A hot air balloon carries no engine and no wings — it flies purely because the air trapped inside its envelope is hotter, and therefore less dense, than the air outside it. That's Charles's law doing genuine, load-bearing work, not just a textbook diagram: heat the air at (roughly) constant pressure, and its volume has to increase.
GCSE coreThe rule, and why it has to be true
Charles's law states that for a fixed mass of gas at constant pressure, volume is directly proportional to temperature measured in kelvin — double the absolute temperature, and the volume doubles too. The reasoning underneath it comes from kinetic theory: heating a gas makes its particles move faster on average, so they collide with the container's walls harder and more often. If the container is free to expand — a balloon, or a piston with a fixed weight on top — that increased collision force pushes the boundary outward until the pressure drops back down to match the constant external pressure again, which only happens once the gas has occupied more volume.
The weight on the piston keeps pressure constant. As the gas is heated, particles move faster and collide harder — the piston has to rise, increasing volume, to bring pressure back down to match.
Why it has to be kelvin, not Celsius
The direct proportionality only works on an absolute temperature scale, one where zero genuinely means zero — no particle motion left at all. Celsius has an arbitrary zero point (the freezing point of water), so doubling a Celsius temperature doesn't double how energetically the particles are actually moving; doubling a kelvin temperature does. Historically, this is more than a convenience: Jacques Charles's own 18th-century measurements of gas volume against temperature, extrapolated as a straight line back to where volume would theoretically reach zero, gave one of the earliest usable estimates of absolute zero — decades before anyone could get anywhere near it in a laboratory.
Volume against temperature in kelvin is a straight line through the origin. Extrapolating real measurements back to V = 0 is genuinely how absolute zero was first estimated, long before it could be reached experimentally.
Exam-style question
A balloon contains 2.4 dm³ of air at 15°C. It is left in direct sunlight and warms to 45°C at constant pressure. Calculate the new volume. [3 marks]
Show model answer and mark breakdown
- Convert to kelvin: T₁ = 15 + 273 = 288 K, T₂ = 45 + 273 = 318 K (1 mark)
- Apply Charles's law: V₁/T₁ = V₂/T₂, so V₂ = V₁ × T₂/T₁ (1 mark)
- V₂ = 2.4 × 318/288 ≈ 2.65 dm³ (1 mark)
Examiner focus: convert both temperatures to kelvin before substituting — this is exactly the reason the law needs an absolute scale, not the ordinary Celsius values.
Common mistake: substituting 15 and 45 directly into the ratio without converting to kelvin, which would give a wrong answer since Celsius isn't a true ratio scale (doubling °C doesn't double the actual thermal energy).
A common mix-up worth clearing up
It's easy to reach for Charles's law to explain a football feeling softer on a cold morning, but that's actually a different gas law: the football's volume barely changes (the casing is fairly rigid), so it's pressure dropping at roughly constant volume — that's the pressure law, not Charles's law. The hot air balloon and the shrinking party balloon are the genuine constant-pressure cases, because both are free to change volume rather than being held rigid. Telling gas laws apart by which quantity is actually being held constant, rather than which example sounds similar, is exactly the kind of thing that's easy to get backwards under exam pressure. If the gas laws or any other GCSE and A-Level physics topic need explaining with the actual mechanism rather than a formula to memorise, that's exactly what our GCSE physics tutoring is for — see the full learning pathway here.
Frequently asked questions
Why does a hot air balloon need the flame running constantly, not just once?
Heat is constantly leaking out through the balloon's fabric into the cooler air outside, so the air inside would gradually cool and contract (Charles's law running in reverse) without ongoing heating. The burner isn't overcoming some one-off resistance — it's continuously replacing heat that's being lost, to keep the internal air at the higher temperature the balloon needs to stay buoyant.
Is this the same reason a balloon shrinks outdoors on a cold day?
Yes, exactly — a party balloon taken outside on a cold day visibly shrinks because the air inside cools and contracts at roughly constant (atmospheric) pressure, precisely what Charles's law predicts. Bring it back into a warm room and it re-expands, without ever needing to be re-inflated, which is a genuinely good way to see the law happen in real time.
Does Charles's law apply to any gas, or just air?
It applies to any gas that behaves close to 'ideally' — which most gases do at ordinary temperatures and pressures, air included. It starts to break down for gases under very high pressure or very close to the temperature at which they'd condense into a liquid, where the simplifying assumptions behind the ideal gas model stop holding up well.
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Sudershan Soni
Founder & Lead Tutor at Mostak Services — an MSc-qualified Mathematics, Science, Computer Science & STEM tutor with 20+ years of professional experience, teaching students from 11+ and GCSE to A-Level and beyond, online worldwide.
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