Yes.

IIRC from high-school chemistry, gases were refered to as occupying a
certain volume at "STP" - "Standard Temperature and Pressure".

This, then, becomes nothing more than a mathematical equation. All you
have to do is move the variables and constants around. That is, in a
tire the Volume is roughly fixed. So you place a cetain number of air
molecues into the tire when it is off the vehicle - or "unloaded".

Assuming that the ambient temperature remains relatively constant,
then the number of air molecues will produce a certain pressure
reading.

Now you mount the tire on a vehicle. This applies a portion of the
vehicle wieght to the tire. So the tire is now "loaded", and by that I
mean that the vehicle load is applying pressure to the tire! Since
that original reading happened with no external pressure applied, the
nominal pressure reading form the tire should go up as a result of the
external force applied to the tire.

Having said that, I have no idea about what the formulas are, so I
have no way to calculate what the actual pressure increase might be.
Also, the nature of the rubber compounds in the tire will have a
buffering effect which would tend to minimize the compression of the
tire and thus the air in the tire. The increase might be so small that
the average tire pressure gauge might not be sensitive enough to
measure it.

Maybe...and maybe not.

Surely: It's not our job to do your physics homework.

In practice, I believe that the pressure does not rise when weight is added
as described.

When the tire is inflated with no weight on it, all the weight is
distributed evenly around the tire as the cords pull equally in all
directions.  When the tire is loaded, the tension of the cords at the bottom
is relieved while the cords opposite the ground pull upwards on the bead.

Probably very slightly.  A pressure increase would require a volume
decrease, remember P1V1=P2V2 (I don't know how to do subscripts in
Netscape!).  The volume may decrease very slightly under the normal load
a tire is rated for.  Now, if you overload the car such that the rim
touches the road, then I'd guess you'd reduce the volume enough to make
a measurable increase in pressure.

Matt

The volume part of it (that some seem to be struggling with) is exlained
by the fact that when a round hoop is compressed into an oval, the
inscribed volume is decreased even though the perimeter circumference is
exactly the same.  The same reason toothpaste comes out of the tube when
you start flattening (ovaling) it - you are decreaseing the volume.

BTW - *if* the answer to your question were 'no', then an inflated tire
would not support a car - the rim would go to the ground as easily as a
deflated tire (or a tire with a huge hole in it).

Bill Putney
(To reply by e-mail, replace the last letter of the alphabet in my
address with the letter 'x')

If the internal air volume (or air space) of the tire changes, then
yes, the internal PSI will change.  Your question can't be answered
completely because we no nothing of the specs of the tire in question
(truck tire, radial, biased ply, tire size, etc).  

If you do google searches for tire "pressure-load" curves you will see
that yes, in many cases tires are designed to have a specific PSI for
a given axle load.  This is to maintain the desired profile of the
contact patch and side-walls as the tire rolls.  A car tire that you
would normally fill to 30 psi would be quite happy with 15 psi if it
were used on a grocery cart.

If you are wondering if you should fill your un-mounted tires at a gas
station to 30 PSI (and if that pressure will be correct when you
subsequently mount the tires on the vehicle) then the answer is yes.
However, I typically put 34 PSI in my (300m) tires.  Many car tires
are spec'd with a max load of 40 to 45 psi.