Is the Formula for Surface Tension Incorrect?

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Discussion Overview

The discussion centers around the formula for surface tension and its relationship to surface area, particularly in the context of a soap film and a liquid bubble. Participants are examining the reasoning behind the increase in surface area being represented as 2lx rather than lx, exploring both theoretical and conceptual aspects of surface tension.

Discussion Character

  • Debate/contested
  • Conceptual clarification
  • Technical explanation

Main Points Raised

  • One participant questions the validity of the formula stating that the increase in surface area should be lx instead of 2lx, suggesting dissatisfaction with their teacher's explanation.
  • Another participant argues that the soap film has two sides, which justifies the factor of 2 in the surface area calculation.
  • Some participants discuss the relationship between the surface area of the soap film and the rectangular frame, with one asserting that the area of the frame is not relevant to the surface tension issue.
  • A participant points out that for a liquid bubble, the increase in surface area is calculated as 4πr², indicating a different approach to surface area compared to the soap film.
  • There is a repeated emphasis on the need to account for both surfaces of the soap film when calculating the total change in surface area.
  • One participant expresses confusion about how the increase in surface area can be represented as 2lx, seeking further clarification on the reasoning behind this calculation.

Areas of Agreement / Disagreement

Participants generally disagree on the interpretation of the increase in surface area related to surface tension. While some agree that the soap film has two sides, the justification for the factor of 2 in the area calculation remains contested.

Contextual Notes

There are unresolved assumptions regarding the definitions of surface area in different contexts (soap film vs. liquid bubble) and the implications of the geometry involved in the calculations.

rajatgl16
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In the image that I've attached with this thread you can see proof of serface energy+surface tension. This scaned image is from my school book. When I was going through this topic I wound that in this
increase in surface area = 2lx
which according to me isn't reasonable. I discussed about it mwith my teacher but I'm not satisfied with his answer.
According to me
increase in surface area should be = lx.
Please post your comments on this
 

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The soap film has two sides. You need to count both, thus the factor of 2.
 
my teacher gave me the same explanation. But the point is 2 sides of soap film is okay for surface tension. But this in no way associated with area.
 
rajatgl16 said:
But this in no way associated with area.
Why do you think that? What do you think you're finding the area of?
 
well i think increase in surface area is denoted by LL'M'M in figure
 
rajatgl16 said:
well i think increase in surface area is denoted by LL'M'M in figure
Surface area of what?
 
rectangular frame
 
rajatgl16 said:
rectangular frame
Why would you care about the area of the rectangular frame? That's not a surface. (Remember that this is a physics issue, not just geometry.)
 
Then you tell me what is this?
 
  • #10
rajatgl16 said:
Then you tell me what is this?
Your trying to find the surface area of the soap film. It has two sides.
 
  • #11
Now check this one. iN THIS for a liquid bubble which too have 2 sides increase in surface area is taken as 4pi*r^2 not 2*4pi*r^2
 

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  • #12
rajatgl16 said:
Now check this one. iN THIS for a liquid bubble which too have 2 sides increase in surface area is taken as 4pi*r^2 not 2*4pi*r^2
I see a factor of 2.
 
  • #13
I too can see. But Thats for surface tension according to me.
As you can see in figure this topic is part b). Actually part one is for liquid drop. In that surface tension is taken to b 'T'. But as for a liquid bubble there are to effective surfaces, surface tension comes out to b '2T'.
 
  • #14
rajatgl16 said:
I too can see. But Thats for surface tension according to me.
As you can see in figure this topic is part b). Actually part one is for liquid drop. In that surface tension is taken to b 'T'. But as for a liquid bubble there are to effective surfaces, surface tension comes out to b '2T'.
OK, so what's the issue?
 
  • #15
Issue is still same In my thread I've asked why increase in surface area is taken as 2lx instead of lx.
 
  • #16
rajatgl16 said:
Issue is still same In my thread I've asked why increase in surface area is taken as 2lx instead of lx.
I answered that (twice): There are two surfaces. You need the total change in area of the surface.
 
  • #17
i'm not getting what you mean.
 
  • #18
please elaborate how increase in surface area= 2lx. It simply makes no meaning that due to 2 surfaces total area becomes twice or 2lx
 
  • #19
rajatgl16 said:
please elaborate how increase in surface area= 2lx. It simply makes no meaning that due to 2 surfaces total area becomes twice or 2lx
I'm not sure what to say without repeating the same words over again. A soap film has two sides. You want the change in total surface area. Each side increases by lx, thus the total is twice that.
 
  • #20
can you mark that area it in figure?
 
  • #21
rajatgl16 said:
can you mark that area it in figure?
No. The figure only shows one side of the film.
 
  • #22
this wire system is 2dimensional or 3d? And sliding has occurred from LM to L'M' or reverse?
 
  • #23
Do you agree that the soap film has two sides? Yes or no.
 
  • #24
yes. And by it i mean that the wire system LM on both (left and right) side is coated with soap film.
 
  • #25
rajatgl16 said:
yes. And by it i mean that the wire system LM on both (left and right) side is coated with soap film.
Not sure what you mean by left and right, since the diagram shows only one side of the film. I'd call the two sides front (shown) and back (not shown).
 
  • #26
ok i got your this point, and my point of left and right is wrong. Now after this what?
 
  • #27
rajatgl16 said:
ok i got your this point, and my point of left and right is wrong. Now after this what?
As the area of the frame increases by lx, the total surface area of the film increases by 2lx, including both surfaces.
 

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