The density, pressure and temperature of a gas are related through physical science laws.
When a gas moves against an object, it pushes on the surface of the object. These small pushes, over the entire surface, are defined as pressure and are measured as force per unit area.
Density is a measure of mass (the amount of molecules) in a given object or volume.
A fluid with a lot of molecules tightly packed together has a high density; one with fewer molecules would have a lower density. Water, for example, has a much higher density than air. A 10-gallon fish tank with water in it has much more mass than a 10-gallon tank with air in it. Since it has more mass, it will weigh more.
Gases (like air) are compressible; they expand to fill a new larger volume. The mass doesn't change, but the volume increases, so the density of the gas decreases in the new volume.
Look at the structure of a tennis ball. It has a fabric covering and a hollow inner core of a rubber-like substance. Inside the core is a gas.
Compare the tennis ball to a round balloon. What happens when you fill a balloon with water? The balloon expands in size. The balloon material is thin and elastic enough to stretch. We can calculate the density of the water by dividing the mass by the volume. Scientists and engineers use the Greek letter r (rho) as the symbol for density, m is used for mass and v for volume.
density= mass/volume or r=m/v
Water has mass and exerts pressure over the inner surface of the balloon. Although you may not be able to see a gas it also has mass. When you blow up a balloon the air expands the balloon just like the water.
Solid objects have well-behaved molecules and atoms that line up in an even pattern and give the object a specific shape. A solid has a fixed shape. In dynamics, this is called a "non-deformable" body (the shape does not change). No matter how hard a solid is squeezed or pulled, its molecules do not move closer together or further apart. The object may break, but the molecules don't move. This is an "incompressible" object.
The molecules in a liquid, however, are not as well organized. When poured from a square container into a round one, a liquid will not retain its square shape but will take the shape of the round container. It is deformable. The liquid will not, however, expand to fill a larger space. The liquid cannot be made larger or smaller by squeezing or pulling. The molecules do not move closer or further apart. Like the solids, a liquid is incompressible.
Gases, like air, have even less-organized molecules. Gases take the shape of their containers, and also expand or contract to fill the container. The gas in a tennis ball fills the entire inner core of the ball. A gas can be expanded or compressed.
Why does a tennis ball bounce? The tennis ball and the gas inside act like a spring. The suspension in a truck works in a similar way. The suspension system uses an air bladder. When your truck hits a bump in the road the wheel rises and compresses the air bladder. As the wheel returns to its original position the air in the bladder acts like a spring and pushes the bladder out again.
As the tennis ball strikes the court the bottom of the ball is pushed in. The tennis ball material is pliable and deforms (bends). The compressed (pressed in) ball has less volume than the original uncompressed ball. As the ball comes off the court the gas and tennis ball material act like a spring and the ball returns to its original shape.
What happens as the temperature of the gas inside the ball rises? As the temperature increases the molecules of the gas expand and move around inside the ball. As the molecules move they strike the inner surface of the ball and apply more pressure to it.
The "perfect gas law" describes the relation between pressure, density and temperature:
where p is the pressure, r is the density, R is a gas constant (there is an individual gas constant for each gas) and T is the temperature of the gas. So if the temperature of the gas inside the ball increases and R and r stay the same, that means the pressure will increase.
With this is mind try the hot and cold tennis ball experiment. Do you think a hot tennis ball will bounce higher or lower than a cool tennis ball? Why?
Balls were once refrigerated before the Wimbledon tournament. Why do you think this was done?