Physics - Pressure

bonkysleuth SG

Water of depth 10 m exerts a pressure equal to atmospheric pressure. An air bubble rises to te surface of a lake which is 20 m deep. When the bubble reaches the surface, its volume is 6cm3. What was the volume of the air bubble at the bottom of the lake?

How do you solve this question?

jiaxing2 SG

p inversely proportional to v ( same temp)

p1v1=p2v2

at bottom pressure = 3 p (atm) compared to 1 atm at the top

thus V bottom = 6/3 = 2 cm3

Darkness_hacker99 SG

This question looked soooo familiar to me.... o.O As if someone asked this before...

Darkness_hacker99 SG

http://www.sgforums.com/forums/2297/topics/309235

bonkysleuth SG

In that post Darkness_hacker99 mentioned, eagle posted the solution as this:

at surface:
pressure, P1 = 1atm (atmospheric pressure equivalent to 10m of water), V1 = 6cm³

at bottom of lake:
pressure, P2 = 3 atm (atmospheric pressure + 20m of water), V2 = unknown

Using Bolye's Law, P1V1 = P2V2

V2 = 2cm³

^{But the thing
is, I haven't learnt about this Boyle's Law thing. Nor have I heard
of it. My brother tried to teach me using this method but he told
me not to attempt this question since I havent been taught about
the law before. why is P1 = 1 atm and P2 = 3 atm?}

eagle SG

the equation means this

original volume multiplied by original pressure equals to final volume multiplied by final pressure

or vice versa

Do you understand the above part first? Understand then we proceed to the next step

Darkness_hacker99 SG

P1V1 = P2V2

This formula is taught in your syllabus under the chapter Pressure:Pressure changes.

UltimaOnline SG

This qn also appears similar to my "Loch Ness Monster" qn, although mine is surely a lot more interesting!

See the most recent at the bottom of my "'O'&'A' Lvls Balancing Equation & Stoichiometry Practice Qns" stickied thread :

http://www.sgforums.com/forums/2297/topics/320107

bonkysleuth SG

the equation means this

original volume multiplied by original pressure equals to final volume multiplied by final pressure

or vice versa

Do you understand the above part first? Understand then we proceed to the next step

So how do you get 1 atm and 3atm? I don't understand this because I havent learnt this before. But I am interested to find out.

bonkysleuth SG

Oh yea and there's this question from the Ten Years series.

2 cubes are made form the same material. one cube has sides that are twice as long as the other. standing on one face, the small cube exerts a pressure p = w/a, where a is the area of the face. what is the pressure exerted by the larger cube standing on ONE of its faces?

I got this answer as 4p but the answer booklet writes 2p. can anyone explain?

eagle SG

So how do you get 1 atm and 3atm? I don't understand this because I havent learnt this before. But I am interested to find out.

1 atm is pressure at the water surface. That's because it is the air pressure.

and at depth of 20m, the total pressure comes from 1atm (at water surface) + 20m of water. Since 10m of water = 1atm, that means total pressure = 3atm

eagle SG

Oh yea and there's this question from the Ten Years series.

I got this answer as 4p but the answer booklet writes 2p. can anyone explain?

if the small cube has face area a, the large cube has area 4a.

Also, if the small cube has weight w, the large cube has weight 8w, since weight is proportional to volume (same material means same density).

Thus, pressure exerted by larger cube = 8w / 4a = 2 w/a = 2p

bonkysleuth SG

if the small cube has face area a, the large cube has area 4a.

Also, if the small cube has weight w, the large cube has weight 8w, since weight is proportional to volume (same material means same density).

Thus, pressure exerted by larger cube = 8w / 4a = 2 w/a = 2p

Thanks. But I somehow dont get this part:

if the small cube has weight w, the large cube has weight 8w, since weight is proportional to volume (same material means same density).

Thus, pressure exerted by larger cube = 8w / 4a = 2 w/a = 2p

i still dont know why weight is proportional to volume. havent heard of that before.

eagle SG

Thanks. But I somehow dont get this part:

if the small cube has weight w, the large cube has weight 8w, since weight is proportional to volume (same material means same density).

Thus, pressure exerted by larger cube = 8w / 4a = 2 w/a = 2p

i still dont know why weight is proportional to volume. havent heard of that before.

Ok.

One of the ways to see it is:

Weight is proportional to mass.
Mass is proportional to volume (since mass = density * volume)

Therefore, Weight is proportional to volume.