Entropy density (entropy per particle)

Asked May 12 '19 at 22:19

Active May 13 '19 at 05:55

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How I can get this definition for an ideal gas: $s=C v \ln (Pρ^{−\gamma})+ \text{constant} $ ?

In this answer it is mentioned that there is a connection with the Sackur-Tetrode relation of the entropy density, but I didn't really get it.
In this answer, there is a mention of that definition but without explanation.

edited May 13 '19 at 05:55

exp ikx

asked May 12 '19 at 22:19

Infro98

That isn't what the entropy per particle of the ideal gas is in the first place (see e.g. https://en.wikipedia.org/wiki/Ideal_gas#Entropy). That looks kind of like the formula for the change in entropy $\Delta s$ per particle, but still isn't quite right even then. – probably_someone May 12 '19 at 22:31
That one can be found in Section 83 of Landau's Fluid Dynamics text, but without any explanaition – Infro98 May 12 '19 at 22:34
Ah, I see. Landau says he discards an "unimportant additive constant", so by $s$ he really means $\Delta s$ from some reference entropy. – probably_someone May 12 '19 at 22:42
Oh, you're right – Infro98 May 12 '19 at 22:46

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