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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
76 The Principles of Thermodynamics
Let us rst illustrate getting a relation between partial derivatives of a different type
than what we have obtained so far. From eqn.(3.36) it is easy to get
U
V
T
= T
S
V
T
P (3.39)
It is to be noted that we got this even though neither of the independent variables in
eqn.(3.36) has been held xed. Once again, the integrability condition for the rst of
eqn.(3.38) is
V
C
V
T
T
=
T
P+
U
V
T
T
V
(3.40)
On using the integrability condition for dU,
V
U
T
V
T
=
T
U
V
T
V
and
C
V
=
U
T
V
, the above equation reduces to
U
V
T
= T
P
T
V
P (3.41)
Eqn.(3.41) is a very important equation in thermodynamics from which
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Publisher Resources

ISBN: 9781466512085