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