determine equation of state from entropy

by A_B
Tags: determine, entropy, equation, state
 P: 84 1. The problem statement, all variables and given/known data The entropy is given as $$S=a \left(VNU \right)^{\frac{1}{3}}$$ Find the equation of state. 2. The attempt at a solution I've tried writing $dS$ in terms of $dP$ and $dT$ then using the fact that $dS$ is a perfect differential equate the partial derivatives of the terms. This got me nowhere. I also tried using Maxwell relations. $$\left( \frac{\partial S}{\partial V} \right) _T = \left( \frac{\partial P}{\partial T} \right) _V$$ Thanks Alex
 P: 84 How about I use the definition of temperature? $$\frac{1}{T} = \left( \frac{\partial S}{\partial U} \right) = \frac{a}{3} \left( \frac{VT}{U^2} \right)^{1/3}$$

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