Weather Balloon

PrideofPhilly

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?

mgb_phys

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

PrideofPhilly

where did you get the 0.33 from?

cepheid

He means to the power of one third (the cube root, as he said).

PrideofPhilly

nevermind, i got it! thank you!