Water of depth 10 m exerts a pressure equal to the atmospheric pressure. An air bubble rises to the surface of the lake which is 20 m deep. When the bubble reaches the surface, its volume is 6 cm3.
What was the volume of the air bubble at the bottom of the lake?
2006-09-06 00:21:00 · 6 answers · asked by unquenchablethirst 2 in Science & Mathematics ➔ Physics
Oh yes, working please?
I really appreciate all your help.
2006-09-06 00:21:31 · update #1
we can use the formula
P(1) * V(1) = P(2) * V(2) (1=initial; 2=final)
3P * V(1) = P * 6 (Let P be the atm pressure, pressure at 20m is thrice the atm pressure)
therefore, V(1) = 2 cm3 (dividing both side by P and 3)
therefore at the bottom of the lake volume was 2 cm3
2006-09-06 00:35:02 · answer #1 · answered by muggle_puff 2 · 1⤊ 0⤋
Answer: 2cm3.
Letting Atmospheric pressure be P:
At the surface, atmospheric pressure is P.
water of depth 20 m means an additional 2 atmospheric pressure.
So it makes it 3P.
Boyle's Law states that the product of the volume and pressure of a fixed quantity of an ideal gas is constant, given constant temperature.
Formula: P1V1 = P2V2
Let volume of bubble at bottom of lake be V
3P x V = P x 6
=> V = 2
Therefore, volume of the air bubble at the bottom of the lake is 2cm3.
2006-09-06 01:55:57 · answer #2 · answered by Wonderous 2 · 0⤊ 0⤋
Prince_1993 is wrong, because at the bottom of the lake the pressure is 2 atmospheres of water plus one atmosphere at the surface, making 3 atmospheres altogether. The correct answer is 2 cm3, like poisoned_flute and klwh_88 said.
2006-09-06 01:46:39 · answer #3 · answered by Anonymous · 0⤊ 0⤋
Assuming your statement that 10m of water exerts a pressure equal to atmospheric pressure is true,
Pressure at bottom of lake = 3x Pressure at lake surface
Also, pV = constant (Boyle's Law)
Therefore, 3v = 1x6 where v is the volume of the bubble at bottom of lake.
This would give v = 2cm3
2006-09-06 00:38:33 · answer #4 · answered by klwh_88 2 · 1⤊ 0⤋
THE ANSWER TO THIS QUESTION IS 3cm3.
DERIVATION:
10m OF WATER = 1 ATMOSPHERIC PRESSURE
THEREFORE 20m OF WATER=2ATMOSPHERIC PRESSURE.
VOLUME OF THE BUBBLE AT THE SURFACE=VOLUME OF THE BUBBLE AT ATMOSPHERIC PRESSURE=1ATMOSPHERE
VOLUME OF THE BUBBLE AT 20m DEPTH=VOLUME OF THE BUBBLE AT 2ATMOSPHERIC PRESSURE.
LET THIS VALUE BE SOME x.
1ATMOSPHERICPRESSURE=6cm3
2ATMOSPHERICPRESSURE=x
PRESSURE IS INVERSELY PROPORTIONAL TO VOLUME.
THEREFORE x=1X6/2=3cm3.
2006-09-06 00:46:53 · answer #5 · answered by Anonymous · 0⤊ 1⤋
prince_1993 is correct.The bubble travel 20m of water so pressure difference is only 20m. Thus answer should be 3cm3.
2006-09-06 03:10:14 · answer #6 · answered by dwarf 3 · 0⤊ 0⤋