Weather Balloon

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?
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 Recognitions: Homework Help Science Advisor 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
 where did you get the 0.33 from?

Mentor

Weather Balloon

 Quote by PrideofPhilly where did you get the 0.33 from?
He means to the power of one third (the cube root, as he said).
 nevermind, i got it! thank you!

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