Suppose the moon has a radius of r miles and a payload weighs p pounds at the surface of the moon (at a distance of r miles from the center of the moon). when the payload is x miles from the center of the moon (x ≥ r), the force required to overcome the gravitational attraction between the moon and the payload is given by the following relation: required force = f(x) = r2px2 poundsfor example, the amount of work done raising the payload from the surface of the moon (i. e., x = r) to an altitude of r miles above the surface of the moon (i. e., x = 2r) iswork = bf(x) dxa = 2rr2px2 dxr = rp2 mile-poundshow much work would be needed to raise the payload from the surface of the moon (i. e., x = r) to the "end of the universe"? work = mile-pounds

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.

Find the dimensions and area of the largest rectangle that can be inscribed in the upper half of the ellipse. (give your answers in terms of a and b. enter the dimensions as a comma-separated list.)

Which of the following bonds would be most polar? a. c-i b. c-br c. c-cl d. c-f e. c-o