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Determine equation of state from entropy 
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#1
Jun1611, 01:21 PM

P: 85

1. The problem statement, all variables and given/known data
The entropy is given as [tex]S=a \left(VNU \right)^{\frac{1}{3}} [/tex] Find the equation of state. 2. The attempt at a solution I've tried writing [itex]dS[/itex] in terms of [itex]dP[/itex] and [itex]dT[/itex] then using the fact that [itex]dS[/itex] is a perfect differential equate the partial derivatives of the terms. This got me nowhere. I also tried using Maxwell relations. [tex]\left( \frac{\partial S}{\partial V} \right) _T = \left( \frac{\partial P}{\partial T} \right) _V[/tex] Thanks Alex 


#2
Jun1911, 05:58 AM

P: 85

How about I use the definition of temperature?
[tex] \frac{1}{T} = \left( \frac{\partial S}{\partial U} \right) = \frac{a}{3} \left( \frac{VT}{U^2} \right)^{1/3} [/tex] 


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