A-Level Physics — 12) Temperature & Ideal Gases (IP-Friendly Guide)

TL;DR
Temperature on the Kelvin scale starts at true zero energy, the ideal-gas equation links macro \((p,V,T)\) to microscopic particle count, and every gas question can be cross-checked with the kinetic-theory identity \(K_{\text{avg}} = \tfrac32 kT\). Nail these three “master keys” and Paper 2 data-based inevitably feels three pages shorter.

1 Thermodynamic temperature: why Kelvin rules

A thermodynamic scale fixes its zero at the point where particles have zero kinetic energy, a universal anchor that does not depend on mercury, platinum or any other material indicator.

Hence the SI defines the kelvin \((\text{K})\) by setting the Boltzmann constant to an exact value \(k = 1.380 649 \times 10^{-23} \space \pu{J.K-1}\) .

1.1 °C ↔ K switch

Convert the lab thermometer reading with

\[ T_{\text{K}} = T_{^{\circ}\text{C}} + 273.15. \]

Mini-drill: Liquid nitrogen boils at \(-196 \space ^{\circ} \text{C}\). What is this in kelvin? Answer: \(77.15 \space \text{K}\).

2 Empirical gas laws (Boyle, Charles, Gay-Lussac)

Exam cue: Quote temperatures in kelvin or the proportionalities break — a common IP trap in Paper 1 MCQ.

3 Ideal-gas equation: macro ↔ micro

The empirical laws blend into a single statement

\[ pV = nR T = N k T, \]

where \(n\) is moles, \(N\) is particle count, \(R = 8.314 \space \pu{J.mol-1.K^-1}\) and \(k = R/N_{\text{A}}\).

3.1 Avogadro constant

One mole contains exactly \(6.022 140 76 \times 10^{23}\) entities , giving the bridge \(Nk = nR\). Parents: this fixed particle count is why chem-physics cross-topic conversions always cancel neatly.

4 Kinetic-theory model of an ideal gas

4.1 Core assumptions

1. Particles are point masses with negligible volume.
2. Motion is random and obeys Newtonian mechanics.
3. Collisions are perfectly elastic.
4. No intermolecular forces except during collisions.

4.2 Microscopic origin of pressure

A molecule hitting a wall reverses its \(x\)-momentum \((2mu_x)\). Summing impulses over collision rate yields

\[ pV = \frac13 N m \langle c^2 \rangle, \]

where \(\langle c^2 \rangle\) is the mean-square speed.

4.3 Temperature as kinetic energy

Equating the kinetic result with \(pV = NkT\) gives

\[ \tfrac12 m \langle c^2 \rangle = \tfrac32 kT, \]

so temperature measures average translational kinetic energy.

Worked example: At \(300 \space \text{K}\) the rms speed of helium is \(\approx 1.36 \times 10^3 \space \pu{m.s-1}\) — faster than any IP badminton smash!

5 IP-style marks maximiser

1. Unit discipline — always state “K” or “Pa” before substituting numbers.
2. Boyle-Charles combo Qs — re-write into \(pV/T = \text{constant}\) early to avoid 2-line algebra traps.
3. Kinetic-theory derivation — memorise the one-dimension proof; SEAB loves the final "x3" step.
4. Graph WA — plot \(p\) v. \(T\) to extrapolate to \(\pu{-273.15 \space ^\circ \text{C}}\); draw dotted line beyond data for method mark.

6 Bridging ahead: link to latent heat & real gases

Knowing that \(K_{\text{avg}} \propto T\) explains why water vapour deviates from the ideal-gas equation near condensation — intermolecular attractions become non-negligible as energy drops. Flag this for Section V (Phase Equilibria) revision.

7 Further reading

• SEAB H2 Physics 9478 syllabus (2026)
• Kelvin — SI base unit
• Boyle's Law explainer
• Charles's Law
• Gay-Lussac's Law
• Ideal Gas Law (LibreTexts)
• Kinetic Theory pressure derivation
• Equipartition theorem
• NIST constants table
• Kinetic-Molecular Theory overview

8 Call-to-action

Parents: book a 60-min Thermodynamics booster to pre-empt Term 4 WA slippage.
Students: try recasting every gas MCQ into \(pV = NkT\) form — even Section B “real-world” stories shrink into a one-line calculation once constants are parked.

Last updated 14 Jul 2025. Next review when the 2027 syllabus draft drops.