Gas Pressure and Absolute Zero

What this lesson covers in the specification

Incandio is aligned to this specification. It is not published by, endorsed by or affiliated with Pearson, and it reproduces none of Pearson's wording — the statement numbers are given so you can check every lesson against your own copy.

• 5.15 — How random molecular motion in a gas exerts a force, and hence a pressure, on the container walls
• 5.16 — Why there is an absolute zero of temperature at −273 °C
• 5.17 — The Kelvin scale, and converting between Kelvin and Celsius

1 · Understand it

No exam language yet. The only question this section answers is: do I actually understand what is happening?

A sealed container of gas pushes outward on its walls, and nothing is touching them except molecules that are mostly empty space apart. Where does the push come from? From the collisions. The molecules of a gas move rapidly and randomly in all directions, and each one that strikes a wall bounces off — which means its momentum changes, which means a force acted on it, which means by Newton's third law it exerted an equal force on the wall.

Statement 5.15 — from random motion to a steady pressure

1. The molecules move RANDOMLY in all directions at high speed.
2. Each one that reaches a wall COLLIDES with it and rebounds, so its momentum changes direction.
3. A change of momentum requires a FORCE on the molecule, and by Newton's third law the molecule exerts an equal and opposite force on the wall.
4. An enormous number of such collisions happen every second, so the individual impulses add up to a STEADY average force on the wall.
5. PRESSURE is that force divided by the area of the wall — which is why the pressure is the same on every wall regardless of orientation, since the motion is random and no direction is favoured.

It is worth pausing on the last point, because it explains something from the pressure page. A gas exerts the same pressure on the ceiling of its container as on the floor and the sides, because the molecules are moving in every direction equally. There is no downward preference at all — which is exactly what 'pressure acts equally in all directions' meant, now with a mechanism behind it.

Think of it like hail on a tin roof rather than a hand pressing on it

Stand under a tin roof in heavy hail and you hear a continuous roar and feel a steady push, even though what is actually happening is a very large number of separate small impacts. No single hailstone pushes for any length of time; each arrives, bounces, and is gone. Yet because thousands arrive every second, the effect is indistinguishable from a steady pressure — and if the hail fell twice as fast, or twice as often, the push would be greater. Gas pressure is exactly this, with molecules instead of hailstones and about 10²⁷ of them arriving per square metre per second, which is why it feels perfectly smooth.

Now cool the gas. The molecules move more slowly, so they strike the walls less often and each collision produces a smaller change in momentum. Both effects reduce the pressure. Keep cooling and the pressure keeps falling — and if you measure it carefully and plot pressure against temperature in degrees Celsius, the points lie on a straight line that, extended backwards, reaches ZERO PRESSURE at about −273 °C.

That is the argument for ABSOLUTE ZERO, and it is worth appreciating what kind of argument it is. Nobody has cooled a gas to −273 °C — every real gas liquefies long before then. The value comes from EXTRAPOLATING the straight line beyond the range where the measurements were made. At that temperature the molecules would have no kinetic energy at all, so there would be no collisions and no pressure, and no lower temperature is possible because nothing can have less than zero kinetic energy.

So the Celsius scale, useful as it is, has its zero in an arbitrary place — the freezing point of water, chosen for convenience. The KELVIN scale puts its zero at absolute zero instead, and keeps the same size of degree. Zero kelvin is −273 °C, and 0 °C is 273 K. To convert, add 273 going from Celsius to kelvin, and subtract 273 going the other way. There is no degree symbol on the kelvin: it is 300 K, not 300 °K.

Converting, and why the choice of scale matters

Convert 27 °C and −73 °C to kelvin. Then consider: if a gas at 27 °C is heated to 327 °C, has its temperature doubled?

1. 27 °C = 27 + 273 = 300 K.
2. −73 °C = −73 + 273 = 200 K.
3. 327 °C = 327 + 273 = 600 K.
4. In Celsius, 27 to 327 looks like a twelvefold increase. In kelvin it is 300 K to 600 K, which is genuinely double.
5. It is the KELVIN temperature that has doubled, and that is the one the gas laws depend on.

Answer: 300 K and 200 K; and yes, the temperature has doubled — but only when measured in kelvin.

That last point is the reason this page comes before the gas laws rather than after them. Any statement that a gas quantity is PROPORTIONAL to temperature is only true on the Kelvin scale, because proportionality requires that zero of the quantity corresponds to zero of the temperature. Doubling 27 °C to 54 °C does nothing like doubling the pressure; doubling 300 K to 600 K does exactly that. Using Celsius in a gas-law calculation is not a small inaccuracy — it gives an answer that is simply wrong.

2 · Grade 9 Notes

A different job from the section above. You have already understood it; this is the precise set of things to LEARN — definitions to reproduce word for word, processes in order, equations with units, and the answers that score full marks.

Statement 5.15 — explaining gas pressure, the sequence to write

1. The molecules move randomly in all directions at high speed.
2. They collide with the walls of the container and rebound, so their momentum changes.
3. A change of momentum means a force acts on the molecule, and by Newton's third law it exerts an equal force on the wall.
4. A very large number of collisions each second gives a steady average force.
5. Pressure is that force divided by the area of the wall.

Learn this definition · Absolute zero

The lowest temperature possible, −273 °C or 0 K, at which the particles would have no kinetic energy and a gas would exert no pressure. It is found by extrapolating a graph of pressure against temperature back to zero pressure.

Learn this definition · The Kelvin scale

A temperature scale whose zero is at absolute zero, using the same size of degree as Celsius. Temperature in K = temperature in °C + 273. There is no degree symbol: write 300 K, not 300 °K.

Learn this definition · Gas pressure

The steady average force per unit area exerted on the walls of a container by the very large number of molecular collisions occurring each second, measured at constant volume for comparison.

Why absolute zero is a real limit rather than a convention

• Pressure falls as a gas is cooled, because the molecules move more slowly and collide less often and less hard
• A graph of pressure against temperature in °C is a STRAIGHT LINE that reaches zero pressure at about −273 °C
• That value is found by EXTRAPOLATION — no real gas gets there, because they all liquefy first
• At absolute zero the particles would have no kinetic energy, so there would be no collisions and no pressure
• Nothing can have less than zero kinetic energy, so no lower temperature is possible

Why the gas laws need kelvin and not Celsius

A. CELSIUS has its zero at an arbitrary point — the freezing point of water. Doubling 27 °C to 54 °C does not double anything physical.

B. KELVIN has its zero at absolute zero, where the molecules have no kinetic energy. Doubling 300 K to 600 K genuinely doubles the average kinetic energy, which is why proportionality only works on this scale.

Model answer [2 marks]

Convert 127 °C to kelvin, and 200 K to degrees Celsius. [2]

127 °C = 127 + 273 = 400 K. 200 K = 200 − 273 = −73 °C.

Model answer [4 marks]

Explain, in terms of molecules, how a gas exerts a pressure on the walls of its container. [4]

The molecules of the gas move randomly in all directions at high speed. When a molecule collides with a wall it rebounds, so its momentum changes, and a change of momentum requires a force to act on it. By Newton's third law, the molecule exerts an equal and opposite force on the wall. An enormous number of these collisions occur every second, so together they produce a steady average force on the wall, and the pressure is that force divided by the area of the wall.

Not this: Absolute zero is just a very cold temperature that nobody has bothered to reach yet.

This: It is a genuine limit. At 0 K the particles would have no kinetic energy at all, and nothing can have less than none — so no lower temperature exists. It has been approached to within a fraction of a degree but cannot be reached.

Mark-losing trap. K = °C + 273, and °C = K − 273. Write 300 K, never 300 °K.

Mark-losing trap. Gas-law proportionality works ONLY in kelvin. Celsius gives a wrong answer, not an approximate one.

Mark-losing trap. Pressure comes from momentum change at each collision — say 'Newton's third law', it is a mark.

Mark-losing trap. Absolute zero is found by EXTRAPOLATION; no gas is ever actually measured there.

3 · Prove it — the five questions

The five questions climb Grade 6 → Grade 7 → Grade 8 → Grade 9 → Grade 9 challenge, and are marked inside Incandio on your own device, by rule, with an authored diagnosis of the mistake you actually made. The mark schemes stay in the app so that the practice is worth doing; the questions themselves are here.

1. Grade 6 · Calculate [1 mark] — Convert 27 °C into kelvin.
2. Grade 7 · State [2 marks] — What would happen to the particles of a gas at absolute zero?
3. Grade 8 · Explain [5 marks] — Select every statement that belongs in a full-mark explanation of how a gas exerts a pressure on the walls of its container.
4. Grade 9 · Explain [6 marks] — Select every statement that belongs in a full-mark explanation of how a graph of gas pressure against temperature shows that there is an absolute zero at about −273 °C.
5. 9+ · Analyse [6 marks] — A student says: 'A gas at 40 °C is twice as hot as one at 20 °C, so it should exert twice the pressure at constant volume.' Select every statement that belongs in a full-mark analysis.

The people behind this science

Two ways into the same idea — the one who first measured what a gas does when you squeeze it, and the one whose work led towards a scale with a real zero. Inside Incandio each of them answers knowing exactly which lesson you have just finished.

Robert Boyle — the one who first measured what a gas does when you squeeze it

Boyle put a quantity of air in the short closed arm of a J-shaped glass tube, poured mercury into the long open arm, and recorded how the trapped air shrank as more mercury was added. It is the first careful quantitative study of a gas, and it established that the volume falls as the pressure rises in a definite numerical relationship. He also had the air pump that let him go the other way — reducing the pressure until a bell could not be heard — so he is the person who mapped the behaviour of gases at both ends.

• “What did you see happen to the trapped air as you poured in more mercury?”
• “Why use a J-shaped tube rather than a straight one?”
• “What did you think air was actually made of?”
• “Could you tell what was happening inside the air, or only what it did?”
• “What happened when you took the air away instead of squeezing it?”

James Prescott Joule — the one whose work led towards a scale with a real zero

The Kelvin scale on this page came out of a collaboration Joule was half of. After William Thomson took his work seriously at Cork in 1847, the two spent years working together on the behaviour of gases, and their joint experiments on gases expanding through a porous plug — the Joule–Thomson effect — fed directly into Thomson's proposal for a temperature scale independent of any particular substance, with its zero at the point where a body has no thermal energy to give. Joule supplied the experimental foundation that made a scale with a real zero mean something.

• “Why should a temperature scale not start at the freezing point of water?”
• “What happens to a gas when you let it expand through a small opening?”
• “What would it mean for something to have no thermal energy at all?”
• “How did your work with Thomson begin?”
• “Can a temperature scale be independent of the substance used to measure it?”

Carry on through the course

• Previous lesson: Specific Heat Capacity
• Next lesson: The Kinetic Theory of Gases
• Density — Not how heavy something is, but how much of it is packed into the space it occupies.
• Pressure, and Pressure in Liquids — Why a drawing pin works, why pressure at a point pushes every way at once, and why depth is the only thing that matters underwater.
• Particles and Changes of State — What the particles are doing in each state — and why a boiling pan stays at 100 °C however hard you heat it.
• Specific Heat Capacity — Why the sand burns your feet and the sea is freezing on the same afternoon.
• The Kinetic Theory of Gases — One picture — fast random molecules bouncing off walls — that predicts everything a gas does.
• All of Physics · Physics key terms · required practicals · equations · Incandio Science · The 4PH1 specification