

December 8, 2017 



How much does a bubble weigh? 



For the holiday season, and inspired by Aaron
Burden's wonderful photo of a frozen soap bubble, I have pulled out my physics
education to estimate the weight of a soap bubble.
First, what is the
volume of a spherical shell?
For a very thin shell, as we have here,
we can approximate the volume as the surface area times the thickness of the
film, so it is 4*pi*R^2*t. Thus a 1 cm diameter bubble shell with a 0.5 micron
thick film would have a volume of 1.6 x104 cubic centimeters. Since there are
no interference colors in the photo above, the bubble must be less than about
1/3 micron thick.
Film thickness
Of course the thickness
of the bubble film varies from the top to the bottom as the liquid runs down.
But when you see interference colors the film is typically less than half a
micron thick. As the bubble dries you can easily be 0.25 microns
thick.
Density Water weighs about 1 gram per cubic centimeter.
The other components in soap weigh about the same, so our the shell of our 1 cm
diameter bubble will weigh about 1.6x104 grams (160 micrograms).
Weight of the air inside At the beach the inside of the
bubble will contain air at about 1 atmosphere pressure, 1.2x103 grams/cubic cm
(at 20°C), up here in the mountains about 10% less. The volume of our 1
cm diameter bubble is 4/3*pi*R^3 = 0.52 cm^3. So the weight of air in our
1cm bubble is 0.52 * 0.0012 = 6.2x104 grams (620
micrograms).
Total So the total weight of the bubble is
6.2 +1.6 = 7.8 x 104 grams (780 micrograms), about one quarter soap film and
threequarters air. So it is no wonder that the bubble will float on the
breeze.
Helium If we fill our bubble with helium the weight
of the helium in the bubble will be a tiny 8.6*106 grams, so most of the
weight of the bubble will be soap film, and the bubble should soar, the bubble
will weigh about a quarter of the air it displaces.
Methane If
we fill our bubble with methane at 20°C, the gas will weigh 3.4x104 grams
(370 micrograms), and the soap film will weigh 1.6 x104 grams (160
micrograms), so the total would be about 5.3 x104 grams (530 micrograms),
still about 2/3 of the weight of the air it is displacing, and it will float
with an upward buoyancy of 90 micrograms.
Buoyancy Which
points out a principle that is sometimes misunderstood. Hydrogen has half the
weight per cubic meter of helium, but it doesn't have twice the buoyancy, which
is the weight of the air displaced minus the weight of the
gas.
Scaling
As the diameter of the bubble increases, the
weight of the shell will increase proportional to the square of the diameter,
and the weight of the gas inside will increase as the cube of the diameter.
This means that a bubble will be more buoyant the larger it is.
Diameter 
Weight of Air 
Weight of shell 
Weight of CH_{4} 
Total 
Buoyancy 
1 cm 
620 µg 
160 µg 
370µg 
530µg 
90 µg 
2 cm 
5026 µg 
628 µg 
3000 µg 
3628 
1400 µg 
4 cm 
40,200 µg 
2513 µg 
24,000 µg 
26,500 
13,700 µg 
Disclaimer: Information presented here is the opinion of the
author. No warranties regarding the correctness or value of this information
are implied or should be assumed. 
