For the relation dG = –SdT + Vdp, a) determine natural and conjugate variables, and b) derive…

For the relation dG = –SdT + Vdp, a) determine natural and
conjugate variables, and b) derive alternate functions using the Legendre
transformation.

With reference to Figure 4.1 extend it by adding the
additional variable N and sketch the result in a 3D flowchart relating the
functions.