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A marine biologist is preparing a deep-sea submersible for a dive. The sub stores breathing air under high pressure in a spherical air tank that measures 78 cm wide. The biologist estimates she will need 5100 L of air for the dive. Calculate the pressure to which this volume of air must be compressed in order to fit into the air tank. Write your answer in atmospheres. Be sure your answer has the correct number of significant digits.

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IthaloAbreu

Answer:

20.5 atm

Explanation:

First, let's calculated the volume of the air tank. For a sphere, the volume is

V = (4/3)xπr³, where r is the radius.

The diamenter given is 78 cm, so r = 78/2 = 39cm, then:

V = (4/3)xπx39³

V = 248,474.84 cm³

Knowing that 1 cm³ = 0.001 L, V = 248.5 L

The gas will reduce its volume, but the temperature will not change, so we can use the Boyle equation for isothermic transformation:

P1V1 = P2V2, supposing that in the initial state the gas is in 1 atm

1x5100 = P2x248.5

P2 = 5100/248.5

P2 = 20.5 atm (3 significant digits)

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