Calculate Force/Pressure of Inflating Balloon

[alexbib]

let's say a rubber balloon is not streched (but almost) when its volume is 1L. what force (or pressure) does the balloon exert on a gas inside it when its volume is stretched by xL? I'm measuring this experimentally, but I'd like to know a theoretical way of calculating it.

 

[Sirus]

The ideal gas law states that:
PV=nRT
where n is amount of gas in moles, T is the kelvin temperature, and R is the universal gas constant. Define initial pressure as P_{1}, and establish a relationship between volume and pressure when amount of gas and temperature are held constant.

Note: think about how to control these variables effectively when you conduct the experiment for best results.

 

[alexbib]

yes, that is not what I was asking. Maybe I misexpressed myself. Let me reformulate. P-inside=P-outside + F-balloon/area. I'm looking to predict what the force exerted by the balloon on the gas will be when the fabric is stretched by a certain amount. I know how to measure it experimentally (as you said, we can use the gas law to do this), but I'm looking for a theoretical answer: is the force exerted by the fabric proportional to the area it's been stretched by?

 

[alexbib]

come on, don't tell me nobody knows

 

[da_willem]

I could have a go using Hooke's law which states that the force the rubber exerts is proportinal to the elongation: F=C \Delta x. This constant C you can ofcourse easily measure, and at the same time check if your baloon indeed obeys Hooke's law!


Let's also make the assumption the balloon is approximately spherical with a radius r when it is unstretched. and r' if you inflate it a little bit. Now if you draw a small circle on it with an angle \delta \theta from the center of the balloon to the side of the circle the circumference is r \delta \theta. The elongation is in this case the extension of the circumference:

\Delta x = 2 \pi (r'-r)

And the force is thus:

F=C 2 \pi (r'-r)

If you would like to calculate the pressure you only take the part of this force in the radial direction. Wich amounts to multipying by \delta \theta. And ofcourse pressure is the force per unit area and you have to divide by \pi (r \delta \theta)^2:

p(r')=2C\frac{r'-r}{r^2}

 

[rcgldr]

The tension versus stretch isn't linear for rubber, I don't have the formula for this, but I have a link to a site concerning the stretch for typical latex rubber used to launch radio control gliders:

http://www.hollyday.com/rich/hd/sailplanes/rubberdata.htm