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inexact differentials

  • To: mathgroup at
  • Subject: [mg121101] inexact differentials
  • From: Rudy <massow at>
  • Date: Sat, 27 Aug 2011 08:17:51 -0400 (EDT)
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Inexact differentials generally occur in pairs. If one of them is zero
the other is exact. For instance:
The contained volume of a vase created by a potter is governed by two
inexact differentials.  dV = D(height change) + D(shape change)
If the potter does not change the shape
    dV = cdH      or    V = Integ(0 to H) c dH
where c is cross-section and H height.
If the potter does not change the height
    dV = integ(0 to H) dc dH
where the potter changed cross-sections of the existing vase. And
    V = Integ(0 to H) c dH
Knowing the content does not give you information how the volume has
been obtained and the vase can be created or collapsed by any portion
of either means.
Similarly in thermodynamics:
    dU = DQ + DW
The internal energy U provides no information how much Q or W was

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