A-Level · 26 September 2026 · 6 min read
Ideal gases and kinetic theory: worked A-Level Physics questions
Gas questions often hide their main decision in a few words: “sealed”, “rigid”, “slowly heated” or “constant pressure”. Translate those words into fixed or changing quantities before choosing a relationship. A sealed container fixes particle number if no gas leaks; it does not automatically fix the volume unless its walls are rigid.
The original problems below develop Edexcel IAL A2 thermal reasoning. They use the ideal-gas model and clearly stated constraints. Real gases can deviate from that model, so a correct calculation should still be connected to the assumptions under which it describes the experiment.
Choose the equation by naming what is fixed
For a fixed quantity of ideal gas, pV/T is constant between two equilibrium states. At fixed volume, pressure is proportional to absolute temperature. At fixed pressure, volume is proportional to absolute temperature. At fixed temperature, pressure is inversely proportional to volume. These are conditional relationships, not three rules that apply simultaneously to every change.
Always convert Celsius to kelvin before using temperature ratios. A temperature rise of 20°C equals a rise of 20 K, but the temperatures 20°C and 40°C are not in a two-to-one absolute ratio. This distinction explains why a correct temperature difference can coexist with an incorrect gas-law ratio.
Worked example: heat a sealed rigid container
A sealed rigid container holds ideal gas at 2.0 × 10⁵ Pa and 300 K. It is heated to 450 K without losing particles. Since N and V stay fixed, p₂/p₁ = T₂/T₁ = 1.5. The final pressure is 3.0 × 10⁵ Pa. Use absolute pressure in the equation; a gauge reading above atmospheric pressure may need conversion if the question supplies one.
Now change the apparatus to a freely moving piston maintaining constant external pressure, with the gas remaining in mechanical equilibrium. The volume can increase instead, and V₂/V₁ = 1.5 for the same temperature change. The initial and final temperatures alone do not decide whether pressure or volume changes: the physical constraint does.
Explain the pressure change at the particle level
In a rigid container, increased absolute temperature corresponds to greater mean translational kinetic energy. Molecules have a distribution of speeds, but their mean square speed increases. Their collisions with the walls transfer momentum; the aggregate rate of momentum transfer determines the force and hence pressure.
A useful explanation identifies both the molecular change and the macroscopic consequence. Do not say every molecule acquires the same speed, or that gas molecules themselves become larger. If volume also changes, collision frequency depends on that geometry as well, so carry the stated constraint through the explanation instead of recycling the fixed-volume answer.
Worked example: count molecules using pV = NkT
Take p = 2.0 × 10⁵ Pa, V = 0.015 m³, T = 300 K and k = 1.38 × 10⁻²³ J K⁻¹. Then N = pV/(kT) = 3000/(4.14 × 10⁻²¹) = 7.25 × 10²³ molecules. N is a count, not a mass in kilograms or an amount in moles.
If you use the equivalent form pV = nRT, n is the amount in moles and R is the molar gas constant. Do not combine n with k or N with R. A useful check is that pV has units of energy, so dividing it by kT gives a dimensionless particle count. Confusing the two constants produces an enormous scale error.
Worked example: temperature and rms speed
For molecules of mass 4.65 × 10⁻²⁶ kg at 300 K, use ½m⟨c²⟩ = 3kT/2. The root-mean-square speed is √(3kT/m) = approximately 517 m s⁻¹. This is the square root of the mean square speed, not necessarily the arithmetic mean speed and certainly not the velocity of the whole container.
At 450 K for the same molecules, the rms speed increases by √(450/300) = √1.5, giving about 633 m s⁻¹. It does not increase by a factor of 1.5. Different gas species at the same temperature have the same mean translational kinetic energy in the ideal-gas model, but heavier molecules have a lower rms speed.
Check the model and build a mixed practice task
The ideal-gas model treats particles as having negligible volume compared with the container and neglects intermolecular forces except during collisions. Use those assumptions when evaluating where the model may become less suitable; do not merely write “real life is different”. For a comparison, identify which assumption becomes questionable in the described conditions.
Practise one constrained gas change, one particle-count calculation and one kinetic-theory explanation. Before marking, underline every fixed quantity and every temperature unit. Then change the container from rigid to expandable and rewrite the explanation. That final variation checks whether you understand the model rather than only its algebra.
Questions, explained
Choose a question for a direct answer, then explore the explanation and supporting resources. Each answer has its own link to save or share.
Why must temperature be in kelvin for gas equations?
The ideal-gas proportionalities use absolute temperature. Celsius has an offset from absolute zero, so Celsius ratios do not describe the required relationship. Temperature differences have the same numerical size in kelvin and Celsius, but absolute temperatures do not.
Does heating a gas always increase its pressure?
No. It depends on the constraints. For a fixed quantity in a rigid container, pressure increases with absolute temperature. At constant pressure with a movable boundary, the gas may expand instead. State which quantities remain fixed before predicting the change.
Is rms speed the same as mean molecular speed?
No. Root-mean-square speed is the square root of the mean of the squared speeds. It differs from the arithmetic mean speed. The kinetic-energy relationship naturally involves the mean square speed, and molecules have a distribution of speeds rather than one shared value.
Do different gases at the same temperature have the same molecular speed?
They have the same mean translational kinetic energy in the ideal-gas model, but not the same rms speed. Since ½m⟨c²⟩ depends on temperature, heavier molecules have a lower rms speed at the same temperature.
What is the difference between N and n in gas equations?
N is the number of particles and is used with Boltzmann’s constant k in pV = NkT. The symbol n usually means amount in moles and is used with the molar gas constant R in pV = nRT. Check the definitions in the question rather than mixing the two forms.