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.

Question

anonymous · Answer

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

anonymous · Answer

yes

anonymous · Answer

and how do i convert Celsius to kelvin

anonymous · Answer

K = C + 273

anonymous · Answer

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 · Answer

i think well have to use ideal gas law

anonymous · Answer

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 · Answer

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

anonymous · Answer

can you show me what to plug in

anonymous · Answer

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

anonymous · Answer

but what do i put in for density

anonymous · Answer

and is the g gravity 9.8

anonymous · Answer

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 · Answer

right right

anonymous · Answer

h would be 43.5

anonymous · Answer

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

anonymous · Answer

right

anonymous · Answer

p.s. your a genius man

anonymous · Answer

what do i put for nRT

anonymous · Answer

8.314

anonymous · Answer

for R. T must be in kelvin.

anonymous · Answer

how did you get that?

anonymous · Answer

The n cancels out. because it does not change.

anonymous · Answer

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

anonymous · Answer

oh ok

anonymous · Answer

help me on the other one