Physics - Pressure

• bonkysleuth

  19 Jul 08, 22:04

  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

  19 Jul 08, 22:33

  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

  19 Jul 08, 22:41

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

• Darkness_hacker99

  19 Jul 08, 23:01

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

• bonkysleuth

  19 Jul 08, 23:22

  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

  20 Jul 08, 00:12

  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

  20 Jul 08, 00:54

  P1V1 = P2V2
  
  This formula is taught in your syllabus under the chapter Pressure:Pressure changes.

• UltimaOnline

  20 Jul 08, 16:21

  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

  21 Jul 08, 16:36

  Originally posted by eagle:

  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

  21 Jul 08, 16:38

  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

  21 Jul 08, 16:59

  Originally posted by bonkysleuth:

  
  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

  21 Jul 08, 17:01

  Originally posted by bonkysleuth:

  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?

  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

  24 Jul 08, 21:07

  Originally posted by eagle:

  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

  25 Jul 08, 00:06

  Originally posted by bonkysleuth:

  
  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.