Ideal Gases

$p V \propto T$

Where:
- p = pressure of the gas (Pa)
- V = volume of the gas (m³)
- T = thermodynamic temperature (K)
According to the relation:
- temperature is directly proportional to pressure, for a constant volume
- temperature is directly proportional to volume, for a constant pressure
- pressure and volume are inversely proportional to each other, for a constant temperature

For a constant volume
When the temperature of a gas is increased
Then the pressure is also increased
- the molecules have a higher kinetic energy
- so move about more and collide more with the walls of their container
- creating more pressure

For a constant pressure
When the temperature of a gas is increased
The volume is also increased
- the molecules have a higher kinetic energy
- so move about more and move further apart from each other
- expanding to create a bigger volume

An ideal gas is in a container of volume 4.5 × 10⁻³ m³. The gas is at a temperature of 30°C and a pressure of 6.2 × 10⁵ Pa.

Calculate the pressure of the ideal gas in the same container when it is heated to 40 °C.

Answer:

Step 1: State the known values

Step 2: Since volume is constant, state the pressure law

$\frac{p_{1}}{p_{2}} = \frac{T_{1}}{T_{2}}$

Step 3: Rearrange to make p₂ the subject

$p_{2} = \frac{p_{1} \times T_{2}}{T_{1}}$

Step 4: Substitute in known values and calculate p₂

$p_{2} = \frac{6.2 \times 10^{5} \times 313}{303} = 6.4 \times 10^{5} Pa$

Make sure to always have the temperature, T in kelvins for all equations in this topic!

Ideal Gases (CIE A Level Physics)