inexact differentials
- To: mathgroup at smc.vnet.net
- Subject: [mg121101] inexact differentials
- From: Rudy <massow at bell.net>
- Date: Sat, 27 Aug 2011 08:17:51 -0400 (EDT)
- Delivered-to: l-mathgroup@mail-archive0.wolfram.com
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
still
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
involved.