ) represents an extraordinarily large number of variables. The statistical approach I These two very different ways of describing the same piece of matter (microscopic and macroscopic) can be related using a statistical approach . I This works because of the very large number of molecules in a typical macroscopic system. Statistical entropy I Entropy is a key quantity in thermodynamics. I The statistical entropy is calculated by S = k B lnΩ where k B is Boltzmann’s constant (again). Ω is the total number of microscopic states which are consistent with a given macroscopic state. I S is a measure of our ignorance of the microscopic state at any given time. Example: Entropy of 12 ¢ I Suppose that I tell you that I have 12 ¢ in my pocket. I Your ignorance of how this 12 ¢ is composed could be considered a form of entropy. I Possible “microstates” of 12 ¢ : I 12 × 1 ¢ I 7 × 1 ¢ + 1 × 5 ¢ I 2 × 1 ¢ + 2 × 5 ¢ I 2 × 1 ¢ + 1 × 10 ¢ I S 12 ¢ = k B ln4 I In information theory , we use the base2 logarithm and set k B = 1 (corresponds to a change of units for the entropy)....
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 Fall '06
 Roussel
 Chemistry, Thermodynamics, Entropy, kB ln, K−1 mol−1, statistical entropy

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