Physics notes / Thermal Physics

Thermal Physics · 100% marks notes

Thermal full marks = label the process or heat path in ≤15s, then run expansion/calorimetry, kinetic averages, first-law cycle, or radiation templates inside 60–90 seconds.

Goal Bank ~10–14 /100 Phys (~full Thermal share)Weight ~12% of Physics tags (2020–2026)Speed 60–90sShare 11.5%Trend Stable

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Jump to topicThermal props KTG Thermo Radiation

Thermal in Advanced is expansion/calorimetry/conduction, kinetic theory, thermodynamics cycles, and radiation. 100% means path before w/q, phase-feasible calorimetry, and kelvin before T⁴ — never start from a random formula. Thermal full marks are process labels + correct state variables.

Topic-wise on this page

Thermal Physics · chapter details

Same content as each topic page — brief, paper asks, methods, formulas, and families — so you can study here first, then open a full topic only when you need samples or trends.

01 · Calorimetry and expansion numericals with a steady conduction lane

Thermal Properties of Matter

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PromiseSeparate expansion, heat balance and conduction in 15 seconds; one conservation or Fourier statement plus unit discipline finishes the stem.

Thermal properties is macroscopic bookkeeping: lengths/volumes change with T, heat reshuffles with c and L, and 1D conduction moves energy down a gradient. Do not drag full Carnot machinery into a calorimetry stem. Thermal template: expansion / calorimetry / conduction / cooling → write the balance → verify final phase or steady-state assumptions.

01. Linear, area and volume expansion: ΔL=αLΔT, ΔA=2αAΔT, ΔV=γVΔT with γ≈3α for isotropic solids. Apparent expansion of liquid in a vessel uses γ_liquid−γ_vessel.

02. Calorimetry conserves energy when losses are neglected: heat lost = heat gained, including mL for phase change at fixed temperature.

03. Conduction (1D steady): H=dQ/dt=KA(ΔT)/x. Series and parallel slabs combine like thermal resistances R=x/(KA).

How Advanced asks this

Rod/clock/gap expansion; bimetallic bend direction
Liquid-in-glass apparent expansion; overflow volume
Mixture calorimetry with or without latent heat; final phase
Steady heat current through composite slab; interface temperature
Newton cooling: time to cool between two temperatures
Mixed statements on good/bad conductors, emissivity cues, or expansion coefficients

Traps that leak marks

Using γ=2α for volume expansion
Ignoring vessel expansion for liquid overflow
Assuming final T without checking phase completion
Adding K instead of combining thermal resistances
Using average rate instead of Newton’s logarithmic law
Importing Stefan–Boltzmann into a pure conduction numerical
Using γ=2α for volume expansion
Ignoring vessel expansion for liquid overflow
Assuming final T without checking phase completion

Must cover (this topic)

Thermal expansion; calorimetry; latent heat; conduction (1D); convection/radiation ideas; Newton’s cooling

60–90s process

0–15s — Classify: solid/liquid expansion, calorimetry/phase change, 1D conduction network, or Newton cooling.
15–35s — Write ΔL/ΔV formulas, ΣQ=0 heat ledger, H=KAΔT/x (or thermal R), or ln cooling integral.
35–75s — Track which body expands, whether phase change completes, and series vs parallel for slabs.
75–90s — Check final T between extremes, energy sign (lost vs gained), and that radiation Stefan law was not forced unless needed.

Methods that change the score

Expansion laws and phase-feasible calorimetry keep thermal numericals physical.

Method 01 · Who expands?

Gap, ring-on-rod and clock stems hinge on which length grows.

Do this: Apply α or γ to the object whose dimension is constrained or measured—not blindly to every length in the figure.

Method 02 · Phase-aware heat ledger

Prevents illegal ‘final T below 0 °C with leftover ice’ style mistakes.

Do this: Bring each substance to the transition T, pay mL, then continue with mcΔT; stop if latent heat budget runs out.

Method 03 · Thermal circuit

Interface temperatures drop out cleanly like voltage dividers.

Do this: Replace each slab by R=x/(KA); series add R, parallel add 1/R; H=ΔT_total/R_eq.

Method 04 · Newton log interval

Avoids treating cooling rate as constant ΔT/Δt.

Do this: Integrate dθ/(θ−θ₀)=−k dt between the two temperatures given.

Quick formulas

Linear / volume expansion: ΔL=αLΔT; ΔV=γVΔT; γ≈3α (isotropic) — Solids and temperature change
Apparent expansion: γ_app=γ_liq−γ_vessel — Liquid expanding in a container
Heat capacity: Q=mcΔT; Q=mL (phase change) — Calorimetry without chemical reaction
Energy balance: ΣQ_lost+ΣQ_gained=0 (ideal calorimeter) — Mixture and phase problems
Conduction: H=KA(T_hot−T_cold)/x — Steady 1D slab
Thermal resistance: R=x/(KA); H=ΔT/R_eq — Series/parallel composites
Newton cooling: dθ/dt=−k(θ−θ₀); ln[(θ₁−θ₀)/(θ₂−θ₀)]=kt — Cooling/heating toward ambient

Common question families

Linear/area/volume expansion

Looks like: Gap closing, apparent expansion, or bimetallic

Fast model: ΔL=LαΔT; γ≈3α; apparent = true − vessel.

Calorimetry and latent heat

Looks like: Mixture to equilibrium temperature/phase

Fast model: ΣQ=0 with mcΔT and mL terms; test phase feasibility.

Heat capacity of solids/liquids

Looks like: Specific heat from mixing or electrical heating

Fast model: Q = mcΔT = VIt or power×time when heated electrically.

Thermal stress

Looks like: Rod fixed between walls heated

Fast model: If expansion prevented, stress = Y α ΔT.

Sample preview · Linear/area/volume expansion

A steel rod (α=10⁻⁵ /°C) of length 1 m is heated by 100 °C. Find free expansion.

Answer: 1 mm

Free expansion ignores stress.

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02 · Ideal-gas micro↔macro bridge; C_V/C_P and adiabatic indices are frequent

Kinetic Theory of Gases

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PromiseLock degrees of freedom and process type (isothermal vs adiabatic) early; then RMS/pressure relations and C_P−C_V=R finish most numericals.

Kinetic theory connects P=⅓ρv_rms² to macroscopic ideal-gas laws and heat capacities. Advanced tests whether you know what stays constant on a path and how γ enters sound speed and adiabatic bulk modulus. KTG template: ideal assumptions → f and γ → microscopic or process ask → SI units for M and R. Mixture ⇒ ⟨C_V⟩ then γ.

01. Ideal gas: PV=nRT; microscopic pressure P=⅓ρv_rms² with ½m v_rms²=(3/2)k_BT for translational motion in 3D.

02. Equipartition: each active quadratic degree of freedom contributes ½k_BT per molecule. Monatomic f=3; diatomic f=5 (near room T, rotation on).

03. C_V=fR/2 per mole, C_P=C_V+R, γ=C_P/C_V. Isothermal: T fixed, U fixed for ideal gas. Adiabatic: Q=0, TV^{γ−1}=const, PV^γ=const.

How Advanced asks this

v_rms, v_avg, v_mp comparison or ratio after T or M change
Pressure/KE from kinetic interpretation; mean KE and total U
C_V, C_P, γ for mono/dia/mixture; heat at constant P or V
Isothermal vs adiabatic curves; work and ΔU on a path
Bulk modulus of gas / speed of sound link
Mixture of gases: mean molar mass, effective γ or C_V

Traps that leak marks

Using γ=5/3 for diatomic air
Averaging γ of mixture instead of C_V
Setting ΔU≠0 for isothermal ideal gas
Using isothermal B for sound speed
Putting M in g mol⁻¹ into SI speed formulas
Confusing v_rms with most probable speed
Using γ=5/3 for diatomic air
Averaging γ of a mixture instead of C_V
Putting M in g mol⁻¹ into SI speed formulas

Must cover (this topic)

Cv/Cp mono & diatomic

60–90s process

0–15s — Classify: speed/KE kinetic, heat capacity/γ, isothermal path, adiabatic path, or bulk modulus/sound.
15–35s — Write f → C_V, C_P, γ; or P=⅓ρv_rms²; or process constraints (T const vs PV^γ).
35–75s — Use moles consistently; for mixtures weight C_V by mole fraction; keep R units matched to energy.
75–90s — Check mono vs dia f, whether U depends only on T, and isothermal B=P vs adiabatic B=γP.

Methods that change the score

Speed definitions and f→C_v→γ convert kinetic theory into ratio algebra.

Method 01 · f → γ pipeline

Prevents using γ=5/3 on a diatomic adiabatic stem.

Do this: Read mono/dia/mixture → f → C_V → C_P → γ before any process formula.

Method 02 · U from T only

Separates state functions from path functions early.

Do this: For ideal gas compute ΔU=nC_VΔT regardless of path shape; path affects Q and W.

Method 03 · Ratio before constants

Fast MCQ ratios without calculator thrash.

Do this: Cancel R,M when comparing speeds or P after T change.

Method 04 · Modulus matches process

Explains why Newton’s old √(P/ρ) underestimates sound speed.

Do this: Sound/rapid compression → adiabatic B=γP; slow isothermal → B=P.

Quick formulas

Ideal gas: PV=nRT=Nk_BT — Macroscopic state
Kinetic pressure: P=⅓ρ v_rms²; v_rms=√(3RT/M)=√(3P/ρ) — Ideal-gas kinetic link
Translational KE: ½m v_rms²=(3/2)k_BT; U_trans=(3/2)nRT — 3D translation
Heat capacities: C_V=fR/2; C_P=C_V+R; γ=1+2/f — Ideal gas, active f
Speeds: v_mp=√(2RT/M); v_avg=√(8RT/πM); v_rms=√(3RT/M) — Maxwell distribution markers
Adiabatic: PV^γ=const; TV^{γ−1}=const; TP^{(1−γ)/γ}=const — Reversible adiabatic ideal gas
Bulk modulus: B_iso=P; B_ad=γP — Gas compressibility / sound
Internal energy: ΔU=n C_V ΔT (ideal gas, any path) — State function U(T) for ideal gas

Common question families

Ideal-gas microscopic averages

Looks like: v_rms, v_avg, pressure from molecular speeds

Fast model: P=(1/3)ρv_rms²; v_rms=√(3RT/M).

Degrees of freedom and C_v, C_p

Looks like: Mono/di/polyatomic heat capacities

Fast model: C_v = (f/2)R; C_p = C_v+R; γ=1+2/f.

Mixture of ideal gases

Looks like: Mean molar mass, γ_mix, or partial pressures

Fast model: Use mole-weighted averages for M and C_v.

Mean free path / collision basics

Looks like: λ or collision frequency order-of-magnitude

Fast model: λ ∼ 1/(√2 π d² n) with n=N/V.

Sample preview · Ideal-gas microscopic averages

Find the ratio v_rms(H₂)/v_rms(O₂) at the same temperature.

Answer: 4

Lighter gases have larger rms speeds at equal T.

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03 · First-law bookkeeping and Carnot limits — Advanced often joins with KTG γ and P–V cycles

Thermodynamics

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PromiseFix the sign convention and process type in 15 seconds; First-law ledger plus Carnot bound controls almost every Advanced thermo stem, including multi-process cycles.

Thermodynamics here is heat–work–internal energy accounting for ideal gases, plus Second-law limits. Papers punish silent sign flips more than missing γ. Recent Advanced styles mix process identification on P–V diagrams with Carnot bounds and irreversible vs reversible statements. State every convention before substituting. Thermo template: convention → process list → ΔU from state → Q,W from constraints → cycle audit. Kelvin for any T ratio.

01. Heat and work are path functions; U is a state function. First law (common Physics convention): ΔU=Q−W with W=work done by the system, or check the paper’s stated form ΔU=Q+W if W is on the system—pick one and never mix mid-solution.

02. For ideal gases, ΔU=nC_VΔT on every path. Isothermal ⇒ ΔU=0; isochoric ⇒ W=0 (P dV); isobaric ⇒ W=PΔV; adiabatic ⇒ Q=0.

03. Second law: heat engines need two reservoirs; Carnot efficiency η=1−T_C/T_H (kelvin) is the upper bound for reversible engines between those temperatures.

How Advanced asks this

P–V diagram: identify process, compute Q, W, ΔU for a cycle or path
Ideal-gas First-law numerical with mixed processes
Heat engine / refrigerator: η, COP, Carnot limit comparison
Reversible vs irreversible adiabatic or isothermal statements
Equivalence of heat and work; mechanical equivalent contexts
Multi-correct on what is state function vs path function
Join with KTG: γ enters adiabatic work and Carnot only through T, not γ itself

Traps that leak marks

Mixing First-law sign conventions mid-problem
Using °C in Carnot formula
Counting heat rejected as part of Q_H
Applying PV^γ to irreversible adiabatics
Claiming ΔU depends on path for ideal gas
Confusing engine η with refrigerator COP
Mixing First-law signs mid-problem
Using °C inside Carnot efficiency
Applying PV^γ to irreversible adiabatics

Must cover (this topic)

First law for ideal-gas processes
Carnot efficiency

60–90s process

0–15s — Write sign convention explicitly; classify process(es) and whether a cycle (ΔU=0).
15–35s — For each leg: ΔU=nC_VΔT; then Q and W from process constraints; for engines use Q_H, Q_C, W.
35–75s — Sum cycle quantities; apply Carnot bound if efficiency is compared to T_C, T_H.
75–90s — Check kelvin temperatures, ΔU=0 on cycle, and that irreversible claims were not given reversible formulas blindly.

Methods that change the score

Path labels fix w and q; state functions fix ΔU — Advanced cycles punish silent sign flips.

Method 01 · Convention stamp

Eliminates the #1 Advanced thermo arithmetic error.

Do this: Write ‘W by’ or ‘W on’ at the top of the rough sheet before any number.

Method 02 · Leg table

Cycles become addition, not narrative.

Do this: For each process column: type | ΔT | ΔU | W | Q.

Method 03 · Carnot ceiling

Instant multi-correct filter on impossible engines.

Do this: Before trusting a claimed η, compute 1−T_C/T_H and reject anything larger.

Method 04 · State vs path split

Blocks irreversible-process traps.

Do this: Compute ΔU from endpoints only; never infer Q from ΔU alone without the path.

Quick formulas

First law: ΔU=Q−W (W by system) — or ΔU=Q+W (W on system); lock one — Every thermo energy balance
Ideal gas U: ΔU=n C_V ΔT (any path) — Ideal gas
Work (quasi-static): W_by=∫P dV; isobaric PΔV; isothermal nRT ln(V₂/V₁) — Ideal-gas paths
Adiabatic work: W_by=(nRΔT)/(1−γ)=−ΔU (Q=0) — Reversible adiabatic ideal gas
Engine efficiency: η=W/Q_H=1−|Q_C|/Q_H — Heat engine
Carnot: η_C=1−T_C/T_H (T in kelvin) — Reversible engine between two reservoirs
Refrigerator COP: COP=Q_C/W=Q_C/(Q_H−Q_C) — Fridge/heat pump definitions differ—read ask
Cycle: ΔU_cycle=0 ⇒ Q_net=W_net (with consistent signs) — Closed cycles

Common question families

First-law process accounting

Looks like: Isochoric/isobaric/isothermal/adiabatic/irreversible

Fast model: Label path; then ΔU=q+w with paper’s sign convention.

PV diagram cycle work

Looks like: Closed loop; efficiency or net work

Fast model: W_net = area; for ideal gas use process formulas on each leg.

Adiabatic and polytropic relations

Looks like: TV^{γ−1}, PV^γ, or polytropic n

Fast model: Use the matching invariant for reversible adiabatic ideal gas.

Carnot and second-law limits

Looks like: η_Carnot, refrigerator COP, or irreversibility

Fast model: η≤1−T_C/T_H; equality only for Carnot.

Sample preview · First-law process accounting

One mole ideal gas is heated isochorically so ΔT=10 K. Take C_v=1.5R. Find ΔU.

Answer: 15R

Isochoric ΔU still follows C_vΔT.

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04 · Stefan/Wien/Kirchhoff numericals and net-rate patterns; deepen exam radiation habits

Heat Transfer & Radiation

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PromiseTreat radiation as power laws in T and e/a; Kirchhoff links e and a, Stefan gives net power, Wien shifts the spectrum—audit T⁴ and kelvin every time.

This topic sharpens radiation and heat-transfer exam patterns beyond the thermal-properties sketch: blackbody powers, Kirchhoff’s law, Wien displacement, Stefan–Boltzmann net exchange, and when conduction/convection language is only qualitative scaffolding. Radiation template: kelvin → emitted vs net → e/a via Kirchhoff → energy balance for cooling. Wien only for λ_max.

01. A blackbody absorbs all incident radiation (a=1) and is the ideal emitter. Absorptive power a and emissive power e are linked by Kirchhoff: e/a is universal for a given λ,T for bodies in equilibrium with radiation—good absorbers are good emitters.

02. Stefan–Boltzmann: power radiated E=σA T⁴ for a blackbody; for grey body eσA T⁴ with emissivity e≤1. Net power when surrounded by T₀ is eσA(T⁴−T₀⁴) (same e on absorb/emit if Kirchhoff applies).

03. Wien: λ_max T=b (displacement). Hotter bodies peak at shorter wavelength; total power still follows T⁴.

How Advanced asks this

Net radiation rate between body and enclosure; time to cool via mc dT/dt
λ_max comparison via Wien; colour/temperature ordering
Kirchhoff statements: absorptive vs emissive power, blackbody limits
Ratio of powers at two temperatures; e unknown cancels
Sphere cooling / same mass different shapes: area dependence
Mixed conduction–radiation qualitative ranking (which dominates)

Traps that leak marks

Leaving temperature in °C inside T⁴
Using P=σAT⁴ when net exchange with T₀ is required
Applying Wien’s constant to total power
Assuming polished surfaces radiate as blackbodies
Confusing emissive power with absorptive power without Kirchhoff
Using Newton cooling linear law when the stem is pure T⁴ radiation
Leaving temperature in °C inside T⁴
Using emitted-only power when net exchange is required
Applying Wien’s constant to total power

Must cover (this topic)

Wien / Stefan / Kirchhoff radiation

60–90s process

0–15s — Classify: Stefan net power, Wien λ_max, Kirchhoff e–a, or cooling differential with radiation.
15–35s — Write P_net=eσA(T⁴−T₀⁴), λT=b, or e/a logic; convert all T to kelvin.
35–75s — Cancel σ,e,A in ratios; for cooling couple P_net to mc dT/dt when asked.
75–90s — Check T⁴ not T, blackbody e=1, and that Wien uses λ_max not arbitrary λ.

Methods that change the score

Thermal resistance networks and net T⁴ radiation replace vague heat-flow talk.

Method 01 · Kelvin-and-fourth audit

Most radiation numerical disasters are °C left in place or linear ΔT habits.

Do this: Convert °C→K before any T⁴; estimate whether T≪T₀ terms matter.

Method 02 · Ratio cancel

Leaves pure (T₁/T₂)⁴ or net (T⁴−T₀⁴) ratios.

Do this: For P₁/P₂ at two T, cancel e,σ,A when unchanged.

Method 03 · Kirchhoff filter

Statement options die without computing σ.

Do this: Translate colour/polish statements into high/low a and hence high/low e.

Method 04 · Area-to-energy couple

Same-volume shape comparisons become pure geometry.

Do this: When mass/c fixed, dT/dt∝−A(T⁴−T₀⁴); maximise A for faster radiative cooling.

Quick formulas

Stefan (black): P=σ A T⁴; σ=5.67×10⁻⁸ W m⁻² K⁻⁴ — Ideal emitter
Grey / net: P_net=e σ A (T⁴−T₀⁴) — Body in large enclosure at T₀
Kirchhoff: e_λ / a_λ = f(λ,T); good absorber ⇒ good emitter — Equilibrium radiation exchange
Wien: λ_max T=b ≈2.89×10⁻³ m·K — Spectral peak vs temperature
Emissive power: E=e E_black; a≤1, e≤1; black a=e=1 — Real surface comparison
Cooling link: mc dT/dt=−eσA(T⁴−T₀⁴) (radiation-dominated) — Rate of fall of temperature
Energy radiated: ΔU_rad=∫P_net dt — Finite-time radiation loss

Common question families

Conduction (1D steady)

Looks like: Slab, composite wall, or rate H=kAΔT/L

Fast model: Series thermal resistances add; parallel conductances add.

Newton’s law of cooling

Looks like: dT/dt ∝ (T−T₀); calorimeter cooling

Fast model: Integrate exponential approach to ambient.

Stefan / blackbody power

Looks like: Net power σA(T⁴−Tₛ⁴) or eσAT⁴

Fast model: Use net radiation when surroundings matter.

Wien displacement

Looks like: λ_max T = b; spectrum peak shift

Fast model: Apply Wien directly; higher T ⇒ shorter λ_max.

Sample preview · Conduction (1D steady)

A slab of thickness 2 cm, area 0.1 m² and k=0.2 W m⁻¹ K⁻¹ has faces at 100 °C and 0 °C. Find heat current.

Answer: 100 W

Steady conduction is a thermal Ohm’s law.

More samples on full topic page →

Open full Radiation notes (samples · trends · joins) →

Read first

How to use these notes for 100%

Point 01

Depth upgrade: Thermodynamics is process accounting (ΔU=Q−W with your sign convention locked). Cycles need state points before efficiency slogans.

Point 02

Radiation laws (Wien/Stefan) are families — identify which quantity is held fixed before writing proportions.

Speed system

60–90 second answer protocol

Use this on every stem — SC, MC, NUM, MATCH.

0
0–15s — Name the family: Expansion / Calorimetry / Kinetic / First-law process / Cycle / Conduction / Radiation/Wien. Circle T units and what is asked (Q, W, ΔU, η, H, λ_max).
15
15–35s — Stamp path (isochoric/isobaric/isothermal/adiabatic) or phase hypothesis; write governing relations only (ΔU=nC_vΔT, ΣQ=0, R=L/(kA), σAT⁴).
35
35–75s — Plug carefully; for cycles fill a leg table and verify ΣΔU=0; for radiation convert °C→K before powers.
75
75–90s — Sanity: sign convention, Carnot bound, phase feasibility, kelvin check. Bubble.

Convert temperatures; use net σA(T⁴−T₀⁴) when surroundings matter; keep Wien separate from Stefan.

Why it saves time

Celsius-in-T⁴ is the classic radiation trap.

Instant recall

Mental bank

Keep these cold — no derivation during the 60–90s window.

ΔL=LαΔT; γ≈3α; thermal stress ≈ YαΔT if fully constrained
Ideal gas: PV=nRT; ΔU=nC_vΔT
C_v=(f/2)R; C_p=C_v+R; γ=1+2/f
Isothermal reversible: w=−nRT ln(V₂/V₁) (paper sign)
Adiabatic: PV^γ, TV^{γ−1}; q=0
Carnot: η=1−T_C/T_H (kelvin)
v_rms=√(3RT/M); P=(1/3)ρ v_rms²
H=kAΔT/L; P_net=eσA(T⁴−T₀⁴); λ_max T=b
Lock sign convention for first law
Ideal-gas ΔU depends on T only
Carnot is a bound, not a default engine

Inside Thermal

Sub-portion playbooks

Each family has a trigger, template, and drill.

01 · Medium–High

Thermal Properties · Calorimetry · Conduction

45s triggerSee gap/α, mixture/latent, or composite slab → expansion law, ΣQ=0, or R network.

Template (write on rough)

Expansion: free vs constrained; include vessel for liquids.
Calorimetry: phase hypothesis → ΣQ=0 → feasibility check.
Conduction: draw R=L/(kA); combine; H=ΔT/R.
Electrical heating: VIt = mcΔT when relevant.

Must automate

Apparent expansion of liquid in vessel
Ice–water–steam heat accounting
Series slab interface temperature

Traps

Latent heat applied away from the phase-change temperature
Parallel slabs treated as series resistances

Drill

Daily: 1 calorimetry or expansion + 1 conduction stem

02 · Highest Thermal yield

Kinetic Theory · Thermodynamics

45s triggerSee v_rms/C_v or w/q/cycle → f→C_v or path label.

Template (write on rough)

Kinetic: identify which speed; use √(RT/M) factor; mixture by moles.
First law: path → ΔU → w → q.
Adiabatic/polytropic: correct invariant.
Cycle: leg table; η vs Carnot bound.

Must automate

Mono/dia C_v, C_p, γ
Isochoric/isobaric/isothermal/adiabatic quick set
Carnot η and refrigerator COP definitions

Traps

Averaging γ of a mixture linearly
Using °C in Carnot formula
Efficiency with |Q_cold| in the denominator

Drill

Daily: 1 kinetic ratio + 1 first-law/cycle NUM

03 · Medium — easy if kelvin-safe

Heat Transfer · Radiation

45s triggerSee cooling rate, Stefan, Wien → net T⁴ or λ_max T=b.

Template (write on rough)

Newton cooling: θ=T−T₀; exponential fit.
Stefan: kelvin; net power if enclosure given.
Wien: λ_max T=b independent of Stefan power.
MC: separate spectral peak from total power claims.

Must automate

Net Stefan numerical
Wien temperature from peak shift
e factor on power only (not on Wien b)

Traps

Forgetting surroundings temperature in net radiation
Using Wien to replace Stefan

Drill

3×/week: 1 Stefan + 1 Wien/cooling stem

Habit

Common practice system

Same system every week — builds transferable speed.

Daily

20 min: 4 Thermal stems across expansion, kinetic, process, radiation — path/phase named by 15s.
Write sign convention once at the top of every thermo solution.
Redo any cycle where ΣΔU≠0 on your table.

Weekly

1 full PV-cycle set with η and Carnot comparison.
1 mixture C_v/γ blitz (6 questions).
Error log: kelvin misses, phase impossibilities, γ averaging.

Before every mock

Flash: process rules, Carnot, v_rms, Stefan/Wien — 6 minutes.
In paper: bank direct first-law and expansion asks early.

Full marks gate

100% checklist for Thermal Physics

Tick these only when true on timed practice — not when “you know the chapter”.

Every first-law stem starts with a path label.
Calorimetry always tests phase feasibility.
Mixture γ never mole-averaged directly.
Cycle efficiency uses Q_in only.
Carnot comparisons use kelvin temperatures.
Radiation uses net T⁴ when T₀ is given.
Wien and Stefan are applied independently when both appear.
Process path named before computing Q or W.
rms / f degrees of freedom match the gas model used.

Paper coverage for Thermal Syllabus map Subject analysis Physics · 300 plan

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