interacting with any of the other molecules except in a collision. In a collision, molecules
exert equal and opposite forces on one another.- Molecular collisions are perfectly elastic: Molecules do not lose any kinetic energy
when they collide with one another.
The kinetic theory projects a picture of gases as tiny balls that bounce off one another whenever
they come into contact. This is, of course, only an approximation, but it turns out to be a
remarkably accurate approximation for how gases behave in the real world.
These assumptions allow us to build definitions of temperature and pressure that are based on the
mass movement of molecules.
Temperature
The kinetic theory explains why temperature should be a measure of the average kinetic energy of
molecules. According to the kinetic theory, any given molecule has a certain mass, m; a certain
velocity, v; and a kinetic energy of^1 / 2 mv^2. As we said, molecules in any system move at a wide
variety of different velocities, but the average of these velocities reflects the total amount of
energy in that system.
We know from experience that substances are solids at lower temperatures and liquids and gases at
higher temperatures. This accords with our definition of temperature as average kinetic energy:
since the molecules in gases and liquids have more freedom of movement, they have a higher
average velocity.
Pressure
In physics, pressure, P, is the measure of the force exerted over a certain area. We generally say
something exerts a lot of pressure on an object if it exerts a great amount of force on that object,
and if that force is exerted over a small area. Mathematically:
Pressure is measured in units of pascals (Pa), where 1 Pa = 1 N/m^2.
Pressure comes into play whenever force is exerted on a certain area, but it plays a particularly
important role with regard to gases. The kinetic theory tells us that gas molecules obey Newton’s
Laws: they travel with a constant velocity until they collide, exerting a force on the object with
which they collide. If we imagine gas molecules in a closed container, the molecules will collide
with the walls of the container with some frequency, each time exerting a small force on the walls
of the container. The more frequently these molecules collide with the walls of the container, the
greater the net force and hence the greater the pressure they exert on the walls of the container.
Balloons provide an example of how pressure works. By forcing more and more air into an
enclosed space, a great deal of pressure builds up inside the balloon. In the meantime, the rubber
walls of the balloon stretch out more and more, becoming increasingly weak. The balloon will pop
when the force of pressure exerted on the rubber walls is greater than the walls can withstand.
The Ideal Gas Law
The ideal gas law relates temperature, volume, and pressure, so that we can calculate any one of
these quantities in terms of the others. This law stands in relation to gases in the same way that
Newton’s Second Law stands in relation to dynamics: if you master this, you’ve mastered all the
math you’re going to need to know. Ready for it? Here it is: