An important property of any gas
is its pressure. We have some experience with air
pressure that we don't have with properties like
viscosity and compressibility.
We've heard meteorologists give the daily
value of the barometric pressure of the atmosphere (29.8 inches of
mercury, for example). And most of us have blown up a balloon or used
a pump to inflate a bicycle tire or a basketball.
Definition of Pressure
There are two ways to look at pressure: (1) the small scale action
of individual air molecules or (2) the large scale action of a large
number of molecules.
The small scale action is described by the
kinetic theory of gases and we have no evidence that the Wright
brothers were familiar with this theory when they designed the aircraft
and engine. So we will not discuss the details of this theory at this web site; if
you wish to explore the kinetic theory of gases you should visit:
http://www.grc.nasa.gov/WWW/K-12/airplane/kinth.html.
The most important result from the small scale view of pressure is that the
pressure in a gas is related to the momentum of the individual moving gas molecules.
Momentum is mass times velocity. So the higher the velocity of the molecules
of a gas, the greater the pressure.
The temperature of a gas depends on the average kinetic
energy (mass times velocity squared) of the molecules of the gas,
so the temperature and pressure
of a gas are related to each other through an
equation of state.
Considering the large scale, pressure P is defined to be the force F acting
on an area A divided by the area that it acts on.
P = F / A
Scalar Quantity
Let us look at a gas that does not appear to move or flow.
Actually, while the gas does not appear to move, the individual
molecules of the gas (which we cannot see) are in constant random
motion. Because we are dealing with a large number of molecules
(nearly infinite) and because the motion of the individual molecules
is random in every direction, we do not detect any motion. If we
enclose the gas within a container, we will detect a pressure in the
gas from the molecules colliding with the walls of our container. We
can put the walls of our container anywhere inside the gas, and the
force per area (the pressure) will be the same. (If the gas as
a whole were moving, the measured pressure would be different in the
direction of the motion, as described by Bernoulli's
equation .) We could shrink the size of our "container" down to
an infinitely small point, and the pressure would have a single value
at that point. Therefore, pressure is a scalar quantity, not a
vector quantity, like velocity that has a specified direction associated with it.
Pressure has a magnitude but no direction associated with
it. Pressure acts in all directions at a point inside a gas. At the
surface of a gas, the pressure force acts perpendicular to the
surface.
Magnitude of Pressure Force
The magnitude of the pressure force
is equal to the pressure (force/area) times the surface area, and the
direction is perpendicular to the surface.
In the figure, we have a gas (in
red) that is confined in a box. A force is applied to the top of the
box. The pressure force within the box opposes the applied force. And
the pressure equals the external force divided by the area of the top
of the box. Inside the gas, the pressure acts in all directions. So
the pressure would also push on the bottom of the box and on the
sides. This is different from simple solid mechanics. If the
red gas were a solid, there would be no forces applied to the sides
of the box; the applied force would be simply transmitted to the
bottom. But in a gas, because the molecules are free to move about
and collide with one another, a force applied in the vertical
direction causes forces in the horizontal direction.
Activities:
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