Gases & Absolute Temperature (Cambridge (CIE) IGCSE Physics): Revision Note

Absolute temperature

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 a temperature θ in degrees Celsius and a temperature T in kelvin, use the following conversion:

$T\left(\mathrm{in}\mathrm{K}\right)=\theta (\mathrm{in}°\mathrm{C})+273$

$\theta (\mathrm{in}°\mathrm{C})=T\left(\mathrm{in}\mathrm{K}\right)-273$

The gas laws

Pressure and volume (constant temperature)

• For a fixed mass of gas, 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

• 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:

  • The balloon is tied, so there are a fixed number of air particles within it

  • At normal pressure, the air pressure outside the balloon is greater than the air pressure inside the balloon

  • When air is removed from the bell jar, the air pressure outside the balloon is less than the air pressure inside the balloon

  • The space between the air particles in the balloon increases, so the volume of the balloon increases

• When a gas is compressed, the molecules will hit the walls of the container more frequently

  • Each wall is struck more often, and so the total force on each wall increases, which increases the pressure

Pressure and temperature (constant volume)

• For a fixed mass of gas, 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 that molecules in the same volume collide with the walls of the container more frequently, and with greater force, as the temperature increases

  • Diagram B shows that the pressure increases steadily as the temperature rises

    • If the temperature is measured in kelvin, pressure is directly proportional to temperature and the line passes through the origin

Boyle's law

Extended Tier Only

• For a fixed mass of gas at constant temperature, Boyle’s law is given by:

$p\propto \frac{1}{V}$

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

• This can also be written as:

$pV=\mathrm{constant}$

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

$p_1{V}_1=p_2{V}_2$

• Where:

  • p₁ = initial pressure (Pa)

  • p₂ = final pressure (Pa)

  • V₁ = initial volume (m³)

  • V₂ = final volume (m³)

• Notice that pressure and volume are measured in Pa and m³ respectively

  • Exam questions often give the pressure and volume in units other than Pa and m³, such as kPa and cm³. You can work in those units, as long as the initial and final units match and you give your answer in the same units