GAS LAW
A better name for
this is the gas approximation, although it is pretty good at low pressures.
Also, it is a fairly common practice to start with Boyle's law and Charles'
law, but these are unnecessary- they are special cases of the universal gas law,
usually written
PV = nRT,
where P is absolute pressure, V is volume, n is the nu
Incidentally,
Boyle's law was first discovered by Towneley and
Powers, but if you call it Towneley & Powers'
law, people won't know what you mean.
Problem solving:
In many
situations you will have enclosed gas with no leaks. Then
PV/T is constant, or P1V1/T1 = P2V2/T2.
If one of those quantities (P, V or T) is known to be constant, cancel it out
of the above equation. If the mass of the gas or the nu
If you want to know
about the theory behind the law, which was found much later than the
experimental discovery of the law itself, check out kinetic
theory of gases.
If you have had
chemistry, you know about moles. The nu
Another way to
write the universal gas law equation like this:
PM = r RT,
where M is
molecular mass and r is density = mass/volume. Some people call M the
"molecular weight," but it is no different on the moon, so it is
mass. The universal constant R is 8.31 Joule/(mole
kelvin), using the conventional gram mole (some texts use kg mole) and if you
are using SI units, convert M to kg/mole, put r in kg/m3 and P
in N/m2 (another name for N/m2 is the pascal, abbreviated
Pa). Note that our equation tells us that for a given P & T, density is
proportional to M. If you listen to baseball broadcasts, you will hear
that "humid air is heavy" and therefore the ball does not carry as
far. Au contraire, the average M is lower, so r is less, and this makes the
air drag less, so the ball goes farther. Related to this stuff is how the velocities of molecules
vary. Check out the Boltzmann factor and the
Maxwell-Boltzmann speed distribution.
If you are careful
to use absolute P and T, and you are careful about units, you should have no
trouble with this equation. Take some time to think about how the variables P, r and T are related, and I
bet that some of you will get the following question wrong anyway:
QUESTION: The picture shows identical
cylinders with identical-weight pistons above the trapped air having the same
temperature. The pistons are frictionless and there are no leaks. Compare the
pressures.
Skip this paragraph
if you know about molecular mass. "Molecular mass" is a quantity that
is proportional to the mass of a molecule, but with convenient nu
It so happens that
under normal conditions, oxygen and hydrogen gases are diatomic (two atoms per
molecule), so M of O2 is 32 g/mol and M of H2
is 2 g/mol. Nitrogen (14 g/mol) is also normally diatomic, so N2 has
M = 28 g/mol. Air is mostly nitrogen, and it turns out that M of
air = 29 g/mol is a pretty good value, although it varies (humidity reduces it,
most pollution gases increase it). Some books use the kilogram mole or kmole: M of air is 29 kg per kmole.
In the equation PM = r RT, if you use SI units and the regular mole, convert M to
kg/mol (Mair = 0.029 kg/mol).
(Think of all the trees we save using mole = mol and dyne = dyn.
No, I am not ful of shi, I spe
the tru.)
Answer to the
question above: The two pressures are the same- the gauge pressure is the weight of
the piston divided by the area, and the absolute pressure is the atmospheric
pressure plus the gauge pressure. The densities of the trapped air must be the
same, so the one on the right has fewer molecules.
Enough of this drivel, back to the main page on fluids,
etc.
Other main pages
mechanics
vibrations and waves
quantum
index
email: fredrick.gram
@ tri-c.edu