How Do You Calculate Pressure Ratio After Multiple Pump Strokes?

[kriegera]

Homework Statement

If the cross-section of the barrel of a pump is 5 square centimeters, the stroke of the piston is 20 centimeters, and the volume of the receiver, in which the air is drawn from, is 1 liter, calculate the ratio of the pressure of the air in the receiver to the original pressure after three strokes of the pump.

Homework Equations

p=F/A

The Attempt at a Solution

Force=m*a = (1 liter)(9.81) = 9.81
Area = (5)(20)=100
p=f/a = 9.81/100=.0981

Is this correct so far? how do calculate the ratio?

 

[anathema]

To calculate the ratio of the pressure of the air in the receiver to the original pressure after three strokes of the pump, we need to use the ideal gas law: PV = nRT, where P is the pressure, V is the volume, n is the number of moles, R is the gas constant, and T is the temperature.

First, let's calculate the number of moles of air in the receiver. We know that the volume of the receiver is 1 liter, which is equal to 0.001 cubic meters. The ideal gas law can be rearranged to solve for n: n = PV/RT. We can assume that the temperature is constant, so n is directly proportional to P and V. This means that the number of moles of air in the receiver is also 0.001.

Now, let's consider the pressure after three strokes of the pump. Each stroke of the pump will push 5 cubic centimeters of air into the receiver. After three strokes, the total volume of air in the receiver will be 0.001 + (3 x 0.005) = 0.016 cubic meters. Again, using the ideal gas law, we can calculate the pressure: P = nRT/V = (0.001)(8.314)(300)/0.016 = 15.73 Pa.

The ratio of the pressure of the air in the receiver to the original pressure is then 15.73/0.0981 = 160.3. This means that the pressure of the air in the receiver is 160.3 times higher after three strokes of the pump compared to the original pressure.

I hope this helps. Let me know if you have any further questions.