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Unformatted text preview: last modified 9/21/2009 1/10 M. S. Shell 2009 Equilibrium and entropy ChE210A What is equilibrium? At its most basic level, the subject of thermodynamics is the study of the properties of systems and substances at equilibrium . What is meant by equilibrium? A simple way of thinking about equilibrium is as the state where time is an irrelevant variable. We can think of thermodynamic equilibrium as the condition where: The properties of a system do not change with time. The properties of a system do not depend on how it was prepared, but instead only on the current conditions of state, i.e., a few indicators such as temperature, pressure, or density. Note that the idea of this history-independence at equilibrium is more specific than the statement that properties do not change with time. Indeed, history- independence is an important factor of thermodynamic equilibrium. The properties of a large number of copies of the same system at the same state condi- tions are identical, whether or not each copy had a distinct preparation and history. On the other hand, one might question whether or not these statements are compatible with the molecular nature of reality. Do not the molecules in a glass of water constantly rotate and move about? Arent their positions, orientations, and velocities constantly changing? How then can the glass of water ever be at equilibrium given this ongoing evolution? The resolution to this seeming conundrum is that thermodynamic equilibrium is concerned with certain average properties that become time-invariant. By average, we mean two things: These properties are measured at a bulk, macroscopic level, and due to the interactions of many molecules. For example, the pressure that a gas exerts is due to the average rate of collisions and momentum transfer of many molecules with a vessel wall. Such bulk properties are typically averaged over very many (~ 10 gG ) molecular interactions. Properties are measured over some window of time that is greater than the time scales in the molecular motion. If we could measure the instantaneous density of a gas at one single moment in time, we would find that some microscopic regions of space could have fewer molecules and hence lower density than others, due to random motions of the constituent molecules. However, measured over a time scale greater than the aver- age collision time, the time-averaged density would appear uniform in space. last modified 9/21/2009 2/10 M. S. Shell 2009 In fact the mere concept of equilibrium requires there to be a some set of choices that a system can make in response to environmental conditions or perturbations. These choices are the kinds of positions, orientations, and velocities of the molecules that a system experiences. Of course, a system does not make a literal, cognitive choice, but rather the behavior of the molecules is determined naturally through their energetic interactions with each other and the surroundings....
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- Spring '09