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Wed Jul 6 14:13:09 CEST 2005

entropy is an state variable, i.e. exact differential, one can drive the =
fundamental equation of thermodynamics, i.e. Euler's equation, which for =
monatomic systems reads:
TS=3DU-P*V-mu*N
where, as you see no differential is used (as opposed to the first and =
second laws). The fundamental equation of thermodynamics with respect to =
Gibbs free energy, G=3DU-TS-PV, can be rewritten as follows:
G=3Dmu*N.=20

Thus for monatomic system (here we also have one type of particle that =
is electron) always we can say that mu=3DG/N (for sure see B.5 formula, =
Appendix B, page 759, Solid state physics, by N. W. Ashcroft, N. D. =
Mermin), and it can be reduced to U/N for the case of T=3D0 and P=3D0.

> can this defination be treated as mu=3DU/N?so do in the WIEN2K?
I hope so.

> Does this mean that the chemical potential alway be negative? so does =
the Fermi energy?
The sign of the chemical potential (Fermi energy at T=3D0 K) depends on =
the Energy reference: as in wien2k sometimes the Fermi energy is set to =
zero eV.

Your,
S. Jalali.
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<DIV>
<DIV>&gt; and i remember the defination of the chemical potential is =
:</DIV>
<DIV>&gt; mu=3Dd(G)/d(N)</DIV></DIV>
<DIV>&nbsp;</DIV>
<DIV>From the first and second laws of thermodynamics, and the fact that =
entropy=20
is an state variable, i.e. exact differential, one can drive the =
fundamental=20
equation of thermodynamics, i.e. Euler's equation, which =
for&nbsp;monatomic=20
systems reads:</DIV>
<DIV>TS=3DU-P*V-mu*N</DIV>
<DIV>where, as you see no differential is used (as&nbsp;opposed to the =
first and=20
second laws). The fundamental equation of thermodynamics with respect to =
Gibbs=20
free energy, G=3DU-TS-PV, can be rewritten as follows:</DIV>
<DIV>G=3Dmu*N. </DIV>
<DIV>&nbsp;</DIV>
<DIV>Thus for monatomic system (here we also have one type of particle =
that is=20
electron) always we can say that mu=3DG/N (for sure see B.5 formula, =
Appendix B,=20
page 759, Solid state physics, by N. W. Ashcroft, N. D. Mermin), and it =
can be=20
reduced to U/N for the case of T=3D0 and P=3D0.</DIV>
<DIV>&nbsp;</DIV>
<DIV>
<DIV>&gt; can this defination be treated as mu=3DU/N?so do in the =
WIEN2K?</DIV>
<DIV>I hope so.</DIV>
<DIV>&nbsp;</DIV></DIV>
<DIV>
<DIV>&gt; Does this mean that the chemical potential alway be negative? =
so does=20
the Fermi energy?</DIV></DIV>
<DIV>The sign of the chemical potential&nbsp;(Fermi energy at T=3D0 K) =
depends on=20
the Energy reference: as&nbsp;in wien2k sometimes the Fermi energy is =
set to=20
zero eV.</DIV>
<DIV>&nbsp;</DIV>
<DIV>Your,</DIV>
<DIV>S. Jalali.</DIV></FONT></DIV></BODY></HTML>

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