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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
124 The Principles of Thermodynamics
The important lesson is that the requirements of extensivity of S,U and V completely
xes the chemical potential
μ
, and furthermore it is xedtobethesameasthemolar
Gibbs potential (note that for one mole of ideal gas RT = PV
m
)! This is not an ac-
cidental result for the ideal gas only. The problem below will show it to be true for
the van der Waals case also. Actually it is true for any system as will be shown now.
Let S
m
,V
m
,U
m
be the molar quantities at T,P. Then the rst law for one mole of the
substance reads:
TdS
m
= dU
m
+ PdV
m
(6.12)
whereas for variable molar systems we have
TdS= dU + PdV
μ
dn (6.13)
Consistency between eqn(6.12), eqn.(6.13), and S = nS
m
,V = nV
m
,U = nU
m
imme-
diately gives
μ
= U
m
TS
m
+ PV
m
, i.e the chemical ...
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Publisher Resources

ISBN: 9781466512085