A thermodynamic system follows the following state equations:

$T=\frac{3A{s}^2}{v}$

$P=\frac{A{s}^3}{v^2}$

Where $A$ is a constant, and $s,u,$ and $v$ represent entropy per mole, internal energy per mole, and

molar volume, respectively.

$($a$)$ Find a relationship for the chemical potential $$ in terms of $s$ and $v.$

$($b$)$ Find the fundamental relationship of the system.