How Many Breaths Can a Diver Take at 25 Meters Depth?

[Syrus]

Homework Statement

A typical diver inhales 0.500 liters of air per breath and carries a 20. L breathing tank containing air at a pressure of 300. bar. As she dives deeper, the pressure increases by 1 bar for every 10.08 m. How many breaths can the diver take from this tank at a depth of 25 m? Assume that the temperature remains constant.

Homework Equations

PV=nRT, T is const.

The Attempt at a Solution

We worked this problem in calss toward the end of the period today, but I am still a bit confused by some of the reasoning. In calculating the final volume of the tank (at 25 m), the initial pressure and volume of the TANK are used, yet the final pressure used is that of the surroundings (i.e. 25 m * 1 bar/10.08 m). I am just looking for an explanation of why this may be carried out as so.

 

[dacruick]

Basically you have 20L of gas at 300 bar.

The question wants to know how many litres of gas you have at 25 m * 1 bar/10.08 m

Simply because, regardless of the pressure, the diver needs 0.500L. So on the surface, when there is lower pressure, 0.500L contains less oxygen than it does at a higher pressure.

Let me know if I'm not explaining this properly.

EDIT: So if you have 20L at 300 bar, and you want to figure out how many Litres you have at 50 bar, then you would do 20 * 300 / 50. Which would be 120.

EDIT2: Maybe I'm totally missing what your question is. The reason the tank pressure is used initally, and the underwater pressure is used finally, is because a diver will need to know how many breaths they have at the underwater pressure. If you then said that the diver on average takes 1 breath a second, then you would be able to calculate how much time the diver has underwater.