Gas volume
If a balloon is squeezed it will get smaller. If the Force exerted over an area. The greater the pressure, the greater the force exerted over the same area. is increased, the The volume of a three-dimensional shape is a measure of the amount of space or capacity it occupies, eg an average can of fizzy drink has a volume of 330 ml. will decrease.
The Irish scientist, Robert Boyle, originally investigated this relationship in the 17th century. Boyle carried out an experiment that provided one of the first pieces of experimental evidence for the The scientific theory used to explain the properties of solids, liquids and gases. It involves the arrangement and movement of the particles in a substance..
By pouring mercury into a J-shaped tube that was sealed at one end, Boyle was able to trap a bubble of air. He then poured more mercury in slowly and watched what happened to the volume of the air bubble.
The higher the column of mercury in the left hand side of the tube, the greater the pressure the trapped air was experiencing and the smaller the bubble became.
So, if there are two situations for a fixed mass of gas held at a constant temperature then:
p1V1 = p2V2
This is when:
- initial pressure, (p1), changes to a second pressure (p2) at the same time as
- initial volume, (V1), changes to a second volume (V2).
This relationship works for any units as long as the same units are used in situations 1 and 2. Normally:
- pressure (p) is measured in pascals (Pa)
- volume (V) is measured in cubic metres (m3)
If the A measure of the average kinetic energy of particles in a substance. of a gas stays the same, the pressure of the gas increases as the volume of its container decreases. This is because the same number of particles collides with the walls of the container more frequently as there is less space. However, the particles still collide with the same amount of force.
Example
A gas occupies a volume of 0.50 m3 at a pressure of 100 Pa. Calculate the pressure exerted by the gas if it is compressed to a volume of 0.25 m3. Assume that the temperature and mass of the gas stay the same.
Rearrange p1 V1 = p2 V2 to find p2:
\(p_{2} = \frac{p_{1} \times V_{1}} {V_{2}}\)
\(p_{2} = \frac{100 \times 0.50}{0.25}\)
New pressure, p2 = 200 Pa
Question
If a gas has a pressure of 200,000 Pa when it is in a volume of 10 m3, what will its pressure be if the volume is reduced to 2.5 m3?
Rearrange p1V1 = p2V2 to find p2:
\(p_{2} = \frac{p_{1} \times V_{1}} {V_{2}}\)
\(p_{2} = \frac{200,000 \times 10}{2.5}\)
New pressure, p2 = 800,000 Pa or 800 kPa