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Weather Balloon

  1. Jun 21, 2009 #1
    1. The problem statement, all variables and given/known data

    A weather balloon is designed to expand to
    a maximum radius of 30 m when in flight at
    its working altitude where the air pressure is
    0.033 atm and the temperature is 95 K.
    If the balloon is filled at atmospheric pres-
    sure and 462 K, what is its radius at lift-off?

    2. Relevant equations

    PV = nRT
    Volume = 4/3πr^3

    3. The attempt at a solution

    First, I used the ideal gas law to find n:

    (0.033)(4/3π(30)^3) = n(8.31)(95)
    n = 4.727610453 mol

    Then, I solved for r:

    V = nRT/P
    4/3πr^3 = (4.727610453)(8.31)(462)/1 atm
    r = 11.30381236 m (WRONG ANSWER)

    What am I doing wrong?
     
  2. jcsd
  3. Jun 21, 2009 #2

    mgb_phys

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    Science Advisor
    Homework Helper

    So PV/T is constant, you don't actually need the number of moles.
    V1 = (T1/P1) * (P2V2/T2)
    = (462/1) * (0.033*V2/95)
    V1 = 0.16 V2

    So the ground volume is 16% off the final volume, an the radius goes as the cube root of volume, so the initial radius is 0.16^0.33 of 30m
     
  4. Jun 21, 2009 #3
    where did you get the 0.33 from?
     
  5. Jun 21, 2009 #4

    cepheid

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    Staff Emeritus
    Science Advisor
    Gold Member

    He means to the power of one third (the cube root, as he said).
     
  6. Jun 21, 2009 #5
    nevermind, i got it! thank you!
     
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