Change in a marine mammal's lung volume when diving to 200 meters

[crystal1001]

Homework Statement

A marine mammal holds its breath and dives 200 m below the sea surface, where the total pressure is 2.061MPa. The volume of the mammal’s lungs when fully inflated at sea surface (air pressure = 101.3kPa) is 7 L. Assuming that the mammal’s core temperature remains constant at 310K, what will the volume of its lungs be when it reaches a depth of 200 m?
Answer: 0.344 litre

Relevant Equations

v^2=P1V1/P2

I attempt the solution on the attachment. The answer is 0.344 litre. Do I change 7L to m, so it is 0.007 cubic meters

 

[haruspex]

Homework Statement: A marine mammal holds its breath and dives 200 m below the sea surface, where the total pressure is 2.061MPa. The volume of the mammal’s lungs when fully inflated at sea surface (air pressure = 101.3kPa) is 7 L. Assuming that the mammal’s core temperature remains constant at 310K, what will the volume of its lungs be when it reaches a depth of 200 m?
Answer: 0.344 litre
Homework Equations: v^2=P1V1/P2

I attempt the solution on the attachment. The answer is 0.344 litre. Do I change 7L to m, so it is 0.007 cubic meters

I do not understand your difficulty. You seem to have the answer. Are you saying 0.344L is wrong?
Why would you want to convert to m^3?

PS. In future, please use more meaningful thread titles.

 

[Cutter Ketch]

In saying the answer is 0.344 l I believe you are saying that you have been given a correct answer but need to figure out how that was calculated, correct?

And I believe your concern is that you got 344 instead of 0.344, correct? I think your only problem is that you ignored that one pressure was in kPa and the other is in MPa. That’s why you are off by 3 orders of magnitude. Put the pressures in the same units.

 

[Tom.G]

Could you show how you derived this equation? I think there is a problem there.

Homework Equations: v^2=P1V1/P2

 

[haruspex]

And I believe your concern is that you got 344 instead of 0.344

Ah! The image was so faint I assumed the period was just invisible.

 

[haruspex]

Could you show how you derived this equation? I think there is a problem there.

Homework Equations: v^2=P1V1/P2

Clearly it is a typo for v2=P1V1/P2 (which is what the OP used).

 

[Cutter Ketch]

Could you show how you derived this equation? I think there is a problem there.

Homework Equations: v^2=P1V1/P2

I think that is just a typo. It is correct in the attached image