An important property of any gas
is its density. **Density** is defined as the mass of
an object divided by its volume, and most of our experiences with
density involve solids. We know that some objects are heavier than
other objects, even though they are the same size. A brick and a loaf
of bread are about the same size, but a brick is heavier--it is more
dense. Among metals, aluminum is less dense than iron. That's why
airplanes and rockets and some automobile parts are made
from aluminum. For the same volume of material,
one metal weighs less than another if it has a lower density.

For solids, the
density of a single element or compound remains fairly constant
because the molecules are bound to one another. For
example, if you found a pure gold nugget on the earth or you found a
pure gold nugget on the moon, the measured density would be nearly
the same. But for gases,
the density can vary over a wide range
because the molecules are free to move.
Air at the surface of the
earth has a very different density than air 50 kilometers above the
earth. An interactive simulator allows you
to study how air density varies with altitude. Understanding density
and how it works is fundamental to the understanding of rocket
aerodynamics
and propulsion.

There are two ways to look at density: (1) the small scale action
of individual air molecules or (2) the large scale action of a large
number of molecules. Starting with the small scale action, from the
kinetic theory of gases, a gas
is composed of a large number of molecules that are very small
relative to the distance between molecules. The molecules are in
constant, random motion and frequently collide with each other and
with the walls of a container. Because the molecules are in motion, a
gas will expand to fill the container. Since **density** is
defined to be the mass divided by the
volume,
density depends
directly on the size of the container in which a fixed mass of gas is confined.
As a simple example, consider Case #1 on our figure. We have 26
molecules of a mythical gas. Each molecule has a mass of 20 grams
(.02 kilograms), so the mass of this gas is .52 kg. We have confined
this gas in a rectangular tube that is 1 meter on each side and 2
meters high. We are viewing the tube from the front, so the dimension
into the slide is 1 meter for all the cases considered. The volume of
the tube is 2 cubic meters, so the density is .26 kg/cubic meter.
This corresponds to air density at about 13 kilometers altitude. If the
size of our container were decreased to 1 meter on all sides, as in
Case #3, and we kept the same number of molecules, that density would
increase to .52 kg/cubic meter. Notice that we have the same amount
of material; it is just contained in a smaller volume. How we
decrease the volume is very important for the final value of
pressure
and temperature.
You can explore the variations in pressure and temperature at the
animated gas lab.

Turning to the larger scale, the density is a
state variable
of a gas and the change in density during a process is
governed by the laws of
thermodynamics.
Actual molecules of a gas are incredibly small. In one cubic meter
the number of molecules is about ten to the 23rd power. (That's 1
followed by 23 zero's !!!) For a static gas, the molecules are in a
completely random motion. Because there are so many molecules, and
the motion of each molecule is random, the value of the density is
the same throughout the container.
Density is a
scalar quantity;
it has a magnitude but no direction associated with it.
As an example, consider Case #1,
in which the mass is .52 kg, the volume is 2 cu m, and the density is
.26 kg/cu m. If we sample a smaller volume of 1 meter on a side as in
Case #2, we will obtain the same density. The volume of the blue box
in Case #2 is only 1 cu m, but the number of molecules in the box is
13 at .2 kg per molecule; and the density is .26 kg/cu m. (This
example REALLY works only for a very large number of molecules moving
at random. Case #2 is just an illustration.) Another way to obtain
the same density for a smaller volume is to remove molecules from the
container. In Case #4, the container is the same size as in Case #3,
but the number of molecules (the mass) has been decreased to only 13
molecules. The density is .26 kg/cubic meter, which is the same
density seen in the blue box of Case #2 and throughout Case #1. A
careful study of these four cases will help you understand the
meaning of gas density.

These rather simple examples help explain a fundamental effect
that we see in nature. Between Cases #3 and #4, the number of
molecules in a given volume decreased, and the corresponding density
decreased. In the atmosphere, air molecules near the surface of the
earth are held together more tightly than the molecules in the higher
atmosphere because of the gravitational pull of the earth on all the
molecules above the surface molecules. The higher up you go in the
atmosphere, the fewer the molecules there are above you, and the
lower the confining force. So in the atmosphere,
density decreases as you increase altitude; there are fewer
molecules.

Gas density is defined to be the mass of gas divided by the volume confining
the gas. There is a related state variable called the
specific volume which is the reciprocal of
the density **r**. The specific volume **v** is given by:

Specific volume is often used when solving static gas problems for which the volume is
known, while density is used for moving gas problems. They are equivalent state
variables.