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Balloon in a vacuum

  1. Mar 20, 2017 #1
    1. The problem statement, all variables and given/known data
    Balloon in vacuum, radius R0 = 5,0 cm, surface tension σ = 25 N/m.

    a/ the pressure in the balloon p in,0 by radius R0………. pin,0 = ?

    b/ relation to the pressure inside the balloon pin, depending on its radius R…?

    c/relation to the pressure inside the balloon pin , depending on the pressure outside the balloon pout and on its radius R, surface tension is σ…….?

    2. Relevant equations
    a/ pin,0=4σ/R0 = 4.25/0,05 = 2kPa

    b/ pin = 4σ/R

    c/ pin = pout + 4σ/R

    3. The attempt at a solution
     
  2. jcsd
  3. Mar 20, 2017 #2

    mfb

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    Looks right.
     
  4. Mar 20, 2017 #3
    in B/ I have to use pressure p in 0.....

    p in = 4σ/R .....R = R0 + ΔR = R0 + ( R-R0)....p in = 4σ/R0 + ( R-R0)
     
  5. Mar 20, 2017 #4

    mfb

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    If you add proper brackets to the denominators, you get the same result as in post 1.
     
  6. Mar 20, 2017 #5
    so:?

    p in = p in 0 + 4σ/ ( R- R0)
     
  7. Mar 20, 2017 #6

    mfb

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    That looks wrong, no matter how I interpret the notation, and I don't see how you got it. In particular, it is undefined for the easiest case of R=R0.

    Why do you want to change a correct answer?
     
  8. Mar 20, 2017 #7
    Because I have to find dependence p in on p in 0 : Find the equation for the pressure p in inside the balloon, depending on the radius R, where
    at radius R 0 is pressure p in 0
     
  9. Mar 20, 2017 #8

    mfb

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    That's not what you write in post 1.
     
  10. Mar 20, 2017 #9
    Yes, it's true, I did not read the assignment to the end :-( I am sorrry.....
     
  11. Mar 20, 2017 #10

    haruspex

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    Your notation is hard to interpret, but I think you are saying:
    With zero external pressure, the radius is R0 and the internal pressure is pin0.
    With some unknown external pressure the radius is R; what is the internal pressure, pin, now?

    If that is right, write out the equation for each of the two circumstances. Please use subscripts, as I have, to make the notation clearer. Use the X2 button above the text entry box.
     
    Last edited: Mar 21, 2017
  12. Mar 21, 2017 #11
    b/ Find the equation for the pressure p in inside the balloon, depending on the radius R, where
    at radius R 0 is pressure p in 0
     
  13. Mar 21, 2017 #12

    haruspex

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    Yes, that agrees with my interpretation. So what two equations can you write, one for the zero external pressure case and one for the general case?
     
  14. Mar 21, 2017 #13
    in vacuum : ......pin = 4σ/R.....for R0 .....pin0 = 4σ/R0
    p in = 4σ/R .....R = R0 + ΔR = R0 + ( R-R0)....p in = 4σ/ (R0 + ( R-R0))
    - But here now I can not express pin0

    for the general case: pin = pout + 4σ/R
     
  15. Mar 21, 2017 #14

    haruspex

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    It's all the same balloon and contents. What does not vary as the external pressure changes?
     
  16. Mar 21, 2017 #15
    surface tension?
     
  17. Mar 21, 2017 #16

    haruspex

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    What else?
     
  18. Mar 21, 2017 #17
    the amount of air in the balloon ?
     
  19. Mar 21, 2017 #18

    haruspex

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    Right. What law can you use?
     
  20. Mar 21, 2017 #19
    p1V1 =p2V2........?
     
  21. Mar 21, 2017 #20

    haruspex

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    Yes. (You can assume the temperature is constant.)
     
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