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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 Kelvin temperature is measured from absolute zero, the ideal-gas equation links macro (p,V,T) to microscopic particle count, and kinetic theory gives Kavg=23kT
for an ideal gas. Mastering these links makes gas questions far more systematic.
Need the rest of the Thermal & Gases playlist? Browse the H2 Physics notes hub for Topic 13 (Thermodynamics), statistical-mechanics extensions, and practice drills that pair with this chapter.
1 Thermodynamic temperature: why Kelvin rules
A thermodynamic scale fixes its zero at absolute zero (0K), 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∝1/V
p1V1=p2V2
Charles
p,n
V∝T
V1/T1=V2/T2
Gay-Lussac
V,n
p∝T
p1/T1=p2/T2
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
TK=T∘C+273.15
Combined gas law
pV/T=constant (for fixed gas amount)
Ideal gas equation
pV=nRT=NkT
Mean-square speed
vrms=m3kT
Average kinetic energy per mole
E=23RT
Average kinetic energy per molecule
E=23kT
Pressure from kinetic model
p=31ρvrms2
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.
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.
