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What did you notice when you pushed the plunger in? What happens to the volume of air inside the syringe? Did it become more or less difficult to push the plunger in as the volume of the air in the syringe decreased? In other words, did you have to apply more or less force to the plunger as the volume of air in the syringe decreased?

As the volume of air in the syringe decreases, you have to apply more force to the plunger to keep pressing it down. The pressure of the gas inside the syringe pushing back on the plunger is greater. Another way of saying this is that as the volume of the gas in the syringe decreases , the pressure of that gas increases .

Conclusion:

If the volume of the gas decreases, the pressure of the gas increases. If the volume of the gas increases, the pressure decreases. These results support Boyle's law.

In the previous demonstration, the volume of the gas decreased when the pressure increased, and the volume increased when the pressure decreased. This is called an inverse relationship . The inverse relationship between pressure and volume is shown in [link] .

Graph showing the inverse relationship between pressure and volume

Can you use the kinetic theory of gases to explain this inverse relationship between the pressure and volume of a gas? Let's think about it. If you decrease the volume of a gas, this means that the same number of gas particles are now going to come into contact with each other and with the sides of the container much more often. You may remember from earlier that we said that pressure is a measure of the frequency of collisions of gas particles with each other and with the sides of the container they are in. So, if the volume decreases, the pressure will naturally increase. The opposite is true if the volume of the gas is increased. Now, the gas particles collide less frequently and the pressure will decrease.

It was an Englishman named Robert Boyle who was able to take very accurate measurements of gas pressures and volumes using high-quality vacuum pumps. He discovered the startlingly simple fact that the pressure and volume of a gas are not just vaguely inversely related, but are exactly inversely proportional . This can be seen when a graph of pressure against the inverse of volume is plotted. When the values are plotted, the graph is a straight line. This relationship is shown in [link] .

The graph of pressure plotted against the inverse of volume, produces a straight line. This shows that pressure and volume are exactly inversely proportional.
Boyle's Law

The pressure of a fixed quantity of gas is inversely proportional to the volume it occupies so long as the temperature remains constant.

Proportionality

During this chapter, the terms directly proportional and inversely proportional will be used a lot, and it is important that you understand their meaning. Two quantities are said to be proportional if they vary in such a way that one of the quantities is a constant multiple of the other, or if they have a constant ratio. We will look at two examples to show the difference between directly proportional and inversely proportional .

  1. Directly proportional A car travels at a constant speed of 120 km/h. The time and the distance covered are shown in the table below.
    Time (mins) Distance (km)
    10 20
    20 40
    30 60
    40 80
    What you will notice is that the two quantities shown are constant multiples of each other. If you divide each distance value by the time the car has been driving, you will always get 2. This shows that the values are proportional to each other. They are directly proportional because both values are increasing. In other words, as the driving time increases, so does the distance covered. The same is true if the values decrease. The shorter the driving time, the smaller the distance covered. This relationship can be described mathematically as:
    y = k x
    where y is distance, x is time and k is the proportionality constant , which in this case is 2. Note that this is the equation for a straight line graph! The symbol is also used to show a directly proportional relationship.
  2. Inversely proportional Two variables are inversely proportional if one of the variables is directly proportional to the multiplicative inverse of the other. In other words,
    y 1 x
    or
    y = k x
    This means that as one value gets bigger, the other value will get smaller. For example, the time taken for a journey is inversely proportional to the speed of travel. Look at the table below to check this for yourself. For this example, assume that the distance of the journey is 100 km.
    Speed (km/h) Time (mins)
    100 60
    80 75
    60 100
    40 150
    According to our definition, the two variables are inversely proportional if one variable is directly proportional to the inverse of the other. In other words, if we divide one of the variables by the inverse of the other, we should always get the same number. For example,
    100 1 / 60 = 6000
    If you repeat this using the other values, you will find that the answer is always 6000. The variables are inversely proportional to each other.

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Source:  OpenStax, Siyavula textbooks: grade 11 physical science. OpenStax CNX. Jul 29, 2011 Download for free at http://cnx.org/content/col11241/1.2
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