If a small weather balloon with a V of 50.0 L at a pressure of 1.00 atmosphere , what was the V of the balloon when it reached the center?

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2018-03-20 9:47 am

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 50.0 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?

回答 (1)

wanszeto

2018-03-20 5:37 pm

✔ 最佳答案

For the weather balloon assumed at constant temperature:
At the edge of Typhoon Odessa: P₁ = 1 atm = 1013.3 mbar, V₁ = 50.0 L
At the center of Typhoon Odessa: P₂ = (1013.3 - 40.0) mbar = 973.3 mbar, V₂ = ? L

For a fixed amount of gas at constant temperature (Boyle's law) : P₁V₁ = P₂V₂
V₂ = V₁ × (P₁/P₂) = (50.0 L) × (1013.3/973.3) = 52.1 L

Volume of the balloon at the center of Typhoon Odessa = 52.1 L

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