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

Learning goal: to understand newton's 1st law. newton's principia states this first law of motion: an object subject to no net force maintains its state of motion, either at rest or at constant speed in a right line. this law may be restated as follows: if the sum of all forces acting on an object is zero, then the acceleration of that object is zero. mathematically this is just a special case of the 2nd law of motion, f⃗ =ma⃗ , when f⃗ =0. when studying newtonian mechanics, it is best to remember the 1st law in two ways: if the net force (i.e., sum of all forces) acting on an object is zero, the object will keep moving with constant velocity (which may be zero). if an object is moving with constant velocity, that is, with zero acceleration, then the net force acting on that object must be zero. complete the following sentences to see if you can apply these ideas. part a if a car is moving to the left with constant velocity, one can conclude that