The severity of a tropical storm is related to the depressed atmospheric pressur

Question

The severity of a tropical storm is related to the depressed atmospheric pressure at its center. Shown below is a photograph of Typhoon Odessa taken from the space shuttle Discovery in August 1985, when the maximum winds of the storm were about 90 mi/hr and the pressure was 40.0 mbar lower at the center than normal atmospheric pressure. In contrast, the central pressure of Hurricane Andrew was 90.0 mbar lower than its surroundings when it hit south Florida with winds as high as 165 mi/hr. If a small weather balloon with a volume of 48.0 L at a pressure of 1.00 atmosphere was deployed at the edge of Typhoon Odessa (in picture), what was the volume of the balloon when it reached the center?

Explanation / Answer

V1 = 48 L

P1 = 1 atm

V2 = ?

P2 = 40 mbar lower than normal atm p --> 0.0394769 atm

so

P1V1 = P2V2

1*48 = V2*(1-0.0394769)

V2 = 48/(1-0.0394769)

V2 = 49.97277L

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