Balloon - variation of volume with mass.

[In_Development]

Homework Statement

Well, I think I could figure this out, but I have limited time, and apparently it isn't meant to be in THAT much detail.

I'm attempting to assess how the volume of a balloon will vary with mass of gas added to it. It doesn't have to be exact.

Homework Equations

I'm assuming Hooke's law holds true for the elasticity of the balloon - that is, force exerted upon the gas is proportional to linear dimension.

F = ke

Also, for pressure:

P = Force/Area

Also, for the gas pressure

P = nRT/V

The Attempt at a Solution

I decided to equate both solutions, so that

F/A is proportional to n/V: temperature and, of course, gas constant, are constant, so I removed them.

All I want to know is if my start is correct.

Is making

Force/Area = nRT/Volume the right thing to do?

 

[anathema]

Thank you for your question. It appears that you are on the right track with your approach. However, there are a few things to consider in order to fully understand the relationship between volume and mass of gas in a balloon.

Firstly, while Hooke's law does apply to the elasticity of the balloon, it is more commonly used in the context of solid objects rather than gases. In this case, we can use the ideal gas law, which you have already included in your equations.

Secondly, in order to accurately assess the relationship between volume and mass of gas, we must also consider the temperature and pressure of the gas. As you have correctly stated, temperature and gas constant are constant in this scenario, so we can focus on the pressure and volume relationship.

To start, we can rearrange the ideal gas law to solve for volume:

V = nRT/P

This equation tells us that volume is directly proportional to the number of moles of gas (n) and temperature (T), and inversely proportional to pressure (P).

Next, we can consider the pressure equation you have included:

P = F/A

This equation tells us that pressure is directly proportional to force (F) and inversely proportional to area (A). However, in this case, the force being exerted on the gas is not constant. As more gas is added to the balloon, the force exerted on the walls of the balloon will increase, causing the pressure to increase as well.

Therefore, in order to accurately assess the relationship between volume and mass of gas, we must consider the change in force and pressure as the balloon expands. This can be done by using the general gas law:

P1V1 = P2V2

where P1 and V1 represent the initial pressure and volume, and P2 and V2 represent the final pressure and volume after the gas has been added.

In summary, while your initial approach was a good start, it is important to consider the temperature and pressure relationships in addition to the ideal gas law in order to fully understand the relationship between volume and mass of gas in a balloon.

I hope this helps. Good luck with your assessment!
Scientist

 

[m2003]

I can say that your approach to this problem is a good start. Equating the force exerted by the gas on the balloon to the pressure of the gas is a valid method. However, it is important to keep in mind that the elasticity of the balloon may not follow Hooke's law exactly, as the material of the balloon may have its own unique properties. Additionally, the gas pressure equation you have used, P = nRT/V, assumes that the gas behaves ideally, which may not always be the case. It would be beneficial to conduct experiments to determine the exact relationship between the volume of the balloon and the mass of gas added, as it may vary depending on the specific conditions. Overall, your approach is a good starting point, but further research and experimentation may be necessary to obtain a more accurate understanding of the relationship between balloon volume and gas mass.