Entropy formula - shock tube problem

ls99wins · October 14, 2015, 13:53

How was the entropy at a state arrived at as, s= $\frac{P}{\rho^{gamma}}$ in the shock tube problem? Does it involve some derivation using statistical thermodynamics?

FMDenaro · October 14, 2015, 17:13

Quote:

Originally Posted by ls99wins

How was the entropy at a state arrived at as, s= $\frac{P}{\rho^{gamma}}$ in the shock tube problem? Does it involve some derivation using statistical thermodynamics?

Are you talking about the integral of the Gibbs relation? that relation is very general, not restricted only to the shock tube

ls99wins · October 14, 2015, 22:38

Yes. But I'm confused as to how a simple s=P/(rho)^gamma, follows from Tds relations? I have not been able to see that explicit relation anywhere else.

LuckyTran · October 15, 2015, 16:37

I'm not familiar with this shock tube problem and this particular formula. Can you provide a link to it?

FMDenaro · October 15, 2015, 16:57

have a look here

http://oai.cwi.nl/oai/asset/10964/10964D.pdf

FMDenaro · October 15, 2015, 17:34

Quote:

Originally Posted by ls99wins

How was the entropy at a state arrived at as, s= $\frac{P}{\rho^{gamma}}$ in the shock tube problem? Does it involve some derivation using statistical thermodynamics?

As you see from the report I linked, Eq.(3.44), the correct relation is

s =Cv ln (p/rho^gamma)

LuckyTran · October 15, 2015, 17:34

FMDenaro's link correctly shows s = Cv ln (P/(rho)^gamma) which is a simple derivation from Tds
but where did s = P/(rho)^gamma come from? The units don't even match.

October 14, 2015, 13:53	Entropy formula - shock tube problem	#1
ls99wins New Member Layne Staley Join Date: Sep 2015 Posts: 7 Rep Power: 10	How was the entropy at a state arrived at as, s= $\frac{P}{\rho^{gamma}}$ in the shock tube problem? Does it involve some derivation using statistical thermodynamics?

October 15, 2015, 16:37		#4
LuckyTran Senior Member Lucky Join Date: Apr 2011 Location: Orlando, FL USA Posts: 5,674 Rep Power: 66	I'm not familiar with this shock tube problem and this particular formula. Can you provide a link to it? Last edited by LuckyTran; October 15, 2015 at 17:38.

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October 14, 2015, 22:38		#3
ls99wins New Member Layne Staley Join Date: Sep 2015 Posts: 7 Rep Power: 10	Yes. But I'm confused as to how a simple s=P/(rho)^gamma, follows from Tds relations? I have not been able to see that explicit relation anywhere else.

October 15, 2015, 16:57		#5
FMDenaro Senior Member Filippo Maria Denaro Join Date: Jul 2010 Posts: 6,768 Rep Power: 71	have a look here http://oai.cwi.nl/oai/asset/10964/10964D.pdf

October 15, 2015, 17:34		#7
LuckyTran Senior Member Lucky Join Date: Apr 2011 Location: Orlando, FL USA Posts: 5,674 Rep Power: 66	FMDenaro's link correctly shows s = Cv ln (P/(rho)^gamma) which is a simple derivation from Tds but where did s = P/(rho)^gamma come from? The units don't even match.