||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 x10-4 cubic centimeters. Since there are
no interference colors in the photo above, the bubble must be less than about
1/3 micron thick.
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
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 1.6x10-4 grams (160 micrograms).
Weight of the air inside
At the beach the inside of the
bubble will contain air at about 1 atmosphere pressure, 1.2x10-3 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 = 6.2x10-4 grams (620
So the total weight of the bubble is
6.2 +1.6 = 7.8 x 10-4 grams (780 micrograms), about one quarter soap film and
three-quarters air. So it is no wonder that the bubble will float on the
HeliumIf we fill our bubble with helium the weight of
the helium in the bubble will be a tiny 8.6*10-6 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.
fill our bubble with methane at 20°C, the gas will weigh 3.4x10-4 grams
(370 micrograms), and the soap film will weigh 1.6 x10-4 grams (160
micrograms), so the total would be about 5.3 x10-4 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.
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
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.
||Weight of Air
||Weight of shell
||Weight of CH4
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.