Calculating Work: Pressure and Volume Relationship for a Blown-Up Balloon

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SUMMARY

The discussion focuses on calculating the work done by air when inflating a balloon, governed by the pressure-volume relationship P = CV³, where C is 100 kPa/m³. The work done, W, is determined by integrating the pressure over the change in volume from 1 m³ to 3 m³. The calculated pressures at these volumes are P1 = 100 kPa and P2 = 900 kPa. The integral W = ∫PΔV is essential for finding the area under the pressure-volume curve, which represents the work done.

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Homework Statement



A balloon behaves such that the pressure is P = CV3 where C = 100 kPa/m3. The balloon is blown up with air from a starting volume of 1 m3 to a volume of 3 m3. Find the work done by the air.

Homework Equations



W=∫PΔV... something to do with integrating to find the work (the area under the curve)

The Attempt at a Solution



I found P1= 100 kPa/m3 x (1m3)3 = 100 kPa
I also found P2 = 100 kPa/m3 x (3m3)3 = 900 kPa
 
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Bahamas said:

Homework Statement



A balloon behaves such that the pressure is P = CV3 where C = 100 kPa/m3. The balloon is blown up with air from a starting volume of 1 m3 to a volume of 3 m3. Find the work done by the air.

Homework Equations



W=∫PΔV... something to do with integrating to find the work (the area under the curve)

So use that formula! (You don't need to find p anywhere).
 

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