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## 16 August 2012

### Lab Idea from Jaime Skiba: Volume of a Rising Air Bubble

 rising bubbles from alaska-in-pictures.com
New York physics teacher Jaime Skiba posed a novel (to me) idea for a thermodynamics laboratory exercise.  She teaches chemistry as well as physics, so she and her colleagues are even more heavily invested in teaching gas laws than we physicists.  Her colleague, she says, long ago took excellent picture s of a gas bubble rising in a long column of liquid.  The diameter of the bubble increases as the bubble rises, because the pressure decreases while the temperature remains essentially constant.

Jaime proposes having students create some rising bubbles in a long, transparent graduated cylinders just by plunging an air hose to the bottom.  Smartphones can created video of the rising bubble; then (if you have the knowing of the software) the frames can be analyzed on a computer.  The diameter of the bubble in a frame can be measured by knowing the diameter of the cylinder itself, and scaling proportionally.

Students would make a graph of bubble diameter d on the vertical axis vs. depth h on the horizontal axis.  A straight line plot can be created by plotting the diameter cubed vs. the reciprocal of the depth.  Why?

Start with the ideal gas law, PV = nRT.  Pressure in the column is ρgh, where ρ is the density of the water.   The volume is the volume of a sphere.  By solving for the cube of diameter, I get

Using this equation and the slope of the d-cubed vs. 1/h graph, you could solve for the number of moles in the gas bubble.

1. I like how you brought in the moles - I'm teaching all physics this year, I wasn't sure how in depth to go with the ideal gas law as this is my first year with Physics B. I will share this with the AP chem and physics teachers at my school. If teaching an analytical chem class all students could measure different bubbles that have gone through the same column using carbon dioxide bubbles in an open dish barometer type apparatus and then titrate to see how the results match up.

-Jaime

2. In my view, you would be getting a lot of error in the measurements. The likely sources are:
1. Bubbles do not remain spherical as they rise in any liquid (if they are not very small )
2. Pressure would not be "ρgh" inside the bubble at any height "h" because the moving bubble changes the pressure around it. Pressure would increase inside the bubble due to the surface tension that compresses the bubble as well as the incoming flow ahead of the bubble.

First error can be accounted for by taking the actual shape into consideration or by experimenting with a small enough bubble so that it remains spherical - but the second error will increase because of this.

So if you get an error in number of moles, don't think that you have found something new.