## anonymous 4 years ago 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.

1. anonymous

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

2. anonymous

yes

3. anonymous

and how do i convert Celsius to kelvin

4. anonymous

K = C + 273

5. 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.

6. anonymous

i think well have to use ideal gas law

7. 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.

8. anonymous

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

9. anonymous

can you show me what to plug in

10. anonymous

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

11. anonymous

but what do i put in for density

12. anonymous

and is the g gravity 9.8

13. 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.

14. anonymous

right right

15. anonymous

h would be 43.5

16. anonymous

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

17. anonymous

right

18. anonymous

p.s. your a genius man

19. anonymous

what do i put for nRT

20. anonymous

8.314

21. anonymous

for R. T must be in kelvin.

22. anonymous

how did you get that?

23. anonymous

The n cancels out. because it does not change.

24. anonymous
25. anonymous

oh ok

26. anonymous

help me on the other one