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Balloon deflation

  1. Mar 21, 2013 #1
    1. The problem statement, all variables and given/known data
    A latex balloon, inflated to an excess pressure of 1kPa and a radius of 30cm, is attached to a
    smooth nozzle, initially stoppered. The stopper is removed, and the balloon deflates in 5
    seconds. Imagine that you are using the air stream exiting the balloon to suspend pennies in midair. How many pennies (3g each) can the balloon suspend in midair as it deflates? To
    simplify the problem, make the following simplifying assumptions: 1) air is an ideal gas, with CV= (5/2)R and a molar mass of 28g/mol (i.e, air is mostly nitrogen); 2) the balloon pressure
    remains constant as it deflates; 3) the volume of the balloon when deflated is small.


    2. Relevant equations
    First and second law of thermo, dU/dt +Δ((v^2/2 + gz +H)m) =Q +Ws


    3. The attempt at a solution
    So, work is done by the balloon deflating. The balloon's actual volume can be calculated given the radius. The Force of the balloon must be equal to the force of the pennies. I'm confused as to what i can assume in this problem. I'm not sure if it's isenthalpic or not. There's no heat being added to the system so Q=0.
     
  2. jcsd
  3. Mar 23, 2013 #2

    rude man

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    Since no one has answered for days, just a stab in the dark:

    ∫F dt = Δp where
    F = force holding up pennies = const.
    integration time is 5 s
    p is change in momentum of the air molecules from when they exit the stopper until after they've impacted on the pennies.

    I would assume an elastic collision so that
    Δp = 2p = mv
    m = mass of air over the 5s
    v = escaping molecules' velocity

    Think Bernoulli for v?
     
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