5.2.3 Gas Laws

Boyle’s Law

• If the temperature T of an ideal gas is constant, then Boyle’s Law is given by:

• This means the pressure is inversely proportional to the volume of a gas

Pressure increases when a gas is compressed

• The relationship between the pressure and volume for a fixed mass of gas at constant temperature can also be written as:

P₁V₁ = P₂V₂

• Where:
  • P₁ = initial pressure (Pa)
  • P₂ = final pressure (Pa)
  • V₁ = initial volume (m³)
  • V₂ = final volume (m³)

Boyle's Law graph representing pressure inversely proportional to volume

• If the temperature increases, the graph is further from the origin and vice versa

Pressure Law

• If the volume V of an ideal gas is constant, the Pressure law is given by:

P ∝ T

• This means the pressure is proportional to the temperature

• The relationship between the pressure and thermodynamic temperature for a fixed mass of gas at constant volume can also be written as:

• Where:
  • P₁ = initial pressure (Pa)
  • P₂ = final pressure (Pa)
  • T₁ = initial temperature (K)
  • T₂ = final temperature (K)

Pressure Law graph representing temperature (in °C) directly proportional to the volume

Worked Example

Exam Tip

• The value of absolute zero can be estimated by using the gas law Charles' Law
• If the pressure P of an ideal gas is constant, then Charles’s law is given by:

V ∝ T

• This means the volume is proportional to the temperature of a gas

• The relationship between the volume and thermodynamic temperature for a fixed mass of gas at constant pressure can also be written as:

• Where:
  • V₁ = initial volume (m³)
  • V₂ = final volume (m³)
  • T₁ = initial temperature (K)
  • T₂ = final temperature (K)

Charles's Law graph representing temperature (in °C) directly proportional to the volume

• The Charles's Law graph for temperature in Kelvin against volume is identical except that it is a straight line through the origin
  • Extrapolating backwards leads to a temperature of absolute zero at which the gas will have a volume of zero m³