Piezoelectricity. If you apply a mechanical force f along a piezoelectric crystal such as quartz, it will develop a polarization po. If you also apply an electric field E, this causes a mechanical deformation. Such devices are used in microphones, speakers, and pressure transducers. For such systems, the energy equation is dU = TdS + fdl + Edpo.

a. Based on the definition G = U − TS − fl − Epo, determine how dG depends on dT, df, and dE.
b. Express the total derivative of G(T, f, E)
c. Derive a Maxwell relation involving (∂po / ∂T) f, E