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1 Thermodynamic temperature: why Kelvin rules
2 Empirical gas laws (Boyle, Charles, Gay-Lussac)
Q: What do these H2 Physics temperature and ideal gases notes cover? A: They cover the Kelvin scale, Boyle-Charles-Gay-Lussac laws, pV = nRT, kinetic theory, and common A-Level 9478 gas-law traps.
TL;DR These H2 Physics notes tie Kelvin temperature, gas laws, pV=nRT, and kinetic theory into one revision workflow. Master the macro-to-micro links and the usual kelvin/unit traps so ideal-gas questions become much more systematic.
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Convert to kelvin before using gas equations
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Temperature, gas laws, and pV=nRT
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The kelvin switch and first gas-law example
10 minutes
Kinetic theory and unit traps
Concrete example: how to use this page
If pressure, volume, and temperature change, convert Celsius to kelvin first, then decide whether the amount of gas is constant. That check tells you whether to use a combined gas law or pV=nRT.
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. For the full topic map and paper weightings, see our H2 Physics Syllabus 2026-27 overview.
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.
Need structured practice on Temperature and Ideal Gases? Our H2 Physics tuition programme covers this topic with weekly problem sets and Paper 4 practical drills.
Comprehensive revision pack
9478 Section IV, Topic 12 Syllabus outcomes
Candidates should be able to:
(a) show an understanding that a thermodynamic scale of temperature has an absolute zero and is independent of the property of any particular substance.
(b) convert temperatures measured in degrees Celsius to kelvin: T/K=T/∘C+273.15.
(c) recall and use the equation of state for an ideal gas expressed as pV=NkT, where N is the number of particles.
(d) state that one mole of any substance contains 6.02×1023 particles, and use the Avogadro constant NA=6.02×1023mol−1
(e) state the basic assumptions of the kinetic theory of gases.
(f) explain how the random motion of gas particles exerts mechanical pressure and hence derive, using the definition of pressure as force per unit area, the relationship pV=31Nm⟨c2⟩ (a simple model considering one-dimensional collisions and then extending to three dimensions using ⟨cx2⟩=31⟨c2⟩
(g) recall and use the relationship that the mean translational kinetic energy of a particle of an ideal gas is (directly) proportional to the thermodynamic temperature (i.e. 21m⟨c2⟩=23kT
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.
