Pressure and volume

If a balloon is squeezed, it will get smaller. If the pressure is increased, the volume will decrease.

J-shaped glass tube, filled with mercury, and a trapped air bubble at the smaller end.

The Irish scientist Robert Boyle originally investigated this relationship in the 17th century. Boyle carried out an experiment that gave one of the first pieces of experimental evidence for the particle theory.

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.

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Boyle was able to show that volume is inversely proportional to pressure.

For a fixed mass of gas at a constant temperature:

pressure × volume = constant

pV = constant

This is when:

  • pressure (p) is measured in pascals (Pa)
  • volume (V) is measured in metres cubed (m3)

If the temperature of a gas stays the same, the pressure of the gas doubles as the volume of its container halves. This is because the same number of particles collide with the walls of the container more frequently as there is less space. However, the particles still collide with the same amount of force because there has been no change in molecular speed. The force will be applied at right angles to the surface of the container.

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Gases can be compressed or expanded. Liquids are incompressible as long as there are no gases dissolved in them.

The change in volume or pressure for gas at a constant temperature changing between two states, one and two, can be calculated using the equation:

p_{1}V_{1} = p_{2}V_{2}

p_{1} and V_{1} are the pressure and volume before either are changed, p_{2} and V_{2} are the pressure and volume after the change.

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 p_{1}V_{1} = p_{2}V_{2} to find p_{2}:

p_{2} = \frac{p_{1} \times V_{1}}{V_{2}}

p_{2} = \frac{100 \times 0.5}{0.25}

New pressure, p_{2} = 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? Assume that the temperature and mass of the gas stay the same.

Rearrange p_{1}V_{1} = p_{2}V_{2} to find p_{2}:

p_{2} = \frac{p_{1} \times V_{1}}{V_{2}}

p_{2} = \frac{200,000 \times 10}{2.5}

New pressure, p_{2}= 800,000~Pa or 800~kPa