Q: What should I revise for H2 Physics ideal gases and kinetic theory? A: For SEAB 9478 Topic 12, revise Kelvin temperature, pV=nRT, pV=NkT, the Boltzmann constant, Avogadro constant, kinetic-theory assumptions, pressure derivation, rms speed, and the link between temperature and mean translational kinetic energy.
TL;DR These H2 Physics notes tie Kelvin temperature, gas laws, pV=nRT
Reviewed by
Chee Wei Jie·Academic Advisor (Physics)
,
pV=NkT
, 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.
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.
Temperature and gas-law decision map
Question clue
First check
Equation family
Trap to avoid
Same sealed sample before and after a change
n is constant
T1p1V1=T2p2V2
Substituting degree Celsius values into T.
Pressure, volume, temperature, and amount are given
Units can be converted to SI
pV=nRT
Mixing L with m3 or kPa
Number of particles is given
N, not n, appears in the question
pV=NkT
Using R with particle count or k
Speed or kinetic energy is requested
The gas is treated as ideal
21m⟨c2⟩=23kT
Misconception check: Kelvin is not just a nicer unit for Celsius. It is an absolute temperature scale, so doubling T in kelvin doubles the average translational kinetic energy of an ideal-gas particle. Doubling a Celsius reading does not mean the same physical thing.
If you searched for a formula sheet
Search intent
Use this part of the page
Then route to
ideal gases a level physics notes
Start with the decision map, then the ideal-gas equation section.
Need the rest of the Thermal Physics sequence? Browse the H2 Physics notes hub for Topic 13 Thermodynamic Systems and the rest of the 9478 notes. For the official document route and paper weightings, see our H2 Physics syllabus guide.
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.
Macro-micro gas equation checkpoint
Before substituting into an ideal-gas equation, identify whether the question describes the gas as a sample in moles or as individual particles.
Given quantity
First conversion
Equation to use
Common trap
Moles of gas, n, are given
Keep amount in mol.
Use pV=nRT.
Multiplying by Avogadro constant when the question already gives mol.
Particle count, N, is given
Keep count as particles.
Use pV=NkT.
Using R with a particle count.
Mass and molar mass are given
Find n=m/M.
Use pV=nRT.
Using mass in kg directly as the amount of gas.
One molecule mass is used in speed questions
Pair molecule mass with k.
Use 21m⟨c2⟩=23kT
Misconception check: R is the gas constant per mole, while k is the gas constant per particle. The equation changes because the amount-counting unit changes, not because the gas behaves differently.
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 gives the pressure relation below.
Pressure derivation checkpoint
Use this map to keep the one-particle collision story connected to the final gas equation.
one molecule hits wall
-> momentum change in x-direction
-> force from impulse per time
-> pressure from force per area
-> sum over all molecules
-> replace x-direction average by one-third of total mean-square speed
Derivation step
Quantity to write
Why it belongs there
Common trap
One wall collision
Momentum change is 2mux.
The molecule reverses its x-component of velocity after an elastic collision.
Using total speed before choosing the wall direction.
Time between hits on the same wall
Time is ux2L.
The molecule travels across the box and back before hitting the same wall again.
Using uxL, which counts the wrong collision spacing.
Average force from one molecule
Force is impulse divided by time.
This turns repeated momentum changes into an average force on the wall.
Treating impulse and force as the same quantity.
All molecules in three dimensions
Use ⟨cx2⟩=31⟨c2⟩
Worked check: the factor 31 does not come from the shape of the container. It comes from random motion in three perpendicular directions, so only one third of the mean-square speed contributes to pressure on a chosen pair of walls.
Misconception check: pressure is not caused by molecules "pushing" continuously on the wall. It comes from many tiny momentum changes during collisions, averaged over time and area.
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.
rms-speed mass checkpoint
For speed questions, decide whether the mass in the question describes one particle or one mole of particles. That choice decides whether the energy equation should use k or R.
Given mass information
Use this form
Mass unit to check
Common trap
Mass of one molecule or atom, m
vrms=m3kT
kg per particle
Substituting molar mass into the per-particle formula.
Molar mass, M
vrms=M3RT
Relative molecular mass only
Convert to molar mass first.
M=Mr×10−3kg⋅mol−1
Worked check: helium has M=4.00g⋅mol−1=4.00⋅10−3kg⋅mol−1. At 300K,
Misconception check: k and R are not interchangeable constants. They match different ways of counting gas: one particle versus one mole.
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 and the final three-dimensional averaging step because Topic 12 explicitly names that extension.
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 practical data-handling 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 SEAB publishes a newer H2 Physics syllabus document.
