The Pressure Law

If the volume V of an ideal gas is constant, the pressure law is given by:

P ∝ T

This means the pressure is proportional to the temperature

Gas Laws Molecular Model (3), downloadable AS & A Level Physics revision notes

Pressure and temperature are proportional. Doubling temperature also doubles the pressure for a gas in a fixed volume.

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

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

Where:
- p₁ = initial pressure (Pa)
- p₂ = final pressure (Pa)
- T₁ = initial temperature (K)
- T₂ = final temperature (K)

Pressure Law, downloadable AS & A Level Physics revision notes

Pressure law graph representing temperature (in °C) directly proportional to the volume

Worked example

The pressure inside a bicycle tyre is 5.10 × 10⁵ Pa when the temperature is 279 K. After the bicycle has been ridden, the temperature of the air in the tyre is 299 K. Calculate the new pressure in the tyre, assuming the volume is unchanged.

Answer:

Step 1: Choose the correct ideal gas law

Volume is constant, so the pressure law must be used

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

Step 2: Write down the known quantities

p₁ = 5.10 × 10⁵ Pa
T₁ = 279 K
T₂ = 299 K

Step 3: Rearrange for p₂ and substitute values into the pressure law

To make p₂ the subject, multiply both sides by T₂to cancel out the T₂ in the fraction under p₂

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

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

Substitute the known quantities

$p_{2} = \frac{5.10 \times 10^{5}}{279} \times 299$

$p_{2} = 5.47 \times 10^{5} Pa$

Examiner Tip

Remember when using gas laws the temperature T must always be in kelvin (K)!

The Pressure Law (Edexcel IGCSE Physics: Double Science)

Revision Note

The pressure law

Worked example

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Author: Katie M