Boyle's Law (Edexcel IGCSE Physics)

Spec point — 5.22 · use the relationship between the pressure and volume of a fixed mass of gas at constant temperature: p1 V1 = p2 V2

Boyle's law

• For a fixed mass of a gas held at a constant temperature, the Boyle's law formula is:

pV = constant

• Where:

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

• This means that the pressure and volume are inversely proportional to each other

  • When the volume decreases (compression), the pressure increases
  • When the volume increases (expansion), the pressure decreases

• This is because when the volume decreases, the same number of particles collide with the walls of a container but more frequently as there is less space

  • However, the particles still collide with the same amount of force meaning greater force per unit area (pressure)

• The key assumption is that the temperature and the mass (and number) of the particles remains the same

Increasing the volume of a gas decreases its pressure

• This equation can also be rewritten for comparing the pressure and volume before and after a change in a gas:

p₁V₁ = p₂V₂

• Where:

  • p₁ = initial pressure in pascals (Pa)
  • V₁ = initial volume in metres cubed (m³)
  • p₂ = final pressure in pascals (Pa)
  • V₂ = final volume in metres cubed (m³)

• This equation is sometimes referred to as Boyle's Law

Initial pressure and volume, p₁and V₁, and final pressure and volume, p₂and V₂. When volume decreases, pressure increases

Worked Example A gas occupies a volume of 0.70 m³ at a pressure of 200 Pa. Calculate the pressure exerted by the gas if it is compressed to a volume of 0.15 m³.Assume that the temperature and mass of the gas stay the same.

Answer:

Step 1: List the known quantities

• Initial volume,V₁ = 0.70 m³
• Initial pressure, p₁ = 200 Pa
• Final volume, V₂ = 0.15 m³

Step 2: Write the relevant equation

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

Step 3: Rearrange for the final pressure, p₂

• Divide both sides by V₂ to get the p₂ term on its own

$\frac{p_{1} V_{1} }{V_{2} } = \frac{p_{2} \cancel{V_{2} } }{ \cancel{V_{2} } }$

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

Step 4: Substitute in the values

$p_{2}=\frac{p_{1}V_{1}}{V_{2}}=\frac{200\times0.70}{0.15}$

$p_{2}=930\mathrm{Pa}$ (2 s.f.)

Exam Hint Always check whether your final answer makes sense. If the gas has been compressed, the final pressure is expected to be more than the initial pressure (like in the worked example). If this is not the case, double-check the rearranging of any formulae and the values put into your calculator.