An air bubble at the bottom of a lake 43.5m deep has a volume of 1.00cm/cubed. If the temperature at the bottom is 5.5 degrees celcius and at the top 21.0 degrees celcius, what is the volume of the bubble just before it reaches the surface.

- anonymous

- schrodinger

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- anonymous

Are we ignoring pressure effects here? These are more substantial than temperature effects.

- anonymous

yes

- anonymous

and how do i convert Celsius to kelvin

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## More answers

- anonymous

K = C + 273

- anonymous

Do you have the volumetric coefficient of thermal expansion for air?
Otherwise, we will have to use the ideal gas law which requires we make some assumptions.

- anonymous

i think well have to use ideal gas law

- anonymous

Then pressure is definitely being accounted for.
First, let's find the pressure at the bottom of the lake. \[P_b = \rho g h + P_{atm}\]where \(P_{atm} = 101 kPa = 1 atm = 14.7 psi\)
Now, from ideal gas law, \[\left [ PV \over n RT \right ]_{bottom} = \left [ PV \over nRT \right ] _{t o p}\]n remains constant so it cancels out. We just calculated the pressure at the bottom, the pressure at the top will be equal to \(P_{atm}\). We know the volume at the bottom and the two temperatures. Leaving the volume at the top the only unknown.

- anonymous

what do i plug in for pressure at the bottom of the lake

- anonymous

can you show me what to plug in

- anonymous

You have to solve for it
It is\[P_{Bottom} = \rho gh + P_{atm}\]

- anonymous

but what do i put in for density

- anonymous

and is the g gravity 9.8

- anonymous

Depends on what units you want. Looks like we are in SI, so density would be 1000 kg/m^3 for water, and g is definitely 9.8.

- anonymous

right right

- anonymous

h would be 43.5

- anonymous

Indeed. The height of the water column above the bubble.

- anonymous

right

- anonymous

p.s. your a genius man

- anonymous

what do i put for nRT

- anonymous

8.314

- anonymous

for R. T must be in kelvin.

- anonymous

how did you get that?

- anonymous

The n cancels out. because it does not change.

- anonymous

http://en.wikipedia.org/wiki/Gas_constant

- anonymous

oh ok

- anonymous

help me on the other one

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