At a frequency ω1, the reactance of a certain capacitor equals that of a certain inductor.
a. if the frequency is changed to ω2 = 2 ω1, what is the ratio of the reactance of the inductor to the reactance of the capacitor? which reactance is larger?
b. if the frequency is changed to ω3 = ω1/3, what is the ratio of the reactance of the inductor to the reactance of the capacitor? which reactance is larger?

What happens in a global convection cell

As part of an industrial process, air as an ideal gas at 10 bar, 400k expands at steady state through a valve to a pressure of 4 bar. the mass flow rate of air is 0.5 kg/s. the air then passes through a heat exchanger where it is cooled to a temperature of 295k with negligible change in pressure. the valve can be modeled as a throttling process, and kinetic and potential energy effects can be neglected. (a) for a control volume enclosing the valve and heat exchanger and enough of the local surroundings that the heat transfer occurs at the ambient temperature of 295 k, determine the rate of entropy production, in kw/k. (b) if the expansion valve were replaced by an adiabatic turbine operating isentropically, what would be the entropy production? compare the results of parts (a) and (b) and discuss.

Engineers find a new metal that is stronger than steel but much lighter. this material is also significantly cheaper than what is currently used for most aircraft, available in large quantities, and easy to manufacture. the engineers are excited because this new material will lower the costs of buying and operating airplanes for companies. what is probably the best step for the engineers to make next?