Ideal Gas Expansion: Finding Depth of Tank

Click For Summary
SUMMARY

The discussion centers on calculating the depth of a water tank based on the expansion of a bubble that triples in volume as it rises. The relevant equation is the ideal gas law, represented as PV=nRT, and the relationship between pressures at different depths is established using P1V1=P2V2. The correct atmospheric pressure at the water's surface is 100 kPa, leading to the conclusion that the depth of the tank is 20 meters, not 30 meters as initially calculated. Misunderstandings regarding pressure units and the atmospheric pressure value were clarified during the discussion.

PREREQUISITES
  • Understanding of the ideal gas law (PV=nRT)
  • Knowledge of pressure units and atmospheric pressure (100 kPa)
  • Concept of hydrostatic pressure and its relation to depth in fluids
  • Ability to manipulate equations involving pressure and volume (P1V1=P2V2)
NEXT STEPS
  • Study hydrostatic pressure calculations in fluid mechanics
  • Learn about the relationship between pressure and depth in liquids
  • Explore the ideal gas law applications in real-world scenarios
  • Investigate the effects of temperature on gas behavior in closed systems
USEFUL FOR

Students studying physics or engineering, particularly those focusing on fluid mechanics and thermodynamics, as well as educators looking for practical examples of gas laws in action.

Tardis Traveller
Messages
5
Reaction score
0

Homework Statement


A bubble comes from the bottom of the tank of water to the surface and triples in its volume. If the temperature of the tank of water doesn't deppend on the depth what is the depth of the tank that the bubble was at?

Homework Equations


##PV=nRT##

The Attempt at a Solution


Since the temperature stays constant i guessed
##P_bV_b=P_uV_u##
##P_bV_b=P_u3V_b##
and i get 30m but the answer states 20m. What is wrong?
 
Physics news on Phys.org
What's the pressure at the surface of the water?
 
SteamKing said:
What's the pressure at the surface of the water?
The atmospheric pressure 1000 kg/m3
 
Tardis Traveller said:
The atmospheric pressure 1000 kg/m3
That's not right; it's not even wrong.

Pressure has units of force per unit area. 1000 kg/m3 is the density of fresh water (approximately).

You should look up what the value of a standard atmosphere is.
 
SteamKing said:
That's not right; it's not even wrong.

Pressure has units of force per unit area. 1000 kg/m3 is the density of fresh water (approximately).

You should look up what the value of a standard atmosphere is.
Oops, your absolutely right i gave you the density, its 100kPa actually at the surface
 
Tardis Traveller said:
Oops, your absolutely right i gave you the density, its 100kPa actually at the surface
You should draw a sketch to help you focus.

Since the top of the tank is presumably open to the atmosphere, the pressure at the water's surface will be atmospheric.

What's the pressure acting on the bubble when it is submerged and starts to rise?
 
P1V1=P2V2 is correct, of course. In order for V2 = 3*V1 it must be P2 = P1÷3
So, you know at depth X, P is 3 times atmospheric. Since you haven't shown any further work about how pressure increases with water depth, I'll stop here.
 

Similar threads

  • · Replies 2 ·
Replies
2
Views
2K
  • · Replies 2 ·
Replies
2
Views
2K
  • · Replies 2 ·
Replies
2
Views
3K
  • · Replies 5 ·
Replies
5
Views
3K
  • · Replies 2 ·
Replies
2
Views
2K
  • · Replies 9 ·
Replies
9
Views
2K
  • · Replies 3 ·
Replies
3
Views
10K
  • · Replies 3 ·
Replies
3
Views
1K
Replies
12
Views
2K
  • · Replies 25 ·
Replies
25
Views
3K