Affinity and the thermodynamic potentials

We now compare (4.23),. .., (4.26) with the corresponding total differentials. For that relative to U we have 

We note that the partial derivative of a thermodynamic potential with respect to the extensive thermal variable 8 gives us the intensive thermal variable T conversely, the partial derivative of a thermodynamic potential with respect to the intensive thermal variable gives us 8, with the sign changed. The same regularity is observed for the pair of mechanical variables p and V and the pair of chemical variables A and 

Among the sets of equations (4.29) we notice particularly those connecting the affinity with the thermodynamic potentials, namely 

If we know one of the thermodynamic potentials as a function of the variables to which it corresponds, we can express all the other thermodynamic variables as a function of this one by using equations (4.29). 

For example suppose that we know G as a function oi T, p and We have now 

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