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Unformatted text preview: Chapter 4 Mathematical foundations of thermodynamics Read Abbott and van Ness, Chapter 3. Read BS, 14.214.4, 14.9, 16.116.4. 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 wellknown 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 counterexample, 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
 ParkSou
 Dynamics

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