- 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: email@example.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.