11 - Chemistry 2000 Lecture 11: Entropy and the second law...

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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- ( T- T ) + ( 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 ln where k B is Boltzmanns constant (again). 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 base-2 logarithm and set k B = 1 (corresponds to a change of units for the entropy)....
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11 - Chemistry 2000 Lecture 11: Entropy and the second law...

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