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 (in L) of the balloon when it reached the center?

(Please show all the steps with brief explanations, thanks!)

Explanation / Answer

Given that;

V1= 48.0 L

P1= 1.00 atm

According to ideal gas law:

PV=nRT

The equation can also be written as

P1V1=P2V2

P1=1atm=1 bar

P2=40mbar=0.04bar

V1=48 L

V2=??

After putting all these values in above equation

P1V1=P2V2

1bar*48L=0.04bar*V2

1*48/0.04=V2

V2=1200L

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