Question

A marine biologist is preparing a deep-sea submersible for a dive. The sub stores breathing air under high pressure in aspherical air tank that measures 73.0 cm wide.The biologist estimates she will need 8200. L of air for the dive. Calculate the pressure to which this volume of air must becompressed in order to fit into the air tank. Write your answer in atmospheres. Round your answer to 3 significant digits.0atm0.0XS ?EoloPEBH

Answer 1

To solve the problem we will assume the following:

1. Air behaves as an ideal gas during all the process.

2. The initial air equivalent to 8200L is at atmospheric pressure. It means 1 atm.

3. The temperature remains constant.

Taking into account the above, we can apply the Boyle-Marriote Law that relates the change in pressure and volume at constant temperature. The equation that we will use will be:

`P_1V_1=P_2V_2`

Where,

P1 is the atmospheric pressure. 1atm

V1 is the initial volume of air required, 8200L

P2 is the final pressure we want to find

V2 is the final volume, it means the volume of the spherical air tank. We will calculate this volume using the volume equation for a sphere:

`V_2=(4)/(3)\pi r^3`

r is the radius of the sphere, r=73cm/2=36.5cm

So, the volume of the spherical air tank will be:

`\begin{gathered} V_2=(4)/(3)\pi*(36.5cm)^3=20.4*10^4cm^3 \\ V_2=20.4*10^4cm^3*(1L)/(1000cm^3)=204L \end{gathered}`

No, we clear P2 from the first equation and replace known data:

`\begin{gathered} P_2=(P_1V_1)/(V_2) \\ P_2=(1atm*8200L)/(204L) \\ P_2=40.3atm \end{gathered}`

The pressure of the gas must be 40.3 atm

Answer: 40.3