BOYLE'S LAW

The Kinetic Theory of Matter

In the second half of the nineteenth century scientists developed the kinetic theory of matter. This was an attempt to explain the properties of matter- regardless of the state the matter is in- gas, liquid or solid. The word kinetic comes from the Greek “kinetikos” meaning moving. So the kinetic theory is based on the idea that particles of matter are always in motion and that this motion has consequences. Here we discuss gases.

But first, let’s look at the assumptions of the kinetic theory.

Matter consists of a large number of tiny particles. In gases, the particles are about 1000 times farther apart than they are either in liquids or solids. This accounts for their lower density and better compressibility.
The particles are in constant motion moving in straight lines and thus have kinetic energy.
all collisions between the gas particles and the sides of the container are elastic.
There are no forces of attraction or repulsion between the particles of a gas.
The average kinetic energy of a particle is directly proportional to the Kelvin Temperature of the gas.




Objectives
In this lesson, you will:
1. Be able to state Boyle’s Law either verbally or mathematically.
2. Be able to define pressure, explain how it is measured and state the standard conditions of Temperature and Pressure.
3. Be able to use Boyle’s Law to calculate the volume-pressure change at a fixed temperature.
4. Perform and analyze a simple experiment demonstrating Boyle’s Law

Intro to Boyle's Law

Pressure Volume Relationships

We are used to living at 1 ATM of pressure, so we rarely even take notice of it. We normally don't feel the pressure on us because the human body is primarily made up of liquid, and liquids are basically non compressible. At times, however, we do notice changes of pressure, primarily in our ears. You may have noticed your ears "popping" when flying, driving in the mountains, or even going up and down in elevators. This is because our ears have an air space in them, and air, like all other gases, is compressible.

A gas will compress proportionately to the amount of pressure exerted on it. For example, if you have a 1 cubic foot balloon and double the pressure on it, it will be compressed to 1/2 cubic foot. Increase the pressure by 4, and the volume will drop to 1/4 the size etc. This theory was discovered by Sir Robert Boyle, a 17th century scientist. The theory known as Boyle's Law states: If the temperature remains constant, the volume of a given mass of gas is inversely proportional to the absolute pressure.

Let's follow an example...

Suppose you had a balloon measuring one cubic foot at the surface of the water. This balloon is under 1 ATM (14.7 psi) of pressure. If we push the balloon underwater, and take it to a depth of 33 feet, it is now under 2 ATM of pressure (29.4 lbs) - 1 ATM of pressure from the air, 1 ATM of pressure from the water. Boyle's Law then tells us that since we have twice the absolute pressure, the volume of the balloon will be decreased to one half. It follows then, that taking the balloon to 66 feet, the pressure would compress the balloon to one third its original size, 99 feet would make it 1/4 etc.

If we bring the balloon in the previous example back up to the surface, it would increase in size due to the lessening pressure until it reached the surface and returned to its one cubic foot size. This is because the air in the balloon is compressed from the pressure when submerged, but returns to its normal size and pressure when it returns to the surface.

We will achieve the same result with an open container, such as an inverted bottle, as we do with a balloon. By inverting a bottle at the surface and descending with it, the pressure from the surrounding water will compress the air and the bottle will start to fill with water. Even with no air escaping, the container will be half full of water at a depth of 33 feet due to the pressure compressing the air to half its original volume.

Along with the volume of air in the balloon or container, the surrounding pressure will affect the density of the air as well. Density, simply stated, is how close the air molecules are packed together. The air in the balloon or container at the surface is at its standard density, but when we descend to the 33-foot level where its volume is reduced to one half, the density has doubled. At 66 feet, the density has tripled. This is because the pressure has pushed the air molecules closer together.