Find an analytic expression for p(v), the pressure as a function of volume, during the adiabatic expansion. express the pressure in terms of v and any or all of the given initial values p0, t0, and v0.

Aball is thrown upward in the air, and its height above the ground after t seconds is h ( t ) = 57 t − 16 t 2 feet. find the time t when the ball will be traveling upward at 14.25 feet per second.

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.

What is the angular momentum of the bar about the axle?