Nuts & Volts

ties can drop to only a few meters and
the dirt will sandblast astronaut’s
visors. So to safely launch a balloon
during a dust storm, astronauts will
have to fill the balloon inside of a
structure, like a shed. After they finish
filling the balloon, they’ll carry it
outside and release it. This is the same
way the National Weather Service fills
and launches their radiosondes.
The Mars Pathfinder, which
landed on Mars in July 1997, carried a
set of wind socks on its ASI/MET
mast. Pathfinder’s windsock data
indicated that the Martian winds are
at their strongest from morning to
noon and weakest in the late
afternoon and early evening.
So it appears astronauts can fill
and launch weather balloons on Mars.
It will be easier if they wait until after
noon local time to fill the balloon. But
if they want to launch during a dust
storm, they’ll need to use a filling shed.
THE COMPOSITION
OF THE MARTIAN
ATMOSPHERE
Let’s assume our astronauts want
to launch a four pound (1,816 grams)
payload and 6.6 pound (3,000 grams)
weather balloon. Mars has a surface
gravity that’s 38% of Earth’s gravity.
Therefore, on Mars, the payload will
only weigh 1.5 pounds and the balloon
2.5 pounds. For our weather balloon to
launch this payload, it must contain
enough helium to displace at least four
pounds of Martian atmosphere (the
weight of the payload and balloon).
Because gravity affects the weight
of air and the payload alike, we won’t
calculate weights on Mars, but just
use mass. So in this case, the balloon
must displace an atmospheric mass
of at least 4,812 grams before the
balloon can begin lifting the payload.
An Avogadro’s number of gas molecules
at standard temperature and
pressure (STP) occupies a volume of
22.4 liters and has a mass that is equal
to the gas’ atomic weight. Did you get
all of that I guess I should explain a
few things about that sentence.
Avogadro’s number is 6.022 x 10 23
and it’s the number of molecules in one
mole of any chemical. One mole of a
chemical is an amount of that chemical
that has a weight in grams that’s equal
to its atomic mass. So one mole of
hydrogen gas weighs two grams, occupies
a volume of 22.4 liters at STP, and
contains 6.022 x 10 23 molecules
(remember that hydrogen gas is diatomic,
or contains two hydrogen atoms).
Standard temperature and pressure
is a temperature of 0 degrees C
(or 273 Kelvins) and a pressure of one
atmosphere (1,013 mb). A Kelvin is
equal to a degree Celsius. The only
difference between them is that the
Kelvin temperature scale begins at
-273 degrees Celsius, or the temperature
of absolute zero, while the
Celsius scale begins at the freezing
point of pure water. The Kelvin temperature
scale doesn’t use the word
“degrees” like Fahrenheit or Celsius.
So please say the temperature is 273
Kelvins and not 273 degrees Kelvin.
The Martian atmosphere is 95%
CO 2 , 3% N 2 , and 2% is trace gases.
We’ll treat the Martian atmosphere as
if it were pure carbon dioxide since
the nitrogen and other trace gases
only affect the density of the Martian
atmosphere by a small amount. Since
the chemical formula of carbon dioxide
is CO 2 , its atomic mass is equal to
the atomic mass of one carbon atom
plus two oxygen atoms. By ignoring
isotopes, I calculate the mass of a carbon
dioxide molecule to be (1 x 12) +
(2 x 16), or 44 atomic mass units.
So an atmosphere of pure carbon
dioxide has a mass of 44 grams per
22.4 liters at STP. Helium has a mass
of four grams per 22.4 liters at STP, so
22.4 liters of helium will displace 40
grams of carbon dioxide at STP.
However, the air temperature at the
Martian surface is -14 degrees C (259
K) and the pressure is seven millibars.
So we must adjust the density of the
carbon dioxide atmosphere on Mars.
You probably learned in your high
school chemistry class that decreasing
the temperature of a fixed amount
of gas causes it to contract in volume
and that decreasing the air pressure
acting on it causes it to expand in volume.
The equation used to calculate
the volume of a gas outside of STP is:
V f = V i X (T f /273) X (1013/P f )
where
V f is the final volume
V i is the initial volume
T f is the final temperature
P f is the final pressure
NEAR SPACE
Weather Balloon, $55. Tank of Helium, $100. Photograph of the Earth from Near Space, PRICELESS.
March 2006 91