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