Calculating the diameter of a bubble

[jdawg]

Homework Statement

Suppose the temperature is 80℃ and we have a soap bubble that has a pressure increase of 40 [Pa]. What is the diameter of the bubble?

Homework Equations

ΔP=4Y/R

The Attempt at a Solution

I'm very confused about how to find the coefficient of surface tension (Y).
In an example my professor gave us in class he gave us Y(20°C)= 0.0728 N/m. So I'm guessing the coefficient changes with temperature? How would I calculate Y(80°C)? Is there a formula I'm missing?

Also I saw a different version of the above formula where they had ΔP=4T/R. Under what condition would you be able to just neglect the coefficient of surface tension and plug the temperature straight in? Or maybe is that formula completely incorrect? Thanks!

 

[haruspex]

Try https://en.m.wikipedia.org/wiki/Eötvös_rule#Water.
In your 4T/r formula, T is surface tension, not temperature. It applies to double surface bubbles, as e.g. a soap bubble in air.

 

[jdawg]

Ok! That makes more sense. So how do you find the coefficient of surface tension?

 

[haruspex]

Ok! That makes more sense. So how do you find the coefficient of surface tension?

Did you try the link I posted?

 

[jdawg]

Does that formula only work for water though? Is there a formula like that for soap?

 

[haruspex]

Does that formula only work for water though? Is there a formula like that for soap?

What if you assume that the difference between water and a soap solution is due to a difference in the critical temperature?

 

[jdawg]

Then you could use that formula?

 

[haruspex]

Then you could use that formula?

Yes. You could use the given datapoint for the soap solution and the formula to estimate the critical temperature for that soap solution. Then you could find the water temperature that should have the same coefficient as the soap solution at 80C.
Mind you, this is just guesswork. I have not been able to find any info online to confirm this approach.

 

[jdawg]

I'll give it a shot, thanks for your help!