Mike is trying to determine the amount of work his experimental air compressor is doing. He finds that the amount of work done (W) depends on the rate of change in pressure created by the pump (dP/dt) with respect to time, the volume of air inside the pump (V) and the speed at which air moves out of the pump (v).

Problem 7:   Mike is trying to determine the amount of work his experimental air compressor is doing. He finds that the amount of work done (W) depends on the rate of change in pressure created by the pump (dP/dt) with respect to time, the volume of air inside the pump (V), and the speed at which air moves out of the pump (v). Part (a)  After an initial test run Mike determines that his pump does 280 J of work (W1). Calculate the amount of work (W2) in J that Mike would expect his pump to do if its volume were 3.5 times greater. W2 = ______ Part (b)  If Mike wanted to reduce the volume of his pump by a factor of 6.5, yet keep it doing the same amount of work at the same airspeed, by what numerical factor (B) would he have to increase the rate of change in pressure (dP/dt) his pump creates? B = ______

A cylinder contains one liter of air at room temperature (300 K) and atmospheric pressure (105 N/m2). At one end of the cylinder is a massless piston, whose surface area is 0.01 m2 . Suppose that you push the piston in very suddenly, exerting a force of 2000 N. The piston moves only one millimeter, before it is stopped by an immovable barrier of some sort. How much work have you done on this system?

A hand-driven tire pump has a piston with a 3.00 cm diameter and a maximum stroke of 35.0 cm. (a) How much work (in J) do you do in one stroke if the average gauge pressure is 2.40 x 105 N/m2 (about 35 psi)? (b) What average force (in N) do you exert on the piston, neglecting friction and gravity? N