Pressure in Liquids: How Does It Affect Volume?

AI Thread Summary
Atmospheric pressure significantly affects the volume of liquids, as demonstrated by the example of an air bubble in a lake. At the surface, the bubble has a volume of 6.0 cm³, which decreases to 2 cm³ at the bottom due to increased pressure, as explained by Boyle's Law (P1V1 = P2V2). The discussion clarifies the difference between gauge pressure and absolute pressure, noting that at a depth of 10 m, the absolute pressure is 2 atmospheres, and at 20 m, it is 3 atmospheres. Understanding these pressure changes is crucial for calculating volume changes in liquids. The application of Boyle's Law confirms the volume reduction of the air bubble under pressure.
Muhammad Danish
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Homework Statement


upload_2018-4-16_18-13-3.png


Homework Equations


How does atmospheric pressure affects the volume of liquid? What will be the volume of the air bubble at the bottom of the lake?

The Attempt at a Solution


At the surface, the volume is 6.0cm3. So at the bottom, more pressure will be exerted so it will be halved to 3cm3. Please explain the concept, that was just a rough idea.

Thanks.
(regards)
 

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The problem says, "Water of depth 10 m exerts a pressure equal to atmospheric pressure". Is this pressure an absolute pressure or a gauge pressure? In other words, if you had a lake that is 10 m deep, what would be the gauge pressure at the bottom of the lake? What would be the absolute pressure at the bottom?
 
TSny said:
The problem says, "Water of depth 10 m exerts a pressure equal to atmospheric pressure". Is this pressure an absolute pressure or a gauge pressure? In other words, if you had a lake that is 10 m deep, what would be the gauge pressure at the bottom of the lake? What would be the absolute pressure at the bottom?
I am not familiar with the terms ''Gauge Pressure'' and ''Absolute Pressure''. Can you make it more simple..
 
Gauge pressure is pressure measured relative to atmospheric pressure. Many pressure gauges measure gauge pressure (such as a gauge for measuring pressure in a tire). Absolute pressure is the "true" or "actual" pressure. A gauge pressure of 0 corresponds to an absolute pressure of 1 atmosphere. A gauge pressure of 0.5 atmospheres corresponds to an absolute pressure of 1.5 atmospheres.

The important thing in this problem is to know what the absolute pressure is at the top of the lake and also at the bottom of the lake.

If the lake is 20 m deep, what is the (absolute) pressure at the top of the lake? What is the (absolute) pressure at the bottom of the lake?
 
TSny said:
Gauge pressure is pressure measured relative to atmospheric pressure. Many pressure gauges measure gauge pressure (such as a gauge for measuring pressure in a tire). Absolute pressure is the "true" or "actual" pressure. A gauge pressure of 0 corresponds to an absolute pressure of 1 atmosphere. A gauge pressure of 0.5 atmospheres corresponds to an absolute pressure of 1.5 atmospheres.

The important thing in this problem is to know what the absolute pressure is at the top of the lake and also at the bottom of the lake.

If the lake is 20 m deep, what is the (absolute) pressure at the top of the lake? What is the (absolute) pressure at the bottom of the lake?
Sorry, I do not understand..
 
Forget the concept of gauge pressure. I didn't know that you are not familiar with it. It is not necessary for this problem.

You have to interpret carefully the meaning of the statement "Water at a depth of 10 m exerts a pressure of 1 atmosphere". This means that for every 10 m deeper that you go down in water, the pressure increases by 1 atmosphere.

If we have a lake of depth 20 m, can you answer the following?

(1) What is the pressure at the top of the lake?
(2) What is the pressure at a depth of 10 m in the lake?
(3) What is the pressure at a depth of 20 m (at the bottom of the lake)?
 
TSny said:
Forget the concept of gauge pressure. I didn't know that you are not familiar with it. It is not necessary for this problem.

You have to interpret carefully the meaning of the statement "Water at a depth of 10 m exerts a pressure of 1 atmosphere". This means that for every 10 m deeper that you go down in water, the pressure increases by 1 atmosphere.

If we have a lake of depth 20 m, can you answer the following?

(1) What is the pressure at the top of the lake?
(2) What is the pressure at a depth of 10 m in the lake?
(3) What is the pressure at a depth of 20 m (at the bottom of the lake)?
1) 0 atmosphere
2) 1 atmosphere
3) 2 atmospheres
Am I right?
 
Muhammad Danish said:
1) 0 atmosphere
2) 1 atmosphere
3) 2 atmospheres
Am I right?
No. You have forgotten that the surface of the lake is exposed to the atmosphere. So, the pressure at the surface is not 0.
 
TSny said:
No. You have forgotten that the surface of the lake is exposed to the atmosphere. So, the pressure at the surface is not 0.
It should be 1 too?
 
  • #10
Muhammad Danish said:
It should be 1 too?
Right. So, what are the answers to the three questions of post #8?
 
  • #11
TSny said:
Right. So, what are the answers to the three questions of post #8?
1) 1 atmosphere
2) 2 atmospheres
3) 3 atmospheres
 
  • #12
Muhammad Danish said:
1) 1 atmosphere
2) 2 atmospheres
3) 3 atmospheres
Yes.
 
  • #13
TSny said:
Yes.
Alright, Now how will we connect these pressures with volumes?
 
  • #14
Have you studied the ideal gas law?
 
  • #15
use Boyle's law : P1V1 = P2V2
 
  • #16
TSny said:
Have you studied the ideal gas law?
I have studied P1V1 = P2V2
 
  • #17
Muhammad Danish said:
I have studied P1V1 = P2V2
OK. That's a special case of the ideal gas law when the temperatures in states 1 and 2 are the same. The equation P1V1 = P2V2 is called "Boyle's law" as mentioned by @patric44

Can you use Boyle's law to get the answer?
 
  • #18
TSny said:
OK. That's a special case of the ideal gas law when the temperatures in states 1 and 2 are the same. The equation P1V1 = P2V2 is called "Boyle's law" as mentioned by @patric44
By using the Boyle's Law, the answer is 2 cm3. Is it correct?
 
  • #19
Muhammad Danish said:
By using the Boyle's Law, the answer is 2 cm3. Is it correct?
Yes.
 
  • #20
TSny said:
Yes.
Thanks a lot for helping me!
 
  • #21
patric44 said:
use Boyle's law : P1V1 = P2V2
Thanks.
 

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