Charles' Law

Charles' Law states that for a fixed amount of ideal gas held at constant pressure, volume is directly proportional to absolute (kelvin) temperature, so V₁/T₁ = V₂/T₂. In AP Physics 2 it's the isobaric special case of the ideal gas law (Topic 2.2).

Verified for the 2027 AP Physics 2 examLast updated June 2026

What is Charles' Law?

Charles' Law says that if you keep the pressure on a gas constant and don't add or remove molecules, the gas's volume grows in direct proportion to its absolute temperature. Double the kelvin temperature, double the volume. As an equation, V/T = constant, which is usually written as V₁/T₁ = V₂/T₂ for comparing two states. The temperature must be in kelvin, not Celsius, because the proportionality runs through absolute zero, not through 0°C.

On the AP exam, Charles' Law isn't really a separate law to memorize. It's what the ideal gas law (PV = nRT, or PV = NkT with the Boltzmann constant) becomes when P and n are locked down. The microscopic picture is what makes it click. Heat the gas and the molecules move faster, slamming into the walls harder and more often. If the pressure is going to stay the same, the container has to expand so those harder collisions get spread over more wall area. Think of a balloon in a hot car. The pressure stays roughly atmospheric, so the balloon swells.

Why Charles' Law matters in AP Physics 2

Charles' Law lives in Topic 2.2 (Pressure, Thermal Equilibrium, and the Ideal Gas Law) in Unit 2 of AP Physics 2. The CED doesn't ask you to recite the named gas laws as separate facts. Instead, it expects you to reason from the ideal gas law about how state variables (P, V, T) relate, and Charles' Law is the constant-pressure case of that reasoning. It also sets up Unit 2's thermodynamics work, because a constant-pressure process is an isobaric process. On a PV diagram, that's a horizontal line, and Charles' Law tells you that moving right along that line means the temperature is rising. Being able to connect the macroscopic relationship (V ∝ T) to the kinetic theory picture (faster molecules, harder collisions) is exactly the kind of multi-representation reasoning the exam rewards.

How Charles' Law connects across the course

Ideal Gas Law (Unit 2)

Charles' Law is PV = nRT with P and n frozen. Solve for V and you get V = (nR/P)T, a straight line through the origin when T is in kelvin. If you know the ideal gas law cold, you never have to memorize Charles' Law separately.

Gay-Lussac's Law (Unit 2)

Same logic, different variable held constant. Gay-Lussac's Law fixes volume and finds pressure proportional to temperature (think of a sealed rigid can heating up). Charles' Law fixes pressure and lets volume grow instead.

Boyle's Law (Unit 2)

Boyle's Law is the constant-temperature case, where pressure and volume are inversely related. Together with Charles' Law, it covers the two classic 'hold one variable, watch the other two' scenarios that show up in PV-diagram questions.

Boltzmann constant (Unit 2)

Writing the gas law as PV = NkT connects Charles' Law to individual molecules. The Boltzmann constant k links temperature to average molecular kinetic energy, which is why heating a gas at constant pressure forces it to expand. The molecules genuinely hit harder.

Is Charles' Law on the AP Physics 2 exam?

No released FRQ names Charles' Law verbatim, and that's the point. The exam tests the relationship, not the label. Expect multiple-choice stems like 'a gas at constant pressure is heated from 300 K to 600 K; what happens to its volume?' (it doubles) or graph questions asking which plot shows V versus T at constant pressure (a straight line through the origin, in kelvin). On FRQs, the same idea appears inside thermodynamics problems as an isobaric process on a PV diagram, where you justify why temperature changes as volume changes along a horizontal line. The classic trap is plugging in Celsius. Going from 20°C to 40°C does not double the volume, because 293 K to 313 K is only about a 7% increase. Always convert to kelvin first.

Charles' Law vs Gay-Lussac's Law

Both laws say something is directly proportional to absolute temperature, so they blur together. Charles' Law holds pressure constant and varies volume (V ∝ T), like a balloon free to expand. Gay-Lussac's Law holds volume constant and varies pressure (P ∝ T), like a sealed rigid container. Quick check on any problem: ask what the container can do. If it can expand, you're in Charles' Law territory. If it's rigid, it's Gay-Lussac.

Key things to remember about Charles' Law

  • Charles' Law states that at constant pressure, the volume of a fixed amount of ideal gas is directly proportional to its absolute temperature, so V₁/T₁ = V₂/T₂.

  • Temperature must be in kelvin; using Celsius breaks the proportionality and is the most common error on these problems.

  • Charles' Law is just the ideal gas law (PV = nRT) with pressure and amount of gas held constant, so you can always derive it instead of memorizing it.

  • Microscopically, heating the gas makes molecules move faster and hit the walls harder, so the volume must expand for the pressure to stay the same.

  • A constant-pressure process is called isobaric and appears as a horizontal line on a PV diagram, where moving toward larger volume means higher temperature.

Frequently asked questions about Charles' Law

What is Charles' Law in AP Physics 2?

Charles' Law says that for a fixed amount of ideal gas at constant pressure, volume is directly proportional to absolute temperature (V₁/T₁ = V₂/T₂). It's tested in Unit 2, Topic 2.2, as a special case of the ideal gas law.

Can I use Celsius in Charles' Law?

No. The direct proportionality only works with absolute temperature in kelvin. For example, heating a gas from 20°C to 40°C raises its kelvin temperature from 293 K to 313 K, increasing volume by only about 7%, not doubling it.

What's the difference between Charles' Law and Gay-Lussac's Law?

Charles' Law holds pressure constant and relates volume to temperature (V ∝ T), like an expandable balloon. Gay-Lussac's Law holds volume constant and relates pressure to temperature (P ∝ T), like a sealed rigid can. Check whether the container can expand to decide which applies.

Do I need to memorize Charles' Law for the AP Physics 2 exam?

Not as a separate formula. The ideal gas law PV = nRT is on the equation sheet, and Charles' Law falls out of it when you hold P and n constant. The exam tests whether you can reason with the relationship, not whether you know the name.

Why does a gas expand when heated at constant pressure?

Higher temperature means higher average molecular kinetic energy, so molecules strike the container walls harder and more often. To keep the pressure (force per area) unchanged, the gas must spread those collisions over a larger volume, so it expands.