|Jun21-09, 11:54 AM||#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?
|Jun21-09, 12:37 PM||#2|
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
|Jun21-09, 12:50 PM||#3|
where did you get the 0.33 from?
|Jun21-09, 12:51 PM||#4|
|Jun21-09, 12:53 PM||#5|
nevermind, i got it! thank you!
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