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The Principles of Thermodynamics
book

The Principles of Thermodynamics

by N.D. Hari Dass
October 2013
Intermediate to advanced content levelIntermediate to advanced
352 pages
13h 56m
English
CRC Press
Content preview from The Principles of Thermodynamics
318 The Principles of Thermodynamics
It is difcult to establish this directly from the denition of the Jacobian given above.
If the independent variables are thought of as coordinates of a two-dimensional man-
ifold, the invariant area element is given by dA =
g dxdy where g is the determinant
of the inverse metric on the manifold. Under changes of coordinates from (x,y) to,
say (a,b), this changes according to
g(x,y)=
(x,y)
(a,b)
2
g
(a,b) (16.18)
The area dA being a geometrical quantity does not depend on the choice of coordi-
nates and one gets the important relation
dxdy =
(x,y)
(a,b)
·dadb (16.19)
Considering the sequence of transformations (
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Publisher Resources

ISBN: 9781466512085