Homework Help: Varying depths of water

1. Sep 8, 2006

dave2945

Hello everyone. Here is my problem:

At 25.1 meters below the surface of the sea (density is 1025 (kg)/m^3),
where the temp is 3.00 C, a diver exhales an air bubble that has a volume of 1.00 cm^3. If the surface temp of the sea is 15.00 C, what is the volume of the bubble just before it breaks the surface.

Here is what I got: (d=density)

pv=nrt under water P+dgh=p
PV=nrT surface so, (P+dgh)v=nrt and PV=nrT

The nr's cancel, so (PV/((P+dgh)(v)))=T/t
Simplifying, I get that V=((P+dgh)vT)/(Pt)

Only thing is, I don't have pressure at surface. I tried using 1.013X10^5 N/m^2 (1 atm) and got .174 m^3. And, I did remember to change to .01 meters from 1.00 cm^3. Answer seems reasonable but wrong. Any help would be appreciated.

2. Sep 8, 2006

Hootenanny

Staff Emeritus
Just a quick check, you know that 1.00 cm3 $\neq$ 0.01 m3 right?

3. Sep 8, 2006

dave2945

Oh yeah. It is 1.00X10^-6 m^3, right??

4. Sep 8, 2006

Hootenanny

Staff Emeritus
Yup, that's right.

5. Sep 8, 2006

dave2945

OK, I tried that, subbing 10^-6 m^3, got 1.74X10^-5 cubic meters and still not right. Hmmmm..

6. Sep 8, 2006

dave2945

Anyone have any ideas???

7. Sep 9, 2006

JMuse

I have a question about the equation you use for the pressure of the gas underwater. Shouldn't the pressure of the gas underwater be equal to the pressure of the water since they are both in equilibrium at that height; which is just "dgh," not "P + dgh."

8. Sep 9, 2006

Astronuc

Staff Emeritus
One must look at the 'absolute' pressure. At the surface of the water, the local or ambient pressure is 1 atm (~14.7 psia). As one descends in the water, the mass of water above contributes to pressure, and the local pressure in the water is given by Pa + $\rho$gh, where h is the depth of water, and $\rho$ is density.

When the air bubble is released, it is at same pressure as the water. Now there is also a difference in temperature which must also be considered for this problem. As the temperature of the bubble increases, it would also expand due to temperature, but the bubble is always at the same pressure as the water around it.

9. Sep 9, 2006

Astronuc

Staff Emeritus
Please show the work. Remember that the temperature scale in °C (Celsius) is a 'relative' scale, and one must convert to an absolute scale K, if one uses ratios.

T (K) = T (°C) + 273.15

10. Sep 10, 2006

dave2945

Oh, ok. I just screwed up by not converting to K's. Thank u much for the help Astronuc.