1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Homework Help: 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


    User Avatar
    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


    User Avatar
    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!
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook