Q: What does A-Level Physics: 12) Temperature & Ideal Gases Guide cover? A: Absolute zero foundations, Boyle-Charles-Gay-Lussac shortcuts, and a kinetic-theory bridge between pressure, volume, and particle energy.
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 Kavg=23kT
. 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(K) by setting the Boltzmann constant to an exact value k=1.380649×10−23J⋅K−1 .
1.1 °C ↔ K switch
Convert the lab thermometer reading with
TK=T∘C+273.15.
Mini-drill: Liquid nitrogen boils at −196∘C. What is this in kelvin? Answer:77.15K.
2 Empirical gas laws (Boyle, Charles, Gay-Lussac)
Law
What stays constant
Proportionality
Equation form
Boyle
\(T,n\)
\(p \propto 1/V\)
\(p_1V_1 = p_2V_2\)
Charles
\(p,n\)
\(V \propto T\)
\(V_1/T_1 = V_2/T_2\)
Gay-Lussac
\(V,n\)
\(p \propto T\)
\(p_1/T_1 = p_2/T_2\)
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=nRT=NkT,
where n is moles, N is particle count, R=8.314J⋅mol−1⋅K−1 and k=R/NA.
3.1 Avogadro constant
One mole contains exactly 6.02214076×1023 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
Particles are point masses with negligible volume.
Motion is random and obeys Newtonian mechanics.
Collisions are perfectly elastic.
No intermolecular forces except during collisions.
4.2 Microscopic origin of pressure
A molecule hitting a wall reverses its x-momentum (2mux). Summing impulses over collision rate yields
pV=31Nmv2,
where v2 is the mean-square speed.
4.3 Temperature as kinetic energy
Equating the kinetic result with pV=NkT gives
21mv2=23kT,
so temperature measures average translational kinetic energy.
Worked example: At 300K the rms speed of helium is ≈1.36×103m⋅s−1 - faster than any IP badminton smash!
5 IP-style marks maximiser
Unit discipline - always state “K” or “Pa” before substituting numbers.
Boyle-Charles combo Qs - re-write into pV/T=constant early to avoid 2-line algebra traps.
Kinetic-theory derivation - memorise the one-dimension proof; SEAB loves the final "x3" step.
Graph WA - plot p v. T to extrapolate to −273.15∘C; draw dotted line beyond data for method mark.
6 Bridging ahead: link to latent heat & real gases
Knowing that Kavg∝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.
Comprehensive revision pack
9478 Section III, Topic 12 Syllabus outcomes at a glance
Outcome (a) - define thermodynamic temperature and convert between °C and K.
Outcome (b) - state and use Boyle's, Charles's and Gay-Lussac's laws.
Outcome (c) - derive and apply the ideal gas equation.
Outcome (d) - explain kinetic theory assumptions and link macroscopic quantities to microscopic motion.
Outcome (e) - perform and interpret gas experiments (pressure-temperature, pressure-volume).
Concept map (in words)
Base everything on the Kelvin scale. Combine empirical gas laws into pV=nRT and translate to particle language with NkT. Use kinetic theory to show that temperature measures average kinetic energy. Experimentally, plot graphs to verify straight-line behaviour and extrapolate to absolute zero.
Key relations
Relation
Comment
Celsius-Kelvin conversion
\(T_{\pu{K}} = T_{\pu{^\circ C}} + 273.15\)
Combined gas law
\(pV/T = \text{constant}\) (for fixed gas amount)
Ideal gas equation
\(pV = nRT = NkT\)
Mean-square speed
\( v_{\text{rms}} = \sqrt{\dfrac{3kT}{m}} \)
Average kinetic energy per mole
\(E = \dfrac{3}{2} RT\)
Average kinetic energy per molecule
\(E = \dfrac{3}{2} kT\)
Pressure from kinetic model
\(p = \dfrac{1}{3} \rho v_\text{rms}^2\)
Derivations & reasoning to master
Kinetic theory pressure derivation: start with one molecule colliding elastically with a wall and sum over particles.
Connection between Celsius and Kelvin: use linear extrapolation of p vs T graph to show intercept at −273.15∘C.
Root-mean-square speed: derive from pV=31Nm⟨v2⟩=NkT.
Molar vs molecular forms: demonstrate how multiplying by Avogadro constant converts between NkT and nRT.
Worked example 1 - combined gas law
A 2.5L sample of nitrogen at 150kPa and 22∘C is heated to 80∘C at constant pressure. What is the new volume? How many molecules does the gas contain?
Solution sketch: Convert to kelvin, apply V2=V1T2/T1. Use n=pV/RT, then multiply by NA for molecule count.
Worked example 2 - rms speed
Calculate the rms speed of oxygen molecules at 320 K. Compare with nitrogen at the same temperature.
Key steps: Use crms=M3RT. Discuss how molar mass differences affect rms speed (lighter molecules move faster).
Practical & data tasks
Perform a pressure vs temperature experiment with a sealed syringe and digital sensor; extrapolate to absolute zero.
Use data logger to record pressure vs volume under constant temperature; confirm inverse proportionality.
Model kinetic theory using computer simulations (e.g., PhET Gas Properties) and note deviations when assumptions break.
Common misconceptions & exam traps
Plugging Celsius values directly into proportional equations.
Forgetting that Boltzmann constant k links to R through Avogadro constant.
Assuming real gases obey ideal behaviour near liquefaction; mention limitations when conditions deviate.
Mixing mass and molar mass when computing rms speeds.
Quick self-check quiz
Why must temperature be in kelvin for gas laws? Because proportional relationships rely on absolute scale starting at zero energy.
What happens to pressure if volume halves at constant temperature? It doubles (Boyle's law).
State two ideal gas assumptions. Point particles with negligible volume; collisions perfectly elastic; no intermolecular forces between collisions.
How is average kinetic energy related to temperature? E=3/2kT per molecule.
Write the ideal gas equation in molecular form. pV=NkT
Revision workflow
Re-derive the kinetic theory expression for pressure weekly.
Create flashcards for each gas law with typical exam question types.
Solve one mixed gas problem (changing p, V, T) and one rms speed calculation per study session.
Summarise real-gas limitations and note where A-level examiners expect you to mention them.
Practice Quiz
Test yourself on the key concepts from this guide.
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.
