Gases & Absolute Temperature (CIE IGCSE Physics)

• 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

Part (a)

Step 1: Choose whether to add or subtract 273 to the value

• • • The question is in kelvin therefore subtract 273 to convert to Celsius

Step 2: Do the calculation

Step 3: Write the answer with units

• • • 0K = −273 °C

Part (b)

Step 1: Choose whether to add or subtract 273 to the value

• • • The question is in Celsius therefore add 273 to convert to kelvin

Step 2: Do the calculation

Step 3: Write the answer with units

• • • 0 °C = 273 K

Part (c)

Step 1: Choose whether to add or subtract 273 to the value

• • • The question is in Celsius therefore add 273 to convert to kelvin

Step 2: Do the calculation

Step 3: Write the answer with units

• • • 20 °C = 293 K

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

Pressure increases when a gas is compressed

• 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:

• 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)

• The average speed of motion of molecules increases when the temperature increases (and vice versa)
• Since the average kinetic energy depends on their speed, the kinetic energy of the molecules also increases if its volume remains constant
  • The hotter the gas, the higher the average kinetic energy
  • The cooler the gas, the lower the average kinetic energy

• As the gas heats up, the molecules will travel at a higher speed
  • They collide with the walls more often, 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 proportional to the pressure, 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

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)

• 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

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