Physics notesThermalRadiation
Independent topic page
Treat 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.
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.
04. Exam patterns stack: rate of cooling from energy loss, sphere vs cube area-to-volume, and comparing polished vs blackened surfaces via e and a.
05. Radiation lives in kelvin. Blackbody emitted power σAT⁴; net exchange with surroundings is eσA(T⁴−T₀⁴). Polished surfaces have low e and low a together.
06. Kirchhoff: good absorbers are good emitters at the same λ and T in equilibrium language—e ↔ a. Wien’s law fixes λ_max∝1/T, not total power.
07. Cooling by radiation: mc dT/dt = −eσA(T⁴−T₀⁴) (plus other channels if present). Do not replace T⁴ by a casual ΔT Newton law when the stem is pure radiation.
Official · 2026
Official syllabus points for Heat Transfer & Radiation only — not the full Thermal portion map. Portion hub: Thermal · Thermodynamics/Kinetic Theory analysis.
No topic-specific exclusions flagged — finish the unit points below for Radiation.
Source: https://jeeadv.ac.in/documents/jee-advanced-2026-syllabus.pdf
Exam focusRadiation laws (Stefan/Wien), Newton cooling, and blackbody ideas.
Syllabus points
2020–2026 paper weight
Topic match inside parent portion Thermodynamics/Kinetic Theory (11.5% of Physics tags). Stats below are portion backdrop; matched subtopics show where Heat Transfer & Radiation sits.
No separate subtopic tag for Radiation — showing Thermodynamics/Kinetic Theory backdrop only.
Portion-wide type/difficulty mix lives on the Thermodynamics/Kinetic Theory analysis — not repeated here so this page stays on Radiation.
Full PCM trends board → · Thermodynamics/Kinetic Theory subject page →
Cross-topic stems
Advanced rarely asks a chapter in isolation. These are tagged multi-idea Physics stems that touch Heat Transfer & Radiation — practise the knowledge bridge, not only the single-chapter drill.
No tagged mixed stem matched this topic’s keywords yet. Still revise the joins listed under Trends, and scan the mixed joins board for Mechanics / EM / Optics bridges.
Why methods matter
Thermal resistance networks and net T⁴ radiation replace vague heat-flow talk.
Most radiation numerical disasters are °C left in place or linear ΔT habits.
Do thisConvert °C→K before any T⁴; estimate whether T≪T₀ terms matter.
Most radiation numerical disasters are °C left in place or linear ΔT habits.
27 °C is 300 K; (300)⁴ vs (27)⁴ is not a small mistake—it is a different universe.
Leaves pure (T₁/T₂)⁴ or net (T⁴−T₀⁴) ratios.
Do thisFor P₁/P₂ at two T, cancel e,σ,A when unchanged.
Leaves pure (T₁/T₂)⁴ or net (T⁴−T₀⁴) ratios.
Same body: P(2T₀)/P(T₀)=16 if T₀=0 surroundings approximation.
Statement options die without computing σ.
Do thisTranslate colour/polish statements into high/low a and hence high/low e.
Statement options die without computing σ.
Polished silver: low a and low e; cools slower by radiation than a blackened surface at same T.
Same-volume shape comparisons become pure geometry.
Do thisWhen mass/c fixed, dT/dt∝−A(T⁴−T₀⁴); maximise A for faster radiative cooling.
Same-volume shape comparisons become pure geometry.
Among equal-volume bodies, the one with larger surface area cools faster by radiation.
Processed examples
Read the impact line first. Then notice which family/model was chosen. The solution is written the way your rough sheet should look in the hall.
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.
This stem rewards early recognition of the conduction (1d steady) model.
Model chosenH=kAΔT/L.
Answer100 W
Takeaway: Steady conduction is a thermal Ohm’s law.
A black body of area 0.1 m² at 727 °C radiates into surroundings at 27 °C. Find net power. Take σ=6×10⁻⁸ SI.
This stem rewards early recognition of the stefan / blackbody power model.
Model chosenP=σA(T⁴−Tₛ⁴).
Answer≈5.95 kW
Takeaway: Always convert Celsius to kelvin before T⁴.
A black body at temperature T is surrounded by a large enclosure at T/2. Find the net power radiated per unit area in terms of σ and T.
This Advanced-level variation couples hidden constraints with the stefan / blackbody power model.
Model chosenNet flux is σ(T⁴−Tₛ⁴).
Answer(15/16)σT⁴
Takeaway: Surroundings enter as Tₛ⁴, not as a linear correction.
Reusable models
Advanced stems cluster. Name the family in 10–15s, write the fast model, then run the same path. Do not invent a new plan each time.
Looks likeSlab, composite wall, or rate H=kAΔT/L
Fast modelSeries thermal resistances add; parallel conductances add.
Recognition fixes the model before arithmetic begins.
Do not start blind expansion or casework before identifying the governing model.
Looks likedT/dt ∝ (T−T₀); calorimeter cooling
Fast modelIntegrate exponential approach to ambient.
Recognition fixes the model before arithmetic begins.
Do not start blind expansion or casework before identifying the governing model.
Looks likeNet power σA(T⁴−Tₛ⁴) or eσAT⁴
Fast modelUse net radiation when surroundings matter.
Recognition fixes the model before arithmetic begins.
Do not start blind expansion or casework before identifying the governing model.
Looks likeλ_max T = b; spectrum peak shift
Fast modelApply Wien directly; higher T ⇒ shorter λ_max.
Recognition fixes the model before arithmetic begins.
Do not start blind expansion or casework before identifying the governing model.
Hall timing
Underline given/asked quantities, free/closed surface labels, idealisations and the exact target. Reject any formula whose assumptions are already violated.
Write the governing relation symbolically before substitution; define a control volume, free body, reference level, or thermodynamic path if the stem mixes regimes.
Keep ratios and differentials exact as long as possible. Carry signs, gauge/absolute pressures, degrees of freedom and units on the rough sheet instead of repairing them later.
Check dimensions, limiting cases and physical sense. For multi-correct, test every option independently rather than forcing one common conclusion.
After the model is locked
P=σ A T⁴; σ=5.67×10⁻⁸ W m⁻² K⁻⁴
Ideal emitter
P_net=e σ A (T⁴−T₀⁴)
Body in large enclosure at T₀
e_λ / a_λ = f(λ,T); good absorber ⇒ good emitter
Equilibrium radiation exchange
λ_max T=b ≈2.89×10⁻³ m·K
Spectral peak vs temperature
E=e E_black; a≤1, e≤1; black a=e=1
Real surface comparison
mc dT/dt=−eσA(T⁴−T₀⁴) (radiation-dominated)
Rate of fall of temperature
ΔU_rad=∫P_net dt
Finite-time radiation loss
Make it automatic