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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.

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  1. anonymous
    • 4 years ago
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    Are we ignoring pressure effects here? These are more substantial than temperature effects.

  2. anonymous
    • 4 years ago
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    yes

  3. anonymous
    • 4 years ago
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    and how do i convert Celsius to kelvin

  4. anonymous
    • 4 years ago
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    K = C + 273

  5. anonymous
    • 4 years ago
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    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
    • 4 years ago
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    i think well have to use ideal gas law

  7. anonymous
    • 4 years ago
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    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
    • 4 years ago
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    what do i plug in for pressure at the bottom of the lake

  9. anonymous
    • 4 years ago
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    can you show me what to plug in

  10. anonymous
    • 4 years ago
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    You have to solve for it It is\[P_{Bottom} = \rho gh + P_{atm}\]

  11. anonymous
    • 4 years ago
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    but what do i put in for density

  12. anonymous
    • 4 years ago
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    and is the g gravity 9.8

  13. anonymous
    • 4 years ago
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    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
    • 4 years ago
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    right right

  15. anonymous
    • 4 years ago
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    h would be 43.5

  16. anonymous
    • 4 years ago
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    Indeed. The height of the water column above the bubble.

  17. anonymous
    • 4 years ago
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    right

  18. anonymous
    • 4 years ago
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    p.s. your a genius man

  19. anonymous
    • 4 years ago
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    what do i put for nRT

  20. anonymous
    • 4 years ago
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    8.314

  21. anonymous
    • 4 years ago
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    for R. T must be in kelvin.

  22. anonymous
    • 4 years ago
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    how did you get that?

  23. anonymous
    • 4 years ago
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    The n cancels out. because it does not change.

  24. anonymous
    • 4 years ago
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    http://en.wikipedia.org/wiki/Gas_constant

  25. anonymous
    • 4 years ago
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    oh ok

  26. anonymous
    • 4 years ago
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    help me on the other one

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