Section 1 of 5Gas Pressure from Collisions
Gas pressure is caused by the countless tiny impacts of moving particles on the surfaces around them.
Random motion
- Gas particles move quickly in straight lines and change direction only when they collide with each other or with a wall.
Force on a wall
- Each particle hitting a wall pushes on it briefly, and billions of impacts together give a steady force.
Pressure
- Pressure is force per unit area, so more frequent or harder impacts on the same wall area mean a larger pressure.
Direction
- The force from the gas acts at right angles to the surface at every point of the container.
Section 2 of 5Squeezing a Gas
Consider a sealed syringe containing a fixed mass of air at constant temperature.
1
Pushing the plunger in reduces the volume available, so the same particles are squeezed into a smaller space.
2
The particles are now closer together, so each one travels a shorter distance between collisions with the walls.
3
More collisions occur on each square metre of wall every second, so the total force on that area becomes larger.
4
Because pressure is force per unit area, the pressure of the gas increases when its volume decreases.
5
Pulling the plunger out does the opposite: the volume increases, collisions become less frequent and the pressure falls.
Section 3 of 5The Relationship pV = constant
The Relationship pV = constant
Condition
- The relationship applies only to a fixed mass of gas kept at a constant temperature.
Equation
- p₁V₁ = p₂V₂ links the pressure and volume of the gas before and after a change.
Inverse proportion
- Halving the volume doubles the pressure, which is the pattern of an inversely proportional relationship.
Units
- Pressure is in pascals, Pa, and volume in cubic metres, m³, but any consistent pair of units gives the right ratio.
| Volume change | Pressure change | Reason |
|---|---|---|
| Halved | Doubled | Twice as many collisions per unit area |
| Doubled | Halved | Half as many collisions per unit area |
Section 4 of 5Worked Example
Question
- A gas has a volume of 0.50 m³ at a pressure of 1.2 × 10⁵ Pa.
- It is compressed to 0.20 m³ at constant temperature.
- Calculate the new pressure.
- Write the equationp₁V₁ = p₂V₂.
- Substitute(1.2 × 10⁵) × 0.50 = p₂ × 0.20.
- Rearrangep₂ = (1.2 × 10⁵ × 0.50) ÷ 0.20 = 6.0 × 10⁴ ÷ 0.20.
- Checkthe volume has fallen, so the pressure must have risen, and 3.0 × 10⁵ Pa is larger than 1.2 × 10⁵ Pa.
Answer p₂ = 3.0 × 10⁵ Pa
Section 5 of 5Exam Checklist & Tips
1.3.2 – Key Points for the Exam
- Pressure Force acting per unit area, measured in pascals (Pa).
- Compression Reducing the volume of a gas by pushing on it.
- Inversely proportional When one quantity doubles the other halves, so their product stays constant.
- Fixed mass No gas enters or leaves, so the number of particles stays the same.
Common Mistakes
- Saying the particles get bigger or hotter when compressed;
- at constant temperature their speed is unchanged and only collisions per second rise.
- Writing that pressure rises because particles move faster, which applies when the temperature changes, not here.
- Using the equation without checking that temperature and mass are constant.
- Getting the answer the wrong way round; always check that a smaller volume gives a larger pressure.