Different gibbs energy equations

For temperature dependence of Gibbs energy, Why we Gibbs-Helmholtz equation rather than finding directly in the same way as Gibbs energy dependence on pressure?


$$\frac{\mathrm dG}{\mathrm dp} = V \Rightarrow \mathrm dG = V\,\mathrm dp \quad\text{for solids and liquids}$$ 


By pressure I mean external pressure applied. Like for gases $\mathrm dG = nRT \ln(p\_\mathrm f/p\_\mathrm i)$. Why we use this equation $(G/T)/T = H/T^2$ for change in Gibbs energy dependence of temperature. Why not this equation $\mathrm dG = \mathrm dT\times(-S)$?





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It depends what problem you want to solve.


$\frac{dG}{dT}$ is of interest, for example, if you want to know the maximum work available from a process at different temperatures.


$\frac{d(G/T)}{dT}$ is of interest, for example, if you want to know how the equilibrium constant changes with temperature (because $\Delta G^\circ = -R T \ln K$).


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