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Gas pressure and temperature Why does a gas push harder when it is heated or squeezed?

Foundation and Higher · AQA · 45 minutes

Students vote on what a hot car does to a football pumped up in the cold, then explain it with moving particles. They squeeze and heat a gas in a simulation, turn °C into kelvin and use p V = constant. Slides to present, a vote that shows who's stuck, practice and homework.

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The idea in one minute

A gas is tiny particles moving fast in random directions. They hit the walls of their container and bounce off, and each hit pushes on the wall: the pressure is the force on each square metre of wall, at right angles to it. The temperature goes with the particles' average kinetic energy, so heating a gas in a sealed, rigid container makes them move faster: they hit the walls more often and harder, and the pressure rises. Kelvin temperatures start at absolute zero, −273 °C, where the particles have the least energy they can: K = °C + 273. Squeeze a fixed mass of gas into a smaller volume at a constant temperature and the particles hit the walls more often: p V stays the same, so half the volume gives double the pressure. Pushing in a pump's piston does work on the gas, and that warms it.

The lesson starts with a prediction before anyone explains: is a football harder, softer or the same after a day in a hot car? Students then squeeze and heat a gas in a simulation (a model of particles in a box, not a substitute for a practical), predicting each reading before they move a slider. It is for Foundation and Higher; p V = constant and doing work on a gas are marked (Higher).

By the end, students can

  • describe a gas as particles in random motion, and explain its pressure as their hits on the walls
  • explain why heating a gas at a fixed volume raises its pressure, using the particles' kinetic energy
  • turn °C into kelvin and back with K = °C + 273, and say what absolute zero is
  • use p₁ V₁ = p₂ V₂ for a fixed mass of gas at a constant temperature
  • (Higher) explain why doing work on a gas, as in a bicycle pump, raises its temperature

Key words

  • particle
  • random motion
  • pressure
  • pascal (Pa)
  • kinetic energy
  • temperature
  • kelvin (K)
  • absolute zero
  • volume
  • internal energy
  • work done

Before this lesson

Students should know the particle model of solids, liquids and gases, and that kinetic energy is the energy an object has because it moves. Density comes first.

Taught in Density.

The lesson, step by step

45 minutes in total. The stretch is optional.

  1. 1 · Think5 min

    A ball left in a hot car

    A football is pumped up in a cold garage at 5 °C.

    It is left all day in a car at 40 °C.

    No air gets in or out. Is it now…

    A: Harder

    B: Softer

    C: The same

    Vote first. Then say why, with particles.

    Write here

    5 min 1 · Hook · students think · the slides say “Think”

    A ball left in a hot car

    A football pumped up in the cold, then left in a hot car: students vote harder, softer or the same before anyone explains.

    Say

    “A football is pumped up in a cold garage at 5 °C. It's left all day in a car at 40 °C, and no air gets in or out. Is it harder, softer, or the same?”

    Ask
    • Nothing got in or out. So what could have changed inside the ball?
    • What if you left it in a freezer instead?
    Watch for

    Saying 'the same, no air got in': keep it, the explain step needs it.

    For the teacher

    Give a minute of silent thinking, then vote. Many say the same, as no air got in; some say hot air 'expands' or 'rises'.

    Don't explain yet. It is harder: the same particles move faster, so they hit the inside of the ball more often and harder. That is the next step.

    Take a vote with Ask the class: harder, softer or the same. Keep the votes on the board for the explain step.

    Shorter: Vote once, no discussion (−2 min).

  2. 2 · Watch12 min

    A gas: particles on the move

    Tiny particles, far apart

    Moving fast, in random directions, at many speeds

    They hit each other and the walls, and bounce off

    Each hit pushes on the wall

    Pressure: the force on each square metre of wall

    Pascals: 1 Pa = 1 N/m²; the air around us ≈ 100 kPa

    The force is at right angles to the wall

    Pressure: the hits on the walls

    2 · Watch

    Temperature: how fast they move

    Temperature: the particles' average kinetic energy

    Hotter: faster, on average

    Heat a gas in a sealed, rigid box:

    • more hits each second

    • and each hit is harder

    so the pressure rises

    The hook: the same air, faster particles, a harder ball

    Hotter: more hits, and harder hits

    2 · Watch

    Kelvin: counting from zero

    Absolute zero: −273 °C = 0 K

    The particles have the least energy they can

    Nothing can be colder

    K = °C + 273 °C = K − 273

    27 °C = 300 K; 100 °C = 373 K

    Double the kelvin temperature:

    double the particles' average kinetic energy

    Into kelvin, add 273: never a negative kelvin

    2 · Watch

    Squeeze it: p V = constant

    Same gas, same temperature

    Smaller volume: more hits a second

    p₁ V₁ = p₂ V₂ (Boyle's law)

    x: volume V (litres)

    y: pressure p (kPa)

    Half the volume: double the pressure

    Move k: p × V stays the same

    2 · Watch

    Try it: squeeze it, heat it

    Now: 300 K, 2 litres, 100 kPa

    1. Halve the volume: predict p

    2. Back to 2 litres, then 600 K: p?

    3. Is 600 K double 27 °C?

    4. 600 K and 1 litre: predict p

    Predict first, then move one slider

    Gas pressurePressure 100 kPa (27 °C) · hotter, smaller or more particles: more hits on the walls

    2 · Watch

    (Higher) A pump: work warms it

    Push a pump's piston in quickly

    Your force moves: you do work on the gas

    Particles bounce off the moving piston faster

    The gas's internal energy rises

    So its temperature rises: the pump gets warm

    Energy in by doing work, not by heating

    Work done on a gas can warm it

    12 min 2 · Explain · you explain · the slides say “Watch”

    Particles, pressure, temperature and volume

    Pressure as the particles' hits on the walls; temperature as their average kinetic energy, which answers the hook; kelvin; then p V = constant and (Higher) the warm pump.

    Say

    “A gas is particles flying about. Everything today, the pressure, the temperature, the pump, comes from what those particles do when they hit the walls.”

    Ask
    • A particle hits the wall and bounces back. What does the wall feel?
    • If the particles moved faster, what two things would change about the hits?
    • Halve the box's volume. What happens to the number of hits each second?
    Watch for

    Saying the particles get bigger or expand when heated: they stay the same size and move faster.

    Celsius into kelvin

    K = °C + 273

    27 °C = 27 + 273 = 300 K

    100 °C = 373 K; 0 K = −273 °C, absolute zero

    Squeezed: p₁ V₁ = p₂ V₂

    100 kPa in 2.0 litres, squeezed to 0.50 litres

    p₂ × 0.50 = 100 × 2.0 = 200

    p₂ = 200 ÷ 0.50 = 400 kPa: a quarter of the volume, four times the pressure

    For the teacher

    Particles: a gas is tiny particles, far apart, moving fast in random directions at many speeds. They hit each other and the walls, and bounce off.

    Pressure: each hit pushes on the wall. The pressure is the force on each square metre of wall, in pascals (1 Pa = 1 N/m²); the air around us is about 100 kPa. The force is always at right angles to the wall.

    Temperature: it goes with the particles' average kinetic energy. Heat a gas in a sealed, rigid container and the particles move faster: they hit the walls more often, and each hit is harder, so the pressure rises. That answers the hook: the ball is harder (5 °C to 40 °C is 278 K to 313 K, about 13% more pressure if its size stays the same).

    Kelvin: absolute zero, −273 °C, is 0 K, where the particles have the least energy they can. K = °C + 273. Doubling the kelvin temperature doubles the particles' average kinetic energy; doubling a temperature in °C does not.

    Try it: the box starts at 300 K, 2 litres and 40 particles, reading 100 kPa. Halve the volume: 200 kPa. Back to 2 litres and heat it to 600 K: 200 kPa, and the readout says 327 °C, not 54 °C. Both at once: 400 kPa.

    Volume: for a fixed mass of gas at a constant temperature, p V = constant (Boyle's law), so p₁ V₁ = p₂ V₂. In a smaller volume the particles reach the walls more often: more hits each second on each square metre.

    (Higher) Work: pushing a pump's piston in, the force moves through a distance, so it does work on the gas. Particles bounce off the moving piston faster, the gas's internal energy rises, and so does its temperature.

    Before the Try it slide, ask the class to predict each reading on mini whiteboards; then move one slider at a time, or let a student drive it.

    Shorter: Skip the graph and the pump slide; say p V = constant in a line (−4 min).

  3. 3 · Your turn12 min

    Your turn: the quiz

    Questions 1–4: particles and kelvin

    Questions 5–6: p₁ V₁ = p₂ V₂

    Bigger or smaller? Decide before you work it out

    Same temperature, same units on both sides

    Do the twins first, then open the quiz.

    3 · Your turn

    Worked, then yours

    I do: −18 °C: −18 + 273 = 255 K

    You do: liquid nitrogen at 77 K: in °C?

    I do: 150 kPa, 4.0 L → 3.0 L: 600 ÷ 3.0 = 200 kPa

    You do: 120 kPa, 5.0 L → 2.0 L: the new pressure?

    I do: 60 cm³ at 100 kPa → 250 kPa: 6000 ÷ 250 = 24 cm³

    You do: 80 cm³ at 100 kPa → 160 kPa: the new volume?

    Write p₁ V₁ = p₂ V₂ first, then fill it in.

    Write here

    Its answers' slide comes with your copy.

    12 min 3 · Your turn · students write

    Kelvin and p V, then yours

    Worked examples beside their twins: °C into kelvin and back, then a new pressure and a new volume with p₁ V₁ = p₂ V₂; then a short quiz.

    Say

    “I do one, you do its twin. Write the formula first, then the numbers.”

    Ask
    • Is the new volume bigger or smaller? So should the pressure go up or down?
    • Into kelvin: should the number get bigger or smaller?
    Watch for

    Dividing the wrong way in p₁ V₁ = p₂ V₂: a squeezed gas whose pressure went down. Ask which way it should go before they work it out.

    Celsius and kelvin, both ways

    A freezer at −18 °C: −18 + 273 = 255 K

    A gas at 350 K: 350 − 273 = 77 °C

    Into kelvin: add 273. Into °C: take 273 away.

    Then theirs

    Liquid nitrogen boils at 77 K. What is that in °C?

    A new pressure

    150 kPa in 4.0 litres, squeezed to 3.0 litres at the same temperature

    p₂ × 3.0 = 150 × 4.0 = 600

    p₂ = 600 ÷ 3.0 = 200 kPa: smaller volume, bigger pressure

    Then theirs

    120 kPa in 5.0 litres is squeezed to 2.0 litres. Its new pressure?

    A new volume

    A sealed syringe: 60 cm³ of air at 100 kPa

    Pushed in until the pressure is 250 kPa

    250 × V₂ = 100 × 60 = 6000; V₂ = 6000 ÷ 250 = 24 cm³

    Then theirs

    80 cm³ of air at 100 kPa is squeezed until it is at 160 kPa. Its new volume?

    Show your working on paper. K = °C + 273. For p₁ V₁ = p₂ V₂ the temperature stays the same; use the same units on both sides.

    1. Gas particles move fast in ___ directions. Each hit on a wall pushes on it; the force on each square metre of wall is the ___. Heat the gas and its particles move ___ on average.
    2. Turn 37 °C, body temperature, into kelvin.
    3. A gas is at 200 K. What is that in °C?
    4. A sealed bottle of air is moved from a warm room into a fridge. What happens to the pressure inside?
      1. It goes down: the particles move more slowly, so they hit the walls less often and less hard
      2. It goes up: cold air is denser
      3. It stays the same: no air got in or out
      4. It goes down: the particles shrink
    5. 1.5 litres of gas at 200 kPa expands, at the same temperature, to 6.0 litres. What is its pressure now, in kPa?
    6. A balloon holds 3.0 litres of air at 100 kPa. It is squeezed, at the same temperature, until the pressure is 120 kPa. What is its volume now, in litres?
    For the teacher

    Kelvin first: say each conversion aloud with its direction (into kelvin, add; into °C, take away) and ask whether the answer should be bigger or smaller before they work it out.

    For p₁ V₁ = p₂ V₂, write the formula, then the four letters with their numbers, then the one to find. Ask first whether the gas was squeezed or let expand: that says whether the answer is bigger or smaller.

    Foundation students who won't meet p V = constant do the kelvin pair and the quiz's questions 1–4; the rest do all three pairs and the whole quiz.

    Students write the twins on paper or the board, then answer the quiz on their own devices. Open the answers slide once most have done the twins.

    Shorter: The kelvin pair and the new pressure pair only (−4 min).

    Longer: Each student writes a squeezed-gas question for a partner, with its answer worked first (+3 min).

  4. 4 · Vote and practise12 min

    Vote first

    A sealed, rigid can of air is heated.

    Why does the pressure inside rise?

    A: The particles get bigger

    B: They move faster: more hits, and harder

    C: Heating makes more particles

    D: They vibrate faster in fixed places

    Choose on your own, then say why.

    4 · Vote and practise

    Practise: show your working

    1. 120 °C in kelvin?

    2. What is absolute zero?

    3. Heated in a sealed box: speed and pressure?

    4. −40 °C in kelvin?

    5. 250 cm³ at 100 kPa → 100 cm³: pressure?

    Into kelvin: add 273.

    Write here

    4 · Vote and practise

    Reason it out

    6. Squeezed at the same temperature: why more pressure?

    7. 20 °C to 40 °C: does the pressure double?

    8. (Higher) Why does a pump warm up?

    9. A bubble rises from 200 kPa to 100 kPa

    10. A cylinder: 0.040 m³ at 1500 kPa

    Stretch: how many balloons does it fill?

    Say what the particles do, then the numbers.

    12 min 4 · Who's stuck? · students vote · the slides say “Vote and practise”

    Vote, then practise

    One question shows who still pictures particles growing, multiplying or vibrating in place; then practice in levels, and a gas cylinder as the stretch.

    Say

    “Choose an answer on your own. Nobody talks until everyone has chosen.”

    Ask
    • Does the number of particles change? Their size? So what does change?
    Watch for

    Choosing 'the particles get bigger': ask what a particle is, and whether heating could make it grow.

    Show your working on paper. K = °C + 273. In p₁ V₁ = p₂ V₂ the mass of gas and its temperature stay the same. Questions marked (Higher) are for Higher; the stretch is optional.

    The question that shows who's stuck

    1. A sealed, rigid can of air is heated. Why does the pressure inside rise?
      1. The particles get bigger
      2. They move faster: more hits, and harder
      3. Heating makes more particles
      4. They vibrate faster in fixed places
    In your Classroom, as they answer (an example)
    • A7
    • B11
    • C3
    • D4

    Each wrong answer is a different mistake. While they answer, your Classroom shows who chose which, so you know in seconds whom to help with what.

    1. Turn 120 °C into kelvin.
    2. What is absolute zero?
      1. 0 °C, where water freezes
      2. −273 °C, where the particles have the least energy they can
      3. −100 °C, the coldest a gas can be
      4. 273 K, where a gas turns into a liquid
    3. A gas is heated in a sealed, rigid box. What happens to the particles' average speed, and to the pressure?
      1. Both go up
      2. The speed goes up; the pressure stays the same
      3. The speed stays the same; the pressure goes up
      4. Both stay the same
    4. A winter night in the Arctic is −40 °C. What is that in kelvin?
    5. A syringe holds 250 cm³ of air at 100 kPa. Its end is sealed and it is pushed in slowly, so the temperature stays the same, to 100 cm³. What is the pressure now, in kPa?
    6. A gas is squeezed into a smaller volume at the same temperature. Why does its pressure rise?
      1. The particles move faster
      2. The particles hit the walls more often: they have less far to go
      3. The particles are squashed smaller
      4. There are more particles in the box
    7. Ali heats a sealed, rigid can of gas from 20 °C to 40 °C. He says the pressure doubles. Is he right?
      1. Yes: the temperature doubled
      2. No: in kelvin it goes from 293 K to 313 K, much less than double
      3. No: heating makes the pressure fall
      4. Yes: twice as many particles hit the walls
    8. (Higher) Pump up a tyre quickly and the air in the pump warms up. Why?
      1. Pushing the piston does work on the air: its particles bounce off the moving piston faster
      2. The particles are squashed together and rub against each other
      3. Squeezing the air makes more particles
      4. The air warms because there is less room for the heat to spread out
    9. A diver breathes out a bubble of 3.0 cm³ where the pressure is 200 kPa. It rises to the surface, where the pressure is 100 kPa. If its temperature stays the same, what is its volume at the surface, in cm³?
    10. A gas cylinder holds 0.040 m³ of helium at 1500 kPa. What volume would that helium take up at 100 kPa and the same temperature, in m³?
    11. Stretch: the helium fills balloons of 0.010 m³ each, at 100 kPa. When it stops, the cylinder is still full of helium at 100 kPa. How many balloons does it fill?

    Support · Draw the box with a few particles and arrows. Hotter: longer arrows. Smaller box: shorter trips to the wall. Then say what happens to the hits: how often, and how hard.

    For the teacher

    Everyone chooses before anyone explains. Then ask in turn: what changed about the particles? Did their number change? Their size? What does faster mean for the hits?

    Questions 1–4 build fluency; 5 changes the look; 6–8 ask for reasons; 9–10 are exam-style. The stretch follows on from 10.

    Students show their working on paper or the board; the quiz keeps their final answers.

    If many chose A or D, act it out before they practise: students as particles walking, then walking fast, inside a marked-out box, counting the hits on one wall.

    Shorter: After the vote, questions 1–5 only (−5 min).

    Longer: The stretch: how many balloons a gas cylinder fills (+8 min).

  5. 5 · Show what you know4 min

    Squeeze it, then heat it

    1. A gas is at 57 °C: in kelvin?

    2. 90 kPa in 4.0 litres,

    squeezed into 1.5 litres: the new pressure?

    3. Then heated at that volume:

    what happens to the pressure, and why?

    Bigger or smaller? Decide first.

    Write here

    4 min 5 · Exit · students show · the slides say “Show what you know”

    Squeeze it, then heat it

    A kelvin conversion, a squeezed gas and a heated one show who adds 273, who divides the right way and who explains with particles.

    Say

    “Which way should each answer go, bigger or smaller? Decide that first.”

    Watch for

    Answering 33.75 kPa: the pressure went down for a squeezed gas.

    Decide first whether each answer should be bigger or smaller.

    1. A gas is at 57 °C. What is its temperature in kelvin?
    2. A gas at 90 kPa fills 4.0 litres. At the same temperature it is squeezed into 1.5 litres. What is its new pressure, in kPa?
    3. The squeezed gas is then heated, its volume kept the same. What happens to its pressure, and why?
      1. It goes up: the particles move faster, so they hit the walls more often and harder
      2. It stays the same: the volume didn't change
      3. It goes up: the particles get bigger and fill the space
      4. It goes down: a hot gas spreads out
    For the teacher

    A gas is at 57 °C: its temperature in kelvin? Then 90 kPa in 4.0 litres, squeezed into 1.5 litres at the same temperature: the new pressure?

    Last, heated at that volume: what happens to the pressure, and why?

    Those who divided the wrong way need p₁ V₁ = p₂ V₂ again next lesson; set the homework.

    Longer: Why does a tyre read a higher pressure after a long, fast drive? Answer with particles. (+4 min).

One to one: before any formula, ask the student to describe one particle's journey across the box and what the wall feels each time it arrives; let them drive the simulation while you only ask what they predict before each move.

Homework: Gas pressure and temperature

K = °C + 273. Explain with particles where a question asks why. For questions 4 and 5 write p₁ V₁ = p₂ V₂ first, then the numbers. Question 6 is Higher.

  1. Turn 15 °C into kelvin, and 450 K into °C.
  2. A sealed tin of air is heated. Explain, using particles, why the pressure inside goes up.
  3. What is absolute zero, in °C and in kelvin? What is true of the particles there?
  4. 2.4 litres of gas at 100 kPa is squeezed, at the same temperature, into 0.80 litres. Find its new pressure.
  5. A weather balloon holds 5.0 m³ of helium at 100 kPa. High up, the pressure is 25 kPa. If its temperature stayed the same, what would its volume be?
  6. (Higher) Pump up a tyre quickly and the pump gets warm. Explain why.

Print the worksheet with working space and homework. Teacher answers come with your Library copy.

Teaching gas pressure and temperature: common questions

Is gas pressure on Foundation and Higher, and in combined science?

In AQA GCSE Physics (8463) the particle model of a gas, and how heating a gas at a fixed volume raises its pressure, are for both tiers, and in combined science too. Pressure and volume (p V = constant) and doing work on a gas are in separate physics only, and doing work on a gas is Higher tier only. The lesson marks the work done on a gas (Higher); Foundation students can do everything else.

Why use kelvin at all?

Because it counts from absolute zero, where the particles have the least energy they can. Doubling a kelvin temperature doubles the particles' average kinetic energy; doubling a temperature in °C does not, which is why 20 °C to 40 °C barely changes a gas's pressure. Students meet kelvin again in chemistry and at A level; the conversion takes a few minutes.

Do the particles stop moving at absolute zero?

At GCSE, absolute zero (−273 °C, 0 K) is where the particles have the least kinetic energy they can, and nothing can be colder; 'they stop moving' is the usual simple way to say it. The exact value is −273.15 °C; GCSE questions use 273.

How does the simulation work out its pressure?

The box is a model of a gas whose particles only hit and bounce: its pressure goes up in proportion to the kelvin temperature and to the number of particles, and p × V stays the same at a fixed temperature. Its numbers are set so 40 particles at 300 K in 2 litres read 100 kPa, about the pressure of the air around us. It is a model, not a substitute for a practical.

Doesn't a football also get a little bigger in a hot car?

A little, but a well pumped ball hardly stretches, so its volume stays nearly the same and most of the change is in the pressure. That is why the lesson says a sealed, rigid container when it explains heating at a fixed volume.

Can I use the lesson without creating an account?

Yes. Read the lesson, print the worksheet and open its slides, with the gas simulation, without signing in; nothing you draw there is kept. A free teacher account keeps the whole lesson in your Library to change and teach, with the quizzes, the answers and the answer slides.

Curriculum reference: AQA GCSE Physics 8463: 4.3.3 (particle model and pressure: particle motion in gases, the temperature of a gas and its pressure at a constant volume; pressure in gases and p V = constant, physics only; increasing the pressure of a gas by doing work on it, physics only, Higher tier only).

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