PARTICLE MODEL OF MATTER · CHAPTER 10 OF 10
Compressing gases
Push the plunger of a sealed syringe and the trapped air resists being squeezed. The particles have less space, but they do not become smaller. How does reducing the volume increase the pressure—and why can compressing a gas sometimes make it warmer?
By the end, you’ll be able to…
- Explain how changing a gas’s volume affects its pressure at constant temperature.
- Describe the inverse relationship between pressure and volume.
- Use p₁V₁ = p₂V₂ to calculate pressure or volume.
- Explain why the mass and temperature must stay constant.
- Higher Tier: explain how doing work on a gas can increase its temperature.
Less space. Greater pressure.
For a fixed mass of gas at constant temperature, reducing the volume increases the pressure.
The particles have the same average kinetic energy, so they do not move faster on average. Instead, they reach the walls more frequently, increasing the average force per unit area.
Increasing the volume has the opposite effect: fewer collisions per second with each unit area of wall, so pressure decreases.
All pressure values in this chapter are absolute pressures, rather than readings above atmospheric pressure.
Squeeze the gas
Predict the pressure when the volume halves. This sealed cylinder contains a fixed mass of gas at constant temperature.
80 cm³ · 100 kPa
Starting volume and pressure.
40 cm³ · 200 kPa
Half the volume → twice the pressure.
20 cm³ · 400 kPa
One-quarter of the volume → four times the pressure.
Compare states at the same temperature. Changes are shown instantly; real measurements require time for temperature to settle. Particle motion is illustrative.
How are pressure and volume linked?
Pressure and volume are inversely proportional when the mass and temperature stay constant.
Halving the volume doubles the pressure. Doubling the volume halves the pressure. Their product stays constant:
The equation
pressure × volume = constant
p × V = constant
p = pressure in pascals (Pa)
V = volume in cubic metres (m³)
“Constant” means a value that stays the same for a fixed mass of gas at constant temperature
Why is the graph curved?
Pressure decreases as volume increases, but the graph is not a straight line. Equal increases in volume do not produce equal decreases in pressure.
At 20 cm³, pressure is 400 kPa. At 40 cm³, it is 200 kPa. At 80 cm³, it is 100 kPa.
Fixed mass · Constant temperature
Calculating a new pressure or volume
For two states of the same fixed mass of gas at constant temperature:
p₁V₁ = p₂V₂
The subscripts 1 and 2 mean before and after. For example, p₁ is the initial pressure and p₂ is the final pressure.
Use the same pressure unit on both sides and the same volume unit on both sides. For example, kPa and cm³ can be used consistently in this equation. If a question specifies Pa or m³, give the answer in those units.
To calculate final pressure:
A sealed syringe contains 60 cm³ of gas at 100 kPa. It is compressed to 20 cm³ at constant temperature. Calculate the final pressure.
p₂ = (p₁ × V₁) ÷ V₂
p₂ = (100 × 60) ÷ 20
p₂ = 300 kPa
To calculate final volume:
Gas in a sealed piston cylinder occupies 0.0040 m³ at 150,000 Pa. It expands at constant temperature until its pressure is 100,000 Pa. Calculate its final volume.
V₂ = (p₁ × V₁) ÷ p₂
V₂ = (150,000 × 0.0040) ÷ 100,000
V₂ = 0.0060 m³
To calculate initial pressure:
A fixed mass of gas expands from 25 cm³ to 50 cm³ at constant temperature. Its final pressure is 90 kPa. Calculate its initial pressure.
p₁ = (p₂ × V₂) ÷ V₁
p₁ = (90 × 50) ÷ 25
p₁ = 180 kPa
Check the direction of your answer: at constant temperature, a smaller volume should give a higher pressure. The relationship does not apply directly if gas escapes or its temperature changes.
Why can a bicycle pump get warm?
AQA: separate Physics · Higher Tier
Work is energy transferred by a force. When you push a pump’s piston, you do work on the trapped air.
During rapid compression, there may be little time for energy to transfer to the surroundings. The gas’s internal energy increases, raising its temperature. Energy can then transfer from the warmer gas to the pump.
From your push to warmer air
This shows compression with little energy transferred out during the push. It is different from the constant-temperature model used in the pressure–volume calculations.
Compression does not always produce a lasting temperature rise. If energy transfers out while the gas is compressed slowly, its temperature can remain approximately constant. Always check which conditions a question gives you.
A fixed mass of gas is compressed at constant temperature. Why does its pressure increase?
Gas at 120 kPa occupies 30 cm³. Its volume increases to 60 cm³ at constant temperature, with no gas lost. What is its new pressure?
Which conditions are needed to use p₁V₁ = p₂V₂?
A sealed syringe contains gas at 100 kPa and 60 cm³. A student compresses it to 20 cm³ and predicts a final pressure of 300 kPa. The gas is warmer after compression. Can the student rely on this prediction?
Explain the condition behind the calculation. Higher Tier: explain why the gas may have become warmer.
No. The 300 kPa prediction assumes that temperature stays constant. The gas is warmer, so p₁V₁ = p₂V₂ cannot be applied directly to these two states.
If the gas is held at 20 cm³ and allowed to return to its original temperature, its pressure becomes 300 kPa, provided no gas has escaped.
Higher Tier: pushing the piston does work on the gas. If little energy transfers out during compression, its internal energy and temperature increase.
Compressing gases
- For a fixed mass of gas at constant temperature, decreasing volume increases pressure. Increasing volume decreases pressure.
- At constant temperature, average particle kinetic energy stays the same. Compression increases the frequency of collisions per unit area of wall.
- Pressure and volume are inversely proportional: p × V = constant, so p₁V₁ = p₂V₂.
- Halving volume doubles pressure; doubling volume halves pressure.
- Use consistent units and absolute pressures. The SI units are pascals (Pa) and cubic metres (m³).
- The pressure–volume equation does not apply directly if gas enters or leaves, or if temperature changes.
- Higher Tier: doing work on a gas transfers energy to it. With little energy transferred out, its internal energy and temperature increase, as during rapid compression in a bicycle pump.