Pressure in gases (Higher Tier)
At GCSE Higher Tier, you need to apply Boyle's law and understand how work done on a gas affects its temperature.
Boyle's law
For a fixed mass of gas at constant temperature:
$pV = \text{constant}$, or equivalently $p_1 V_1 = p_2 V_2$.
- $p$ — pressure (Pa).
- $V$ — volume (m³).
So if you halve the volume (compression), the pressure doubles.
Particle explanation
Compressing a gas:
- Same number of particles, smaller volume.
- Particle density rises.
- Collisions per second on each unit area of wall increase.
- Pressure rises in proportion to 1/V.
✦Worked example— Worked example 1
A gas occupies 600 cm³ at 100 kPa. The volume is reduced to 200 cm³ at the same temperature. New pressure?
- $p_1 V_1 = p_2 V_2$.
- $100 \times 600 = p_2 \times 200 \Rightarrow p_2 = 300$ kPa.
✦Worked example— Worked example 2
A balloon containing 0.50 m³ of gas at 1.0 × 10⁵ Pa is squeezed to 0.20 m³ at constant T. Find the new pressure.
- $p_2 = (1.0 \times 10^5) \times (0.50/0.20) = 2.5 \times 10^5$ Pa.
Work done on a gas
If you compress a gas by pushing a piston in, you do work on the gas. This work is transferred to the internal energy of the gas. If insulated, the gas heats up.
- This is why a bicycle pump gets hot when you pump quickly: the air is being compressed, raising its internal energy and so its temperature.
The reverse is true: gas pushing out a piston does work on the surroundings and cools (think of a refrigerant or aerosol spray feeling cold as it expands).
Combining temperature and Boyle (preview)
For a gas changing both pressure, volume and temperature, the combined gas law is:
$\dfrac{p_1 V_1}{T_1} = \dfrac{p_2 V_2}{T_2}$
(beyond strict GCSE in some tiers, but useful).
⚠Common mistakes
- Using volumes in different units on each side of the equation — both must be the same unit.
- Forgetting the "constant temperature" requirement of Boyle's law.
- Forgetting that compressing without insulation lets heat escape — the gas may not actually heat up much.
- Mistaking "doing work on a gas" for adding heat. They both raise internal energy, but they're different processes.
➜Try this— Quick check
A syringe at atmospheric pressure (100 kPa) holds 60 mL of air. The plunger is pushed in to 20 mL with the tip blocked, at constant temperature. New pressure?
- $p_2 = 100 \times (60/20) = 300$ kPa.
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