# Air bubble in water at 50m

1. May 16, 2009

### soopo

1. The problem statement, all variables and given/known data
The problem is at
http://dl.getdropbox.com/u/175564/volumePressureTemperature.JPG [Broken]

2. Relevant equations
I know the equation for ideal gases
pV = nRT
and
the definition of pressure
p = F / A

3. The attempt at a solution

The change in T is 10.
V_i = 1 cm^3

We need to first consider how the change in Temperature affects
the depth at which the bubble is.
It will goes up because the volume of the bubble increases.

The increase in Volume causes the boyonce force to increase.
Thus, the net force in f direction is zero at both depths:
F_boyonce - F_gravity = 0
g( m_Water - m_airBubble ) = 0

There is a linear relation between p and T if we assume the
situation for ideal gases.

I have apparently ignored some critical part.
It seems that the ideal Gas equation is not valid here.
The right answer is 6.2cm^3 that is (f).

Last edited by a moderator: May 4, 2017
2. May 16, 2009

### Staff: Mentor

Sure it is--it's all you need for this problem. How does the pressure change? The temperature? Use the ideal gas law to determine how the volume changes. (Set up ratios.)

3. May 16, 2009

### soopo

I have the following

V1 / V2 = $$\frac { T1 / P1 } { T2 / P2}$$

V1 / V2 = $$\frac {290(p1 + 5atm)} {p1 * 300}$$
= 290/300 + 1450/(P1 * 300)

The problem is now P1 which is the initial pressure.
It seems that we need to approximate it, since we do not know it.

4. May 16, 2009

### Staff: Mentor

P1V1/T1 = P2V2/T2

You should know it. What's the pressure at the surface?

5. May 16, 2009

### soopo

It is one atm :)

I get the following result
V1 / V2 = 6 * 290/300
= 5.8

whrere 290 kelvins is 17 celcius and 300 kelvins is 27 celcius.

Taking inverse

V2 / V1 = 0.17
where V2 is the volume at the surface.

Both answers seem to be wrong: I cannot get 6.2.
I have likely ignored some small volume.

6. May 16, 2009

### LowlyPion

Are you sure it's not 6*300/290 ?

7. May 16, 2009

### Staff: Mentor

Good.

Once again, you're flipping things around somehow.

(P1V1)/T1 = (P2V2)/T2

Then solve for V1.

8. May 16, 2009

### soopo

I finally got the right answer.

V1 = P2 V2 T1 / T2 P1

= 6 * 30 / 29
= 6.2