Question

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 60.0 cm wide. The biologist estimates she will need 8100. 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. ? Check

Answer 1

Given, diameter = 60.0 cm

radius ,r = = 30cm

60.0 cm 2

now assume the 8100 L of air is measured at 1 atm pressure,

then using Boyle’s law

P1V1=P2V2

Where P1 =1 atm

V1 = 8100L

Now calculating V2

Volume of spherical air tank V2 = $1585368356288_blob.png$πr3

                                             = $1585368355962_blob.png$$1585368356228_blob.png$(30)3 = 113,142 cm3

                                             = 113.142 L

Using P1V1=P2V2

P2 = = 71.591L

1 atmx 81002 113.142 L

P2 = 72 atm