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 42.0 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

Given information is:

pressure was 40.0 mbar lower at the center than normal atmospheric pressure. and from question balloon when it reached the center?

1 mbar = 0.000986923 atm therefore 40 mbar = 0.0394769 atm

P1V1 = P2V2 since they have not mentioned any temperature, assume it was constant

P1 = 1 atm; V1 = 42.0 L; P2 = 1 - 0.0394769 atm = 0.9605231 atm; then

V2 = (P1V1) / P2 = (1 atm)(42.0L) / 0.9605231 atm = 43.7261737901 L = 43.7 L

volume of the balloon when it reached the center = 43.7 L

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