Find the mass and center of mass of a wire in the shape of the helix x = t, y = 5 cos(t), z = 5 sin(t), 0 ≤ t ≤ 2π, if the density at any point is equal to the square of the distance from the origin.

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.

Why is the energy that results from a roller coaster's position at the top of a hill referred to as potential energy?

The amount of potential energy possessed by an elevated object is equal to what?