We know now that the pressure of a gas is
inversely proportional to the volume of the gas, provided the temperature stays the same. We can write this relationship symbolically as
This equation can also be written as follows:
where
is a proportionality constant. If we rearrange this equation, we can say that:
This equation means that, assuming the temperature is constant, multiplying any pressure and volume values for a fixed amount of gas will always give the same value. So, for example, p
V
= k and p
V
= k, where the subscripts 1 and 2 refer to two pairs of pressure and volume readings for the same mass of gas at the same temperature.
From this, we can then say that:
In the gas equations,
is a "variable constant". This means that k is constant in a particular set of situations, but in two different sets of situations it has different constant values.
Remember that Boyle's Law requires two conditions. First, the amount of gas must stay constant. Clearly, if you let a little of the air escape from the container in which it is enclosed, the pressure of the gas will decrease along with the volume, and the inverse proportion relationship is broken. Second, the temperature must stay constant. Cooling or heating matter generally causes it to contract or expand, or the pressure to decrease or increase. In our original syringe demonstration, if you were to heat up the gas in the syringe, it would expand and require you to apply a greater force to keep the plunger at a given position. Again, the proportionality would be broken.
Investigation : boyle's law
Shown below are some of Boyle's original data. Note that pressure would originally have been measured using a
mercury manometer and the units for pressure would have been
millimetres mercury or mm Hg. However, to make things a bit easier for you, the pressure data have been converted to a unit that is more familiar. Note that the volume is given in terms of arbitrary marks (evenly made).
|
Volume |
Pressure |
Volume |
Pressure |
| (graduation |
(kPa) |
(graduation |
(kPa) |
| mark) |
|
mark) |
|
| 12 |
398 |
28 |
170 |
| 14 |
340 |
30 |
159 |
| 16 |
298 |
32 |
150 |
| 18 |
264 |
34 |
141 |
| 20 |
239 |
36 |
133 |
| 22 |
217 |
38 |
125 |
| 24 |
199 |
40 |
120 |
| 26 |
184 |
|
|
- Plot a graph of pressure (p) against volume (V). Volume will be on the x-axis and pressure on the y-axis. Describe the relationship that you see.
- Plot a graph of
against
. Describe the relationship that you see.
- Do your results support Boyle's Law? Explain your answer.
Interesting fact
Did you know that the mechanisms involved in
breathing also relate to Boyle's Law? Just below the lungs is a muscle called the
diaphragm . When a person breathes in, the diaphragm moves down and becomes more 'flattened' so that the volume of the lungs can increase. When the lung volume
increases , the pressure in the lungs
decreases (Boyle's law). Since air always moves from areas of high pressure to areas of lower pressure, air will now be drawn into the lungs because the air pressure
outside the body is higher than the pressure
in the lungs. The opposite process happens when a person breathes out. Now, the diaphragm moves upwards and causes the volume of the lungs to
decrease . The pressure in the lungs will
increase , and the air that was in the lungs will be forced out towards the lower air pressure outside the body.
