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Unformatted text preview: Chapter 4 Mathematical foundations of thermodynamics Read Abbott and van Ness, Chapter 3. Read BS, 14.2-14.4, 14.9, 16.1-16.4. See Vincenti and Kruger, Chapter 3, for more background. 4.1 Exact differentials and state functions In thermodynamics, one is faced with many systems of the form of the well-known Gibbs equation, Eq. (1.1): du = Tds Pdv. (4.1) This is known to be an exact differential with the consequence that internal energy u is a function of the state of the system and not the details of any process which led to the state. As a counter-example, the work, w = Pdv, (4.2) can be shown to be an inexact differential so that the work is indeed a function of the process involved. Here we use the notation to emphasize that this is an inexact differential. Example 4.1 Show the work is not a state function. If work were a state function, one might expect it to have the form w = w ( P,v ) , provisional assumption, to be tested. (4.3) In such a case, one would have the corresponding differential form...
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- Fall '11