If a small weather balloon with a volume of 44.0 L at a pressure of 1.00 atmosphere was deployed at the edge of Typhoon Odessa, what was the volume of the balloon when it reached the center?

Question

The severity of a tropical storm is related to the depressed atmospheric pressure at its center. In August 1985, Typhoon Odessa in the Pacific Ocean featured maximum winds of about 90 mi/hr and pressure that was 40.0 mbar lower at the center than normal atmospheric pressure. In contrast, the central pressure of Hurricane Andrew (pictured) was 90.0 mbar lower than its surroundings when it hit south Florida with winds as high as 165 mi/hr.

Answer 1

The question asks to find a volume after a change in pressure. There is no mention of the temperature, so one must assume this is constant. In this case, we are dealing with Boyles Law: P1V1 = P2V2

P1 = initial pressure =1.00 atm

V1 = 44.0 L

P2 = 1.00 atm - 0.04 atm = 0.96 bar (assuming 1 bar = 1 atm and a decrease of 40.0 mbar = 0.040 atm)

V2 = ?

V2 = P1V1 / P2 = (1.00 atm)(44.0 L) / 0.96 atm

V2 = 45.8 L

(note: the unit of bar is not a recognized standard unit of pressure. One bar is very close to 1 atm, so hopefully the assumption used in the above calculation is acceptable)