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 wide. The biologist estimates she will need 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. Round your answer to significant digits.

Answer 1

The complete question is;

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 78.0 cm wide. The biologist estimates she will need 2600 L of air for the dive. Calculate the pressure to which this volume of air must be compressed in order to fit in to the air tank. Write you answer in atmospheres

Answer:

10.5 atm

Explanation:

Formula for Volume of a sphere is;

V = (4/3)πr³

r = 78/2 = 39 cm

V = (4/3)π(39)³

V = (4/3)*π*59319

V = 248475 cm³

Now, from conversions, 1000 cm³ = 1L

So,

V = 248475/1000

V = 248.5 L

This is the volume of the storage tank

If we assume that the 2600 L of air is measured at 1 atmosphere pressure, then we will obtain the following relationship:

From Boyles law,

P1 × V1 = P2 × V2

Thus;

(1 atm) × (2600 L) = (P2) × (248.5 L)

P2 = 2600/248.5

P2 = 10.463 atmospheres

Approximating to 3 significant figures is; P2 = 10.5 atm