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

with the invention of the automobile, the woman of the house could drive to the store and get groceries. women were also free to socialize more. during world war ii women were allowed to work in factories to the war effort and could drive to work or ride mass transit buses to their jobs.

the earths atmosphere is made up of nitrogen and oxygen. solids can turn into gasses through a process called sublimation. sublimation is the transition of a substance directly from the solid to the gas phase, without passing through the intermediate liquid phase.

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