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Unformatted text preview: © M. S. Shell 2009 1/13 last modified 10/13/2009 Ideal gases ChE210A Until now, most of what we have discussed has involved general relationships among thermo- dynamic quantities that are valid for any substance or system. The fundamental equation, reversibility, Legendre transforms, and Maxwell equations are all features of every system. Here, we will also start to investigate properties of specific systems. Our consideration of specific systems will mostly entail very simple models, in which only the essential physics are included. Simple models give insight into the basic features of solids, liquids, and gases, and actually are sufficient to learn quite a bit about their general behavior. Of course, there are also many detailed theoretical and empirical models for specific sub- stances, but for the most part, these theories simply improve upon the accuracy of the simple approaches, rather than introduce new physical behavior. Where do all of these models come from? Usually they are developed using statistical mechan- ical theory. That is, some relatively simplistic description of the relevant atomic interaction energetics is postulated, and the entropy or the free energy is determined. We will find that our strategy for most of these simple models will be to determine the chemi- cal potential gG¡, ¢£ . Recall that, for a single component system, this is equal to the Gibbs free energy per particle, gG¡,¢£ ¤ ¥G¡,¢£ . Thus, we can extract all intensive thermodynamic properties from this fundamental thermodynamic function. Basic properties of ideal gases The first simple model we will consider is that of an ideal gas. A single-component collection of ideal gas molecules is characterized by the fol- lowing properties: 1) There are no potential energies, but only kinetic energy only, i.e., molecules do not interact with each other. 2) Each molecule has a mass ¦ . 3) Each molecule has zero volume, i.e., it is a point particle. Essentially all gases behave like ideal gases in the limit where molecules don’t really “see” each other. This happens under two conditions: © M. S. Shell 2009 2/13 last modified 10/13/2009 • The low density limit, g G ¡ ¢ £ 0 , or alternatively, ¤ £ 0 . • High temperatures, ¥ ¦ 0. How do we begin to evaluate the thermodynamic properties of an ideal gas? We simply need to know how many different microstates exist for a given macroscopic § , ¨ , and © . To do that, we need to know what those microstates are, i.e., what energies ideal gas molecules can attain. Classically, we can specify any velocity, and hence any kinetic energy, we want. Here, however, we will pursue a quantum-mechanical treatment of these systems so that we can calculate the absolute entropy....
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This note was uploaded on 12/29/2011 for the course CHE 210a taught by Professor Staff during the Fall '08 term at UCSB.
- Fall '08