Gases & Absolute Temperature

Absolute Temperature

Absolute Temperature

• The Kelvin temperature scale begins at absolute zero

  • Absolute zero, or 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

Kelvin Scale and Celsius Scale

Conversion chart relating the temperature on the Kelvin and Celsius scales

The Gas Lawsvideo

The Gas Laws

• The gas laws describe the relationships between the pressure, volume and temperature of a gas

Pressure & Volume at Constant Temperature

• If the temperature of a gas remains constant, the pressure of the gas changes when it is:

  • Compressed – decreasing the volume causes pressure to increase

  • Expanded – increasing the volume causes pressure to decrease

Decreasing Volume Increases 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 of a tied up balloon when the pressure of the air around it decreases:

Decreasing Pressure Increases Volume

Decreasing pressure from the air surrounding the balloon on the right allows the pressure from the air particles within to increase the volume of the balloon

• 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

Volume & Temperature at Constant Pressure

• If a gas is placed in a container which allows it to expand and compress (e.g. a piston) then its pressure can be kept constant

• As a result, changes in temperature at constant pressure will affect the volume only

• If the pressure of a gas remains constant, the volume of the gas changes when:

  • The gas gets hotter – increasing the temperature causes the gas to expand (volume increases)

  • The gas gets cooler – decreasing the temperature causes the gas to compress (volume decreases)

Relationship between Volume & Temperature

At constant pressure, an increase in the temperature of the gas causes it to expand

• In the diagram above:

  • Diagram A shows molecules expanding into a greater volume as the temperature increases

  • Diagram B shows that the volume of the gas is directly proportional to the temperature

Pressure & Temperature at Constant Volume

• If the temperature of a gas is increased, the particles move faster and gain kinetic energy

  • As a result, they will collide more often leading to an increase in pressure

• If the volume of a gas remains constant, the pressure of the gas changes when:

  • The gas gets hotter – increasing the temperature causes the pressure to increase

  • The gas gets cooler – decreasing the temperature causes the pressure to decrease

Relationship between Pressure & Temperature

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

• In the diagram above:

  • Diagram A shows molecules in the same volume colliding with the walls of the container more often as the temperature increases

  • Diagram B shows that the temperature of a gas is directly proportional to the gas pressure

Boyle's Lawvideo

Boyle's Law

• For a fixed mass of a gas held at a constant temperature:

pV = constant

• Where:

  • p = pressure in pascals (Pa)

  • V = volume in metres cubed (m³)

• This means that the pressure and volume are inversely proportional to each other

  • When the volume decreases (compression), the pressure increases

  • When the volume increases (expansion), the pressure decreases

• This relationship is known as Boyle’s Law and can also be written as:

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

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

Graph Showing Boyle's Law

Boyle's Law shows that pressure is inversely proportional to volume

• 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 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

Calculating Changes in Pressure & Volume

Initial pressure and volume, P₁ and V1, and final pressure and volume, P₂ and V₂