There are a number laws relating to gasses that show a proportional
relationship. One of these is Charles’ Law. Jacques Charles was the uncommon
combination scientist/balloonist. He co-developed and rode in the first
hydrogen balloon in 1783. Manned balloon flight was it its golden age and
Charles played an important part.
Charles’ Law states that with pressure
remaining constant, the volume of a gas are in direct variation. The experts
say that tire pressure should be measured before driving as the act of driving
will cause the air in the tire to heat up and thus expand.
You might be aware that a basketball left
in the cold doesn’t bounce very well. That is because the decreased temperature
means a reduced volume of air in the ball. If it is brought inside or run under
hot water it will regain its bounciness.
A similar law, Gay-Lussac’s Law, states a
directly proportional relationship between temperature (measure in degrees
Kelvin) and pressure.
Some examples:
- A basketball is left outside at 8
degrees Celsius. Its volume was 444 cubic inches. Brought inside, it warmed up
to 32 degrees. What is its volume now?
First of all, we need to be in Kelvins,
so K = C+273, means the ball’s temperature went from 281 to 305 degrees Kelvin.
Now setting up our proportion we see,
444 : 281 = x : 305 →
x = 483 cubic inches
- NFL Rule 2.1 states that “The
ball shall be made up of an inflated (12 1/2 to 13 1/2 pounds) urethane
bladder…”. It is claimed that the Patriots football team has under-inflated the
ball to try to gain an advantage. A league report claims that at least one of
the balls was inflated to only 10.5 pounds per square inch. Suppose the
Patriots then claim that according to Gay-Lussac’s Law
the football would naturally lose pressure as it was brought from the warmth of
the locker room to the field. If the locker room was 75° F (297.04° K) and the
field temperature was 40° F (277.5944° K), might the Patriot’s claim that the
football was actually within the guidelines?
Our proportion comparing pressure and temperature could be written as:
10.5 : 277.59 = x : 297.04
We get an answer of 11.2 psi, which is still under the 12.5 minimum.
