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

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In summary, to find the work done by the air in blowing up the balloon from a volume of 1 m3 to 3 m3, you can use the equation W=∫PΔV, where P = CV3 and C = 100 kPa/m3. This formula involves finding the area under the curve of the pressure-volume graph.
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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).
 

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

How do you calculate the work done on a blown-up balloon?

The work done on a blown-up balloon can be calculated by multiplying the pressure inside the balloon by the change in volume of the balloon. This can be represented by the formula W = P x ΔV, where W is the work done, P is the pressure, and ΔV is the change in volume.

What is the relationship between pressure and volume in a blown-up balloon?

The pressure and volume in a blown-up balloon have an inverse relationship. This means that as the volume of the balloon increases, the pressure inside the balloon decreases. Similarly, as the volume decreases, the pressure increases.

How does the temperature of the air inside the balloon affect the pressure and volume relationship?

The temperature of the air inside the balloon can affect the pressure and volume relationship. If the temperature of the air increases, the pressure inside the balloon increases as well, causing the volume to also increase. On the other hand, if the temperature decreases, the pressure decreases and the volume also decreases.

Can the pressure and volume relationship of a blown-up balloon be represented by a graph?

Yes, the pressure and volume relationship of a blown-up balloon can be represented by a graph. The graph will show an inverse relationship, with pressure on the y-axis and volume on the x-axis. As the volume increases, the pressure decreases, creating a curve on the graph.

How does the elasticity of the balloon material affect the pressure and volume relationship?

The elasticity of the balloon material can affect the pressure and volume relationship. A more elastic material will allow the balloon to expand more easily, resulting in a larger change in volume for a given change in pressure. On the other hand, a less elastic material will require more pressure to change the volume of the balloon. This can be seen in the graph as a steeper or flatter curve, depending on the elasticity of the balloon material.

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