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

Awind turbine is initially spinning at a constant angular speed. as the wind's strength gradually increases, the turbine experiences a constant angular acceleration 0.173 rad/s2. after making 2870 revolutions, its angular speed is 132 rad/s. (a) what is the initial angular velocity of the turbine? (b) how much time elapses while the turbine is speeding up?

Consider two metallic rods mounted on insulated supports. one is neutral, the other positively charged. you bring the two rods close to each, but without contact, and briefly ground the the neutral rod by touching it with your hand. show answer correct answer what would be resulting charge (if any) on the initially neutral rod

Steam is generated in a boiler of a cogeneration plant at 10 mpa and 450°c at a steady rate of 5 kg/s. in normal operation, steam expands in a turbine to a pressure of 0.5 mpa and is then routed to the process heater, where it supplies the process heat. steam leaves the process heater as a saturated liquid and is pumped to the boiler pressure. in this mode, no steam passes through a condenser, which operates at 20 kpa. (a) determine the power produced in the turbine and the rate at which process heat is supplied in this mode. (b) determine the power produced in the turbine and the rate of process heat supplied if only 60 percent of the steam is routed to the process heater and the remainder is expanded to the condenser pressure. (3.32 mw; 9.69 mw; 4.25 mw; 5.82 mw)