Gas Laws (DP IB Physics)

Gas Laws

• An ideal gas is one which obeys the relation:

pV ∝ T

• Where:

  • p = pressure of the gas (Pa)

  • V = volume of the gas (m³)

  • T = thermodynamic temperature (K)

• Turning this into an equation gives:

• This is derived from the empirical gas laws for constant pressure, constant temperature and constant volume

Empirical Gas Laws

• The ideal gas laws are the experimental relationships between pressure P, volume V and the temperature T of an ideal gas

  • Boyle’s Law (constant temperature)

  • Charles’s Law (constant pressure)

  • Gay-Lussac's Law (constant volume)

• The mass and the number of molecules of the gas are assumed to be constant for all experiments

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

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

• Where:

  • P₁ = initial pressure (Pa)

  • P₂ = final pressure (Pa)

  • V₁ = initial volume (m³)

  • V₂ = final volume (m³)

• The variation of volume and pressure at a constant temperature is shown below:

Boyle's Law graph showing pressure is inversely proportional to volume when temperature is constant

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

Boyle's law: gas pressure is inversely proportional to the volume it occupies

Charles's Law

• If the pressure P of an ideal gas is constant, then Charles’s law is given by:

• 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)

• The variation of volume and temperature at a constant pressure is shown below:

Charles's Law graph showing temperature (in K) is directly proportional to the volume when pressure is constant

Charles's law: the temperature of a gas is proportional to the volume it occupies

Gay-Lussac's (Pressure) Law

• If the volume V of an ideal gas is constant, the Gay-Lussac's or Pressure law is given by: 

• 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)

• The variation of pressure and temperature at a constant volume is shown below:

Gay-Lussac's Law graph showing temperature (in K) is directly proportional to pressure when volume is constant

Pressure law: the temperature of a gas is proportional to the gas pressure

• Changes in the pressure, temperature or volume of an ideal gas are normally represented on a pressure-volume graph

• These are covered in more detail in the thermodynamics topic