Question

Submarines need to be extremely strong to withstand the extremely high pressure of water pushing down on them. An experimental research submarine with a volume of 5,000 liters has an internal pressure of 1.6 atm. If the pressure of the ocean breaks the submarine forming a bubble with a pressure of 155 atm pushing on it, how big will that bubble be?mm

Answer 1

Answer:

• The diameter of the bubble would be about 400mm

Explanation:

This problem is solved using Boyle's law because you assume a fixed amount (number of moles) of air and that the temperature remains constant:

       $PV=constant\\\\P_1V_1=P_2V_2$

Where:

• P₁ = 1.6 atm
• V₁ = 5,000 liters
• P₂ = 155 atm
• V₂ = unknown

Substitute and solve for V₂:

       $V_2=\dfrac{1.6atm\times 5,000liters}{155atm}\\\\\\V_2=52liters$

Since the number 5,000 has one significant figure, you must round your answer to one significant figure. That is 50 liters.

Now, you must calcualte the diameter of the bubble, assuming the shape is a sphere:

Remember that 50 liters = 50dm³.

     $Volume=\dfrac{4}{3}\pi\ (radius)^3$

    $50dm^3=\dfrac{4}{3}\pi (radius)^3\\\\radius = 2dm$

The diameter is twice the diameter = 4 dm = 40cm = 400mm