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This formula is more commonly known as the 'spectroscopic entropy'. It is basically the derivative of the free energy in terms of T with V held constant. Λ is h/(2 pi m k T)^1/2. The formula differs from yours only by the inclusion of a factor representing the weight of the lowest electronic state, w.
S/N V/N γ
----- = ln w----- + ----- k Λ^3 γ-1
Wilson: Thermodynamics and Statistical Mechanics, Cambridge, 1960
Bob at PC
-----Original Message-----Λ >
From: phys-l-bounces@carnot.physics.buffalo.edu [mailto:phys-l-
bounces@carnot.physics.buffalo.edu] On Behalf Of John Denker
Sent: Wednesday, January 20, 2010 12:44 AM
To: Forum for Physics Educators
Subject: [Phys-l] polytropic Sackur-Tetrode
Alas on 01/17/2010 04:17 PM, I mentioned the Sackur-Tetrode
formula in connection with the entropy of air:
which is not correct. Equation [1] only applies to
monatomic gases. My apologies.
This led me to derive a generalization of this formula
for use with polytropic gases. To wit:
S/N V/N γ
----- = ln ----- + ----- [2]
k Λ^3 γ-1
V/N Df
= ln ----- + 1 + ----- [3]
Λ^3 2
where Df is the effective number of degrees of freedom,
to the extent that any such thing exists. /snip/