Thermodymanics dealing with pressure, temperauture, and constants

[name_ask17]

Homework Statement

A bubble of air, 0.010m^3 in volume , is formed at the bottom of a lake which is 30m deep and where the temoperature is 8 degrees c. The bubble risees to the surface, where the water temp is 26 deg c and where the pressure is atmospheric pressure. What is the volume of the bubble just as it reaches the surface?

Homework Equations

Im not sure how to attempt this problem but i used pv=nrt
r=8.31

The Attempt at a Solution

i know that the n and the R have to stay constant, so i attempted by saying 100000(atmospheric pressure)*(.01)=(n)*(8.31)*(26-8)
but when i do that, i don't understand what i am solving for
will you please tell me if i am headed in the correct direction to solve this problem? thanks in advance.

 

[Doc Al]

You want to compare conditions at the bottom of the lake to those at the top:
What's the pressure at the bottom?

Hint: You know that nR must be constant, thus PV/T = nR must also be constant.

(Make sure you measure temperature using the Kelvin scale.)

 

[name_ask17]

how do i find pressure at the bottom?
and am i attempting to use the right equation?

 

[Doc Al]

how do i find pressure at the bottom?

The pressure at the bottom will be greater due to the weight of the water. How does pressure increase with depth?

and am i attempting to use the right equation?

Yes, the ideal gas law is the correct equation. But make use of my hint.

 

[name_ask17]

im still confused on how to do this. the pressure at the bottom of the lake would be 294000 and at the top it would just be atmospheric pressure, which is 100000.
and i understand what you are saying in the hint but can you please explain to me how i will use that in the problem? i think i am missing an important concept to understand thsi problem

 

[Doc Al]

P₁v₁/t₁ = p₂v₂/t₂

 

[name_ask17]

when i do this, i get the answer of .09555, but the answer should be .0419. what am i doing wrong?
i did 294000*.010/8=100000v/26

 

[name_ask17]

i can't seem to see where i am going wrong

 

[gneill]

What lies above the water's surface? What's the pressure at the surface? How about a mm below the surface? 30m below?

 

[name_ask17]

What lies above the water's surface? What's the pressure at the surface? How about a mm below the surface? 30m below?

wouldnt the pressure at the surface just be air pressure (100000)
and 30m below the surface would be pgh=1000(9.8)(30)=294000?

 

[Doc Al]

and 30m below the surface would be pgh=1000(9.8)(30)=294000?

pgh is just the increase in pressure due to the water. Don't forget that the air also presses down on the water.

 

[name_ask17]

gneill, can you check above at the problem abd see what i am doing wrong? i have been working on this problem forever and i don't get it. please help me. thanks

 

[name_ask17]

doc al, i still don't understand what i am doing wrong

 

[name_ask17]

so it woulld be 294000 +100000?

 

[name_ask17]

OHHHH! i got it! Thank you so much DOC AL and GNEILL!

 

[Doc Al]

so it woulld be 294000 +100000?

Yes. The pressure at the bottom of the lake = atmospheric pressure + pgh.