Boyle's law pressure calculation

In summary: This is a very complex problem.In summary, the question is asking about the pressure increase within a pillow when a weight is placed on it. Using Boyle's law, the pressure in the pillow is calculated to be 1033 hPa. The gravitational force of the weight is countered by an opposing force within the pillow, resulting in a pressure of 3270 hPa. However, the actual pressure difference between P2 and P3 is difficult to calculate accurately due to the complex geometry and forces involved.
  • #1
Daan van Driel
2
0

Homework Statement



An pillow is inflated with an pressure of let's say 20 hPa. Afterwards we place a weight of 10 Kg on the pillow, what is the pressure increase within the pillow?

P athmosthere = 1013 hPa
P cushion = 1013 + 20 = 1033 hPa
m = 10 Kg
g = 9.81 m/s^2

Amount of air in the pillow stays the same

Homework Equations


[/B]
Boyle's law: P1 * V1 = P2 * V2
Gravitational force: F = m * g
Pressure: P = F / A

The Attempt at a Solution

pressure-calc-illustration.png

[/B]
The added weight creates a force F. This creates an apposing force within the pillow (Newton's third law) which is devided over the enitre inner surface of the pillow. Therefore P = F / A = m * g / A.

Lets assume that the surface area of the pillow is equal to 300 cm^2. P = (10 * 9.81) / 0.03 = 3270

Would this be right? If so, how do I translate this 3270 back to the pressure difference between P2 ane P3?
 

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  • #2
Is this an actual homework problem? Is the geometry exactly as you have shown it in the figure?
 
  • #3
Chestermiller said:
Is this an actual homework problem? Is the geometry exactly as you have shown it in the figure?

No, this is a problem I'm trying to answer for a project. The geometry is not exactly as it is shown in the picture, i just made it to substantiate my explanation.
 
  • #4
Daan van Driel said:
No, this is a problem I'm trying to answer for a project. The geometry is not exactly as it is shown in the picture, i just made it to substantiate my explanation.
This is a pretty complicated problem, since the shape and curvature of your surface changes. You also omitted the force on the other side of the cushion required to hold it in place. It might be possible to model this more easily if the cushion were sandwiched between two infinite flat surfaces, but that too would be somewhat complicated. If the outer boundary of the cushion were considered inextensible, then pressing it between flat surfaces (or any other surfaces for that matter) would cause the boundary to buckle and form folds.
 

Related to Boyle's law pressure calculation

1. What is Boyle's Law?

Boyle's Law is a gas law that states the pressure of a gas is inversely proportional to its volume, when temperature is held constant.

2. What is the formula for Boyle's Law?

The formula for Boyle's Law is P1V1 = P2V2, where P1 and V1 are the initial pressure and volume, and P2 and V2 are the final pressure and volume.

3. How do you calculate pressure using Boyle's Law?

To calculate pressure using Boyle's Law, you need to know the initial pressure, initial volume, and final volume. Then, you can rearrange the formula to solve for final pressure (P2 = (P1V1)/V2).

4. What are the units for pressure in Boyle's Law?

The units for pressure in Boyle's Law are usually expressed in atmospheres (atm) or kilopascals (kPa).

5. How does temperature affect Boyle's Law?

In Boyle's Law, temperature is held constant. However, if temperature were to increase, the volume of the gas would also increase, according to Charles' Law. This would result in a decrease in pressure, following Boyle's Law.

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