Volume of a bubble rising in a lake

  • Thread starter Nathanael
  • Start date
  • #1
Nathanael
Homework Helper
1,650
239

Homework Statement


An air bubble of volume 20 cm^3 is at the bottom of a lake 40 m deep, where the temperature is 4.0°C. The bubble rises to the surface, which is at a temperature of 20°C. Take the temperature of the bubble’s air to be the same as that of the surrounding water. Just as the bubble reaches the surface, what is its volume?


Homework Equations


[itex]PV=kT[/itex]
[itex]ΔP=40ρg[/itex]

The Attempt at a Solution


I don't understand how the answer doesn't depend on the atmospheric pressure. If the atmospheric pressure were greater, then wouldn't the change in volume be smaller?
 

Answers and Replies

  • #3
Nathanael
Homework Helper
1,650
239
Right... But that only gives you the difference in pressure. Isn't the atmospheric pressure still relevant?
 
  • #4
Bystander
Science Advisor
Homework Helper
Gold Member
5,203
1,225
Yes. What are the initial and final pressures? Don't feel that adding the "stack" is an unjustified ad hoc step to take. Pressure is the result of the sum of all masses above a certain point x "g."
 
  • #5
Nathanael
Homework Helper
1,650
239
Initial pressure would be [itex]P_{atm}+40ρg[/itex] (where ρ is the density of water) and the final pressure would be [itex]P_{atm}[/itex]

This gives me a final volume of [itex]V_f=V_i(\frac{T_f}{T_i})(\frac{P_{atm}+40ρg}{P_{atm}})[/itex]
 
  • #6
Bystander
Science Advisor
Homework Helper
Gold Member
5,203
1,225
That's the way to play it. Hopefully whoever wrote the problem remembered it the same way.
 

Related Threads on Volume of a bubble rising in a lake

  • Last Post
Replies
8
Views
45K
Replies
28
Views
22K
Replies
25
Views
711
  • Last Post
Replies
2
Views
4K
  • Last Post
Replies
1
Views
3K
Replies
8
Views
4K
  • Last Post
Replies
3
Views
2K
Top