GCSE · Physics · Edexcel · Spec 1PH0

Boyle's law: P1 V1 = P2 V2

Squeeze a trapped gas into half the space, without warming it, and its pressure doubles.

Squeeze a trapped gas — same gas, same temperature

Volume V (cm³): 30. Pressure p (kPa): 200. p × V: 6000 kPa cm³

Drag the dot left to squeeze the gas. Try 40 → 20 cm³, then 20 → 10 cm³, and keep an eye on p × V.

Watch out: It's a curve, not a straight line. Squeezing from 40 to 30 cm³ adds 50 kPa, but squeezing from 20 to 10 cm³ adds 300 kPa — equal squeezes do not give equal pressure rises.

Squeeze it into a quarter of the space

A fixed mass of gas at 120 kPa is squeezed, at constant temperature, into a quarter of its starting volume. What is its new pressure?

Your estimate

300 kPa

A fixed mass of gas at 120 kPa is squeezed, at constant temperature, into a quarter of its starting volume. What is its new pressure? Estimate between 0 kPa and 600 kPa.

0 kPa600 kPa

When does p × V actually stay the same?

You want to use p × V = constant on some gas, comparing it before and after a change.

Which is closest to what you think right now?

Only the temperature has to stay the same. It doesn't matter if some gas gets in or out.Only the amount of gas has to stay the same. The temperature can change.Both: the mass of gas must stay fixed and the temperature must stay constant.Neither. p × V stays the same for any change to any gas.

How sure are you?

I'm sureI think soI'm guessing

Only the temperature has to stay the same. It doesn't matter if some gas gets in or out.

This is a common misconception

Temperature is one of the two conditions — but the amount of gas matters too. If gas leaks out or more is pumped in, you are no longer comparing the same gas in two states, and p × V is no longer the same number. The mass of gas has to stay fixed.

Only the amount of gas has to stay the same. The temperature can change.

This is a common misconception

Keeping the gas sealed in is half of it. If the gas warms up or cools down during the change, p × V does not stay the same either, so the rule would give the wrong answer. The temperature has to stay constant too.

Both: the mass of gas must stay fixed and the temperature must stay constant.

This matches the evidence

Exactly. Seal the gas in so none gets in or out, and keep its temperature steady. Under those two conditions — and only then — p × V stays the same, whatever you do to the volume.

Neither. p × V stays the same for any change to any gas.

This is a common misconception

It's tempting, because the rule looks so tidy. But it is not true for every change. Let gas escape, or heat it, and p × V changes. The rule only holds for a fixed mass of gas at constant temperature.

Fixed mass, constant temperature: check both before you use P1 × V1 = P2 × V2.

Your turn to make the decisions

A fixed mass of gas has a volume of 40 cm³ at a pressure of 150 kPa. At constant temperature the pressure is raised to 200 kPa. What is its new volume?

Known: P1 = 150 kPa, V1 = 40 cm³, P2 = 200 kPa. Unknown: V2.Label each value 1 (before) or 2 (after) first — it makes the next steps automatic.
P1 × V1 = P2 × V2This is just 'p × V stays the same', written for the gas before (1) and after (2) the change.
missing step

Which line is step 3?

V2 = (P2 × V1) ÷ P1V2 = (P1 × V1) ÷ P2V2 = P1 × V1 × P2V2 = (P1 × P2) ÷ V1

Find the line where the mark is lost

A gas has a volume of 0.0006 m³ at a pressure of 100 kPa. It is compressed at constant temperature until its volume is 200 cm³. Calculate its new pressure.

A student's answer — which line goes wrong?

P1 = 100 kPa, V1 = 0.0006 m³, V2 = 200 cm³
P1 × V1 = P2 × V2, so P2 = (P1 × V1) ÷ V2
P2 = (100 × 0.0006) ÷ 200
P2 = 0.06 ÷ 200
P2 = 0.0003 kPa

WHAT YOU'VE LEARNED

A quick recap of today's lesson.

Squeeze a trapped gas at a steady temperature and it pushes back harder — and the maths behind it is one multiplication.

What you need to know

Boyle's law only applies to a fixed mass of gas kept at a constant temperature.
Under those two conditions, pressure × volume stays constant (p × V = constant).
Pressure is inversely proportional to volume: halve the volume and the pressure doubles; double the volume and the pressure halves.
P1 × V1 = P2 × V2 links the gas before (1) and after (2) a change; rearrange it for the unknown pressure or volume.
Both pressures must be in the same unit and both volumes in the same unit; the answer then comes out in that unit.

The big picture

For a fixed mass of gas kept at a constant temperature, pressure multiplied by volume always gives the same number. That makes pressure inversely proportional to volume: halve the volume and the pressure doubles; double the volume and the pressure halves. Written for a gas before and after a change, the rule becomes P1 × V1 = P2 × V2, which you can rearrange to find a missing pressure or volume — as long as both pressures share a unit and both volumes share a unit.

Key points

1Seal it in, keep it at the same temperature — only then does p × V stay put.

2Pressure and volume move in opposite directions.

3Divide the volume by any number and the pressure is multiplied by that same number.

4The p–V graph is a curve, not a straight line.

5Match units in pairs before you substitute.

.we-_R_18slubsnpfiv5ubrb_ [data-we-step]{display:flex !important}.we-_R_18slubsnpfiv5ubrb_ [data-we-solution]{display:block !important}.we-_R_18slubsnpfiv5ubrb_ [data-we-reveal]{display:none !important}

Worked example

Problem

A gas has a volume of 0.030 m³ at a pressure of 100 000 Pa. It is compressed at constant temperature to a volume of 0.012 m³. Calculate its new pressure.

⚠ Watch out

Treating pressure and volume as rising and falling together. For a fixed mass of gas at constant temperature, when one goes up the other goes down.

🧠

Memory hook

Picture p × V as a rectangle with a fixed area: make it half as wide and it has to be twice as tall.

✓

Check yourself

Explain why P1 × V1 = P2 × V2 says exactly the same thing as 'p × V is constant'.

Flashcards

(10)

What two conditions must hold for Boyle's law to apply?

The mass of gas stays fixed (none gets in or out) and the temperature stays constant.

Under Boyle's-law conditions, what stays the same as you squeeze or expand a gas?

The product of pressure and volume: p × V = constant.

A fixed mass of gas at constant temperature has its volume halved. What happens to its pressure?

It doubles. (Double the volume instead, and the pressure halves.)

What does 'pressure is inversely proportional to volume' mean?

Whatever number the volume is divided by, the pressure is multiplied by that same number — so p × V never changes.

In P1 × V1 = P2 × V2, what do the 1s and 2s mean?

1 = the gas's pressure and volume before the change; 2 = its pressure and volume after the change.

Rearrange P1 × V1 = P2 × V2 to find V2.

V2 = (P1 × V1) ÷ P2

Rearrange P1 × V1 = P2 × V2 to find P2.

P2 = (P1 × V1) ÷ V2

What is the unit rule for P1 × V1 = P2 × V2?

Both pressures in the same unit and both volumes in the same unit. The answer comes out in that same unit.

What are the SI units of pressure and volume?

Pressure: pascals (Pa). Volume: cubic metres (m³).

What shape is a pressure–volume graph for a fixed mass of gas at constant temperature?

A curve, not a straight line: equal changes in volume do not give equal changes in pressure.

Tap any card to flip it, or use Study as deck to go through them one at a time. In the full lesson these run as a spaced-repetition deck — you rate each card Hard, Good or Easy and the tricky ones keep coming back until they stick.

Learning with Lightbulb is opening soon

You can use this lesson now. Join the waitlist and we'll let you know when the full Lightbulb experience is ready.

Keep me posted

Squeeze a trapped gas — same gas, same temperature

Squeeze it into a quarter of the space

When does p × V actually stay the same?

Your turn to make the decisions

Find the line where the mark is lost

More Edexcel GCSE Physics topics