Calculating Pressure & Work in a Piston-Cylinder Assembly

[krnhseya]

Homework Statement

Warm air is contained in a piston-cylinder assembly oriented horizontally. The air cools slowly from an initial volume of 0.003m^3 to a final volume of 0.002m^3. During the process, the spring exerts a force that varies linearly from an initial value of 900N to a final value of zero. The atmospheric pressure is 100kPa, and the area of the piston face is 0.018m^2. Friction is neglected between piston and cylinder. For the air, determine the initial and final pressures and work.

Homework Equations

Pressure x Area = Force

Work = $$\int$$ p dV

The Attempt at a Solution

Initial Pressure of Air x Area = Atmospheric Pressure x Area + Spring Force
Initial Pressure of Air x 0.018m^2 = (100x10^3Pa x 0.018m^2) + 900N
Initial Pressure of Air = 150kPa

Final Pressure of Air x Area = Atmospheric Pressure x Area
Final Pressure of Air = Atmospheric Pressure
Final Pressure of Air = 100kPa

Work = $$\int$$ p dV

Volume is changing from 0.003m^3 to 0.002m^3, which can be used as an interval of this integration. I am not sure about how I should use pressure to calculate the work.

Also, I am not really sure if I got those pressures correctly.
Thank you.

 

[mgb_phys]

Physics tip - don't do the maths until you understand the problem.
If you can solve the problem with simple maths do so.

Pressure - at the start the pressure is atmopshere+spring, at the end it is just atmosphere
Work - work is force*distance. Since the force is varying linearly you don't need to integrate just use the average/mid point force

 

[krnhseya]

Physics tip - don't do the maths until you understand the problem.
If you can solve the problem with simple maths do so.

Pressure - at the start the pressure is atmopshere+spring, at the end it is just atmosphere
Work - work is force*distance. Since the force is varying linearly you don't need to integrate just use the average/mid point force

Did I do it wrong? I thought those calculations for pressure were quite simple...?

Well for the work part, here's what I did.

Since the area for both initial and final are constant, find the distance traveled by dividing volume by area. (Initial Volume/Area and Final Volume/Area)
Once I get those, subtrace one to another to final the distance travelled.
Then like you mentioned earlier, average force (450N) times the distance that I got to find the work done, which is 25J or 0.03kJ)

 

[mgb_phys]

Sounds correct

 

[krnhseya]

Sounds correct

Thank you very much. Have a great day! :)