Thermodynamics Weather Balloon Problem?

Question

A meteorological balloon had a radius of 1.0 m when released at sea level at 20 °C and expanded to a radius of 3.0 m when it had risen to its maximum altitude where the temperature was -20 °C. What is the pressure inside the balloon at that altitude?

im assuming i need to use the gas laws, but first i found the volumes and temperatures of each

v1= 4/3 PI r^3

= 4.2 m^3

v2=4/3 PI (3.0)^3

=110 m^3

t1= 293K

t2=253 K

i am stuck here, I have no idea how to solve for pressure in any of the gas laws, the best i could do is get a ratio of p1/p2

help me

Answer 1

This is a combined gas law problem because you have a confined gas that is undergoing a change in P, V and T.

P1V1/T1 = P2V2/T2

Solve for P2

P2 = P1V1T2 / (T1V2)

P2 = (1 atm) (4.2 m^3) (253 K) / (293 K) / (113 m^3)

P2 = 0.0320 atm

The downside is that balloons should not be used for doing gas law problems. The reason comes from the properties of the balloon itself.  If the balloon itself has any resistance to changing its volume, then pressure of the gas inside will be determined not only from the volume and temperature of the gas, but also by the force exerted on it by the stretched balloon.

Since that latter force is unknown, then it is impossible to accurately model the pressure inside the balloon with only the combined gas law.