Calculating Pressure in a Meteorological Balloon at -20.0C

[LFoschiatti]

Homework Statement

A meteorological balloon had a radius of 1 m when released from sea level and expanded to a radius of 3 m when it had risen to it's maximum altitude, where the temperature was -20.0C. What is the pressure inside the balloon at that altitude?

Homework Equations

PV = nRT (I assumed ideal behavior)
n & R are constant, so
P1V1/T1 = P2V2/T2

The Attempt at a Solution

known:
initial volume= 4/3pi (1m)^3=4.187 m^3
final temp = 253K
final volume = 4/3 pi (3)^3=113.04 m^3

Can I assume STP at sea level and use 1 atm for initial pressure and 273K for initial temperature? Or is there more to it than that?

If I do that I get .03 atm. This sounds reasonable, but I am not sure the assumtions I made are correct.

 

[Dick]

Your assumptions sound pretty reasonable to me.