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
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:
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.