Air pressure changes in a vessel as the vessel volume increases

In summary, as the volume of a vessel increases, the air pressure inside the vessel decreases, following Boyle's Law, which states that pressure and volume are inversely proportional in a closed system. This relationship indicates that when the space available for gas expands, the molecules have more room to move, resulting in lower pressure.
  • #1
shotdove
3
3
Homework Statement
Pneumatics
Relevant Equations
Unknown
As an example, you have a 100-gallon capacity sealed pressure vessel containing 100 psi of air pressure. What is the change in air pressure as the vessel volume is increased? If the volume is doubled is the pressure reduced to 50 pounds psi. On a graph, is the reduction rate a straight line? Is the pressure drop a percentage of the reduction in volume? What would the formula be for answering this question? Thank you
 
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  • #2
Hello,
:welcome:​

Here at PF we promote self-sufficiency ! Just google pressure versus volume and out comes the answer !

:smile:

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  • #3
shotdove said:
Homework Statement: Pneumatics
Relevant Equations: Unknown

As an example, you have a 100-gallon capacity sealed pressure vessel containing 100 psi of air pressure. What is the change in air pressure as the vessel volume is increased? If the volume is doubled is the pressure reduced to 50 pounds psi. On a graph, is the reduction rate a straight line? Is the pressure drop a percentage of the reduction in volume? What would the formula be for answering this question? Thank you
Truthfully, it depends on the nature of the expansion. I assume you have not examined the Ideal Gas Law in any detail (or perhaps not at all)?
 
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  • #4
BvU said:
Hello,
:welcome:​

Here at PF we promote self-sufficiency ! Just google pressure versus volume and out comes the answer !

:smile:

##\ ##
Perfect, thank you.
 
  • #5
BvU said:
Hello,
:welcome:​

Here at PF we promote self-sufficiency ! Just google pressure versus volume and out comes the answer !

:smile:

##\ ##
Perfect. Thank you, and my Mom said thank you very much for being so helpful.
 
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  • #6
shotdove said:
Perfect. Thank you, and my Mom said thank you very much for being so helpful.
You are most welcome. That's what PF is for.

Next step could be the ideal gas law

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  • #7
There are many different state equations relating Pressure Temperature , Volume and density of gas. The ideal gas law is just one of them.

Not sure if the air behaves as ideal gas at 100Psi and at the given temperature (btw you omit the Temperature, not that it matters if we are given that air behaves as ideal gas for this problem).
 
  • #8
Delta2 said:
Not sure if the air behaves as ideal gas at 100Psi and at the given temperature (btw you omit the Temperature, not that it matters if we are given that air behaves as ideal gas for this problem).
An ideal gas with a non-zero density will have its temperature affected by an adiabatic expansion.
 
  • #9
Let's not make things more complicated than needed to help the OP ...

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FAQ: Air pressure changes in a vessel as the vessel volume increases

What happens to air pressure inside a vessel when its volume increases?

When the volume of a vessel increases, the air pressure inside the vessel decreases, assuming the temperature and the amount of air remain constant. This relationship is described by Boyle's Law, which states that pressure and volume are inversely proportional.

How does temperature affect air pressure changes when the vessel volume increases?

If the temperature is kept constant, increasing the volume of the vessel will decrease the air pressure. However, if the temperature changes, it can either amplify or counteract the pressure change depending on whether the temperature increases or decreases.

Can the air pressure inside a vessel ever become zero if the volume increases infinitely?

No, the air pressure inside a vessel cannot become zero by merely increasing the volume. As the volume increases, the pressure will continue to decrease but will asymptotically approach zero without ever actually reaching it.

What role does the amount of air play in the pressure changes when the vessel volume increases?

The amount of air (or the number of air molecules) inside the vessel plays a critical role. If the amount of air remains constant, the pressure will decrease as the volume increases. However, if air is added or removed, the pressure change will be affected accordingly.

How can Boyle's Law be applied to predict air pressure changes in a vessel with increasing volume?

Boyle's Law can be applied by using the formula P1V1 = P2V2, where P1 and V1 are the initial pressure and volume, and P2 and V2 are the final pressure and volume. By knowing any three of these variables, the fourth can be calculated, allowing for the prediction of pressure changes as the volume increases.

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