Finding the equations of state for a system (entropy)

[ragnarokmonk]

Homework Statement

Suppose the entropy of a system is given by the relation:

S(E,V,N) = a(E,V,N)^(1/3)

Determine three equations of state for this system

Homework Equations

there were no equations given on the sheet but I'm assuming that this might help.

dS=(1/T)*dE+(p/T)*dV+Ʃμ*dN for a quasistatic process

The Attempt at a Solution

So with this, i was trying to determine the partial derivative of the function a(E,V,N)^(1/3). Similar to the way we can find:

(∂S(E,V,N)/∂E)*dE+(∂S(E,V,N)/∂V)*dV+Ʃ(∂S(E,V,N)/∂N)*dN

through partial differentials for S(E,V,N). The only problem is finding the partial differential when there's a power of 1/3 involved. How do i go about obtaining a result like the one above? Also, do i relate it to the equation dS to obtain the equations of state, or am i looking in the wrong direction?

Thanks for all the help everyone.

 

[TSny]

I think you're on the right track. Use the chain rule. For example, ∂S/∂E =( dS/da)(∂a/∂E)