Calculating Pressure in a Meteorological Balloon at -20.0C

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To calculate the pressure inside a meteorological balloon at -20.0°C, the ideal gas law is applied using the formula PV = nRT. The balloon's initial volume at sea level is 4.187 m³ with an assumed initial pressure of 1 atm and temperature of 273K. At maximum altitude, the balloon's volume expands to 113.04 m³ and the temperature drops to 253K. Using the equation P1V1/T1 = P2V2/T2, the calculated pressure at altitude is approximately 0.03 atm. The assumptions made regarding standard temperature and pressure (STP) are considered reasonable for this calculation.
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Homework Statement

A meteorological baloon 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.
 
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Your assumptions sound pretty reasonable to me.
 

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