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6.6–6.7 Gas Pressure, Temperature and Volume

GCSE Physics · AQA · Chapter 6: Molecules and Matter

A free GCSE Physics lesson for AQA (8463) from OBA School: gas pressure from molecular impacts, pressure and temperature, Brownian motion, Boyle’s law p V = constant, work done on a gas. Watch the video, read the explanation and worked examples, then try the revision questions. You can work through the full lesson, with every video, practice quizzes and printable worksheets with mark schemes, in our free online course.

What you will learn

  • Explain gas pressure in terms of molecules colliding with surfaces, and why it increases when a sealed gas is heated
  • Link the temperature of a gas to the average kinetic energy of its molecules, and explain random (Brownian) motion of smoke particles
  • Describe how the pressure of a fixed mass of gas at constant temperature depends on its volume, and explain why
  • Use p V = constant (p₁V₁ = p₂V₂) for a fixed mass of gas at constant temperature
  • (Higher tier) explain why doing work on a gas, e.g. in a bicycle pump, can raise its temperature

Key words

  • Gas pressure: The total force per unit area exerted by gas molecules hitting a surface. It acts at right angles to the surface.
  • Average kinetic energy: The mean kinetic energy of the gas molecules. The higher the temperature, the greater the average kinetic energy.
  • Random motion: Unpredictable motion: speed and direction keep changing because of collisions.
  • Brownian motion: The jerky, random movement of small visible particles (e.g. smoke) caused by collisions with fast-moving molecules.
  • Fixed mass of gas: A sealed sample, so the number of molecules does not change.
  • Boyle’s law: For a fixed mass of gas at constant temperature, p V = constant.

Gas pressure and temperature

Gas molecules move at high speed in random directions. Each time one hits a wall and bounces off, it exerts a tiny force on the wall. Billions of impacts every second add up to a steady force. The force per square metre is the pressure, and its total effect is a net force at right angles to each wall.

The temperature of a gas is linked to the average kinetic energy of its molecules. If a gas in a sealed container (fixed volume) is heated:

  • its molecules gain kinetic energy and move faster on average
  • they hit the walls more often (more impacts per second)
  • each impact is harder (bigger force)
  • so the pressure increases.

Safety: Never heat a sealed can or aerosol. As the temperature rises, the gas pressure inside can rise enough to burst it.

Pressure–temperature experiment

A flask of dry air is connected to a pressure gauge and placed in a water bath. The water is heated in stages; at each stage it is stirred so the water and air are at the same, even temperature, then the temperature and pressure are read. (This is done by a teacher behind a safety screen.)

The graph is a straight line: the pressure rises by the same amount for each equal rise in temperature. It does not go through the origin, because the air still has a pressure (about atmospheric pressure, 100 kPa) at 0 °C – the molecules are still moving.

Evidence for moving molecules: Brownian motion

Air molecules are far too small to see. But if smoke is put into a small glass cell, lit from the side and viewed through a microscope, the smoke particles are seen as tiny specks of light that jiggle about at random, constantly changing direction.

The air molecules are moving fast in random directions and hit each smoke particle unevenly, giving it a push in a random direction each time. This is evidence that gas molecules are in constant, fast, random motion. If the air is warmer, the molecules move faster and the smoke particles jiggle more.

Pressure and volume: Boyle’s law

If a fixed mass of gas is squashed into a smaller volume slowly (so its temperature stays constant), its pressure increases. The molecules have the same average speed, but they have less distance to travel between impacts, so they hit the walls more often. More impacts per second on each square metre means a greater pressure.

p V = constant (fixed mass of gas at constant temperature)

p = pressure in pascals (Pa); V = volume in metres cubed (m³)

For a change from state 1 to state 2: p₁ V₁ = p₂ V₂

Pressure is inversely proportional to volume: double the volume, halve the pressure.

Worked example: a bike tyre pump

A pump contains 60 cm³ of air at 100 kPa. The outlet is blocked and the handle is pushed in slowly until the volume is 25 cm³. Calculate the new pressure.
p₁V₁ = p₂V₂: 100 × 60 = p₂ × 25
p₂ = 6000 ÷ 25 = 240 kPa

Answer: 240 kPa

Worked example: a gas cylinder

A cylinder holds 0.050 m³ of gas at 1.2 × 10⁶ Pa. What volume will this gas take up at 1.0 × 10⁵ Pa, at the same temperature?
V₂ = p₁V₁ ÷ p₂ = (1.2 × 10⁶ × 0.050) ÷ 1.0 × 10⁵

Answer: 0.60 m³

Exam tip: In p₁V₁ = p₂V₂ you may use kPa and cm³ instead of Pa and m³, as long as you use the same units on both sides.

Doing work on a gas (Higher tier)

To compress a gas you must push against the force from its pressure, so work is done on the gas. This energy goes into the gas’s internal energy store. If the gas is compressed quickly, the energy cannot be transferred to the surroundings fast enough, so the molecules’ average kinetic energy increases and the temperature of the gas rises. That is why a bicycle pump gets warm when you pump hard.

If the gas is compressed slowly, energy is transferred to the surroundings by heating at the same rate as work is done, so the temperature stays constant – the condition for Boyle’s law.

Common mistakes

  • Saying the molecules “get bigger” or “expand” when a gas is heated. The molecules move faster; they do not change size.
  • Explaining pressure only as “more collisions”. Say collisions with the walls, more often and (for heating) with more force.
  • Using p V = constant when the temperature changes. It only works for a fixed mass at constant temperature.
  • Mixing units, e.g. kPa on one side and Pa on the other, in p₁V₁ = p₂V₂.

Revision questions

Try these, then check your answers below each one.

Question 1. What causes the pressure of a gas on the walls of its container? (Choose from: Gas molecules colliding with the walls, Gas molecules attracting the walls, The weight of the container, Gas molecules expanding when they are hot.)

Answer: Gas molecules colliding with the walls

Working: Each molecule that hits a wall and bounces back exerts a small force on it. The total force per unit area of all these impacts is the gas pressure.

Question 2. The temperature of a gas is linked to which property of its molecules? (Choose from: Their average kinetic energy, Their size, Their number, Their mass.)

Answer: Their average kinetic energy

Working: The higher the temperature, the greater the average kinetic energy (and speed) of the molecules.

Question 3. True or false? Smoke particles in air move about at random because they are hit unevenly by fast-moving air molecules.

Answer: True

Working: True. This random (Brownian) motion is evidence that air molecules are moving fast in random directions.

Related lessons

Continue in the full course

This lesson is section 6.6–6.7 (AGCPH0606) of our free GCSE Physics course for AQA. In the full course you get every video for this section, a self-marking practice quiz, a printable worksheet with a mark scheme, chapter tests, and your progress saved. Go to the full GCSE Physics course.

 

 

 

 

 

 

 

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