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Subsections
 Definition:
 Ideal Gas is the system where interaction is absent
 Configuration Integral:
 This is factorizable!
 Partition Function:

Let us calculate for :
with
Pressure of ideal gas does not depend on the nature of the gas!
Entropy:
 
(4) 
or, substituting V by NkT/P
 
(5) 
Heat capacity:
We obtained:
C_{p}C_{v} = kN

E = A+TS = Nf(T)NTf'(T)

(6) 
Suppose we have a container of the volume 2V with 2N particles,
divided into two parts. We deleted the divider. What
is the entropy change?
 First Method:
 Let us paint the particles in the left in white,
and particle in the right in black. After we deleted the divider,
``white'' and ``black'' particles mix. From equation (4) the
change of entropy for ``white particles'' is
For ``black particles'' . Total change of
entropy is
 
(7) 
 Second Method:
 Entropy is an extensive variable, so the entropy for
2N molecules in the volume 2V is twice the entropy for N
molecules in the volume V
and
 
(8) 
What is wrong? Why we obtained different answers?
 Solution:
 The distinguishability is a quantum effect: it
is either there, or not (particles cannot be a little bit
different!). If they are identical, we cannot speak about entropy
of white or black particles separatelyand only (8)
works. If they are not identical, only (7) works.
 Consequence:
 There is an entropy change when mixing different
isotopeseven while the molecules are quite similar!
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Up: Systems with Many Particles.
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© 1997
Boris Veytsman
and Michael Kotelyanskii
Wed Sep 17 22:58:45 EDT 1997