Question

3) A weather balloon contains 12.0 m2 of hydrogen gas when the balloon is released from a location at which the temperature is 22.0°C and the ambient air pressure is 101 kPa. The balloon rises to a higher altitude where the temperature is -30.0°C and the ambient air pressure is 20.0 kPa. 

If the balloon is free to expand so that the pressure of the gas inside is equal to the ambient pressure outside, what is the new volume of the balloon? Assume that in both cases the hydrogen gas is in thermal equilibrium with the outside air.

Answer 1

We know,

(p1×v1)/T1 = (p2×v2)/T2

here, p1 = initial pressure = 101000 Pa

v1 = volume of the gas initially = 12 m³

T1 = Initial temperature of the gas = 22°C= 295 K

p2 = final pressure= 20000 Pa

v2 = final volume

T2 = final temperature= -30°C = 243 K

So, 101000×12/295 = 20000×v2/243

=> 20000×v2 = 998359.322

=> v2 = 49.918 m³

The new volume will be 49.918 m³.