For a system subjected to only P-V work, entropy is given by (I) $-\left(\frac{\partial G}{\partial T}\right)_P$ (II) $\left(\frac{\partial G}{\partial P}\right)_T$ (III) $-\left(\frac{\partial A}{\partial V}\right)_T$ (IV) $-\left(\frac{\partial A}{\partial T}\right)_V$