Motorists are told to check the pressure in
their tires before going on a long trip for
safety. Car tires are designed to operate within
a specific pressure range as specified by the
tire's manufacturer. The manufacturer determines
this pressure based on the design and
composition of the tire as well as from tests
that they run. The reason that you check the
pressure in the tire while the tires are cold
(i.e. before you start driving the car) is
because, when the tire heats up from friction
while you drive, the air in the tire expands and
actually increases the pressure in the tire. The
pressure of a gas as a function of volume,
amount, and temperature can be approximated by
the ideal gas law: P*V=n*R*T.
In this equation P is the pressure of the gas, V
is the volume that the gas is contained in, n is
the amount of gas (usually measured in moles
which is a measure of the number of atoms of the
gas), R is called the ideal gas constant and is
just a number (people typically use the units J/
(mol*K) so R in these units equals 8.314), and T
is the absolute temperature (this is the
temperature on a thermodynamic absolute scale
meaning it starts at absolute zero which is 0
Kelvin). Using this equation, say your tire has
a volume of 0.5 m3 (I am just making
this number up for demonstration purposes. I do
not know the actual volume of a tire), say it is
about 70 degrees F outside (this is equal to
about 294 K), and say your tire is at 25 psi
(26psi ~ 179263.7 Pa).
From the ideal gas law: n=179263.7*0.5/
(8.314*294)= 36.7 mols.
If the manufacturer specified a pressure of 30
psi (206,843 Pa), and you look at the tire while
it is hot (lets say 340 K), then you would see a
pressure of P=36.7*8.314*340/0.5=207308.9 ~ 30
psi and would think that the tire is fine, when
in fact the tire is under pressure.
This calculation was just for demonstration
purposes and should not be used in actually
filling up a tire. For that, always follow the
directions specified by the tire's manufacturer.
This demonstration; however, shows why you
should check your tire pressure while it is at
normal ambient temperature, and not while the
tire is too hot (i.e. not after having been
driven for a long period of time).
Tires are sealed, so the air inside them
get out. Air exerts a certain amount of pressure
on the container that confines it. Warm air
exerts more pressure than cold air. Driving on
roads produces friction, which heats up the
tires and the air within. If the air inside
heats up too much, the pressure can increase to
where the tire will no longer hold it and the
tire will pop - catastrophically.
Motorists have to check the pressure in car
tires while the tires are cold because the air
in the tire gets heated during driving, and
since the volume of the tire is constant; that
means that the tire pressure goes up as the air
inside heats up.
Then you want to set the suggested pressure when
the air in the tire is at same temperature as
outside air, hence before you drive a bunch.
If we look at the ideal gas equation, PV =
nRT, we can see that pressure is proportional to
temperature. Now, while the air in our tires do
not behave as "ideal gasses," they do still
exhibit a proportionality between pressure in
temperature. This means that when temperature
decreases so does pressure. So on cold days, the
pressure in our tires is lowered, and we should
check to make sure that the pressure is at
the "appropriate level." If we don't, we could
compromise our safety in terms of the stability
of the car, how well the car can turn corners,
and how well the car will break. I hope this
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