Gases & Absolute Temperature (CIE IGCSE Physics)

What is absolute temperature?

• Temperature measured in kelvin is called absolute temperature
• The kelvin temperature scale begins at absolute zero
  • 0 K is equal to -273 °C 
  • An increase of 1 K is the same change as an increase of 1 °C

• It is not possible to have a temperature lower than 0 K
• This means a temperature in kelvin will never have a negative value

• To convert between temperatures θ in the Celsius scale, and T in the Kelvin scale, use the following conversion:

θ / ^°C = T / K − 273

T / K = θ / ^°C + 273

Conversion chart relating the temperature on the Kelvin and Celsius scales

Pressure & volume (constant temperature)

• If the temperature of a gas remains constant, the pressure of the gas changes when it is:
  • Compressed – decreases the volume which increases the pressure
  • Expanded – increases the volume which decreases the pressure

At constant temperature, changing the volume changes the pressure

• Similarly, a change in pressure can cause a change in volume
• A vacuum pump can be used to remove the air from a sealed container
• The diagram below shows the change in volume to a tied up balloon when the pressure of the air around it decreases:

At constant temperature, changing the pressure changes the volume

• When a gas is compressed, the molecules will hit the walls of the container more frequently
  • This creates a larger overall net force on the walls which increases the pressure

Pressure & temperature (constant volume)

• Increasing temperature increases the pressure of a gas which is kept at a constant volume
• The average speed of molecules increases when the temperature increases (and vice versa)
• As the gas heats up, the molecules will travel at a higher speed
  • They collide with the walls more often and with greater force, increasing the pressure
• Therefore, at a constant volume, an increase in temperature increases the pressure of a gas and vice versa
  • Diagram A shows molecules in the same volume collide with the walls of the container more as the temperature increases
  • Diagram B shows that since the temperature is directly proportional to the pressure (at constant volume), the graph is a straight line

At constant volume, an increase in the temperature of the gas increases the pressure due to more collisions on the container walls

Extended tier only

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

• This can also be written as:

• 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)

• Notice that volume and pressure are measured in m³ and Pa respectively
  • In calculations if units are given in cm³ or MPa this is a rare case where calculations can be done using the original units as long as answers are reported in the same, original units and the final and initial units match

Boyle's Law graph: Pressure is inversely proportional to volume