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Thermal Properties of Matter

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

Portion ThermalFocus Calorimetry and expansion numericals with a steady conduction laneTarget 60–90sPortion share 11.5%Trend Stable
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.

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

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).

04. Convection and radiation appear as qualitative or Newton-cooling contexts here; deep blackbody laws live in heat-transfer-radiation. Newton’s law: dθ/dt∝−(θ−θ₀) for cooling under stated assumptions.

05. Expansion: ΔL=αLΔT; volume γ≈3α for isotropic solids. Liquid-in-vessel overflow needs apparent expansion—liquid γ minus vessel γ.

06. Calorimetry is heat balance with phases: Q=mcΔT between phase changes and mL at the change. Hypothesis the final phase, then verify it is consistent.

07. Steady conduction: H=KAΔT/x; series shares H, parallel shares ΔT. Newton cooling is rate ∝ excess temperature—integrate when asked for time, do not linearise blindly.

Official · 2026

Syllabus for this topic

Official syllabus points for Thermal Properties of Matter only — not the full Thermal portion map. Portion hub: Thermal · Thermodynamics/Kinetic Theory analysis.

Syllabus on this page is topic-scoped: Thermal Properties of Matter. The parent portion (Thermodynamics/Kinetic Theory) also covers other topics — use the portion hub for the full map.

Must cover (this topic)

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

Gaps / watch-outs

No topic-specific exclusions flagged — finish the unit points below for Thermal props.

Source: https://jeeadv.ac.in/documents/jee-advanced-2026-syllabus.pdf

Unit 01

Thermal Properties of Matter

high

Exam focusThermal expansion, calorimetry, latent heat, and conduction.

Syllabus points

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

Full Physics syllabus →

Cross-topic stems

Mixed joins for this topic

Advanced rarely asks a chapter in isolation. These are tagged multi-idea Physics stems that touch Thermal Properties of Matter — 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.

All mixed joins →

Why methods matter

Common methods that change your score

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

01

Who expands?

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

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

Why it works

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

See it once

Hole in a plate expands as if filled with the same material: diameter uses α of the plate.

02

Phase-aware heat ledger

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

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

Why it works

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

See it once

Ice + water: if Q available < m_ice L_f, final state is ice–water at 0 °C.

03

Thermal circuit

Interface temperatures drop out cleanly like voltage dividers.

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

Why it works

Interface temperatures drop out cleanly like voltage dividers.

See it once

Two slabs in series: (T₁−T_i)/R₁=(T_i−T₂)/R₂.

04

Newton log interval

Avoids treating cooling rate as constant ΔT/Δt.

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

Why it works

Avoids treating cooling rate as constant ΔT/Δt.

See it once

Same k from one timed interval predicts another: ratios of log excess temperatures.

Processed examples

Sample questions · full working

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.

01

bankFamily · Linear/area/volume expansion

Sample question

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

This stem rewards early recognition of the linear/area/volume expansion model.

Model chosenΔL=LαΔT.

Processed solution

  1. ΔL=1×10⁻⁵×100=10⁻³ m.

Answer1 mm

Takeaway: Free expansion ignores stress.

02

standardFamily · Calorimetry and latent heat

Sample question

100 g water at 20 °C mixes with 50 g water at 80 °C. Find final temperature (no loss).

This stem rewards early recognition of the calorimetry and latent heat model.

Model chosenΣm c ΔT=0.

Processed solution

  1. 100(T−20)+50(T−80)=0.
  2. 150T=6000 ⇒ T=40 °C.

Answer40 °C

Takeaway: Heat lost equals heat gained.

03

twistFamily · Calorimetry and latent heat

Sample question

50 g ice at −10 °C is mixed with 100 g water at 50 °C in an insulating calorimeter. Use c_ice=0.5 cal g⁻¹ °C⁻¹, c_water=1 cal g⁻¹ °C⁻¹, L_f=80 cal g⁻¹. Find the final state.

This Advanced-level variation couples hidden constraints with the calorimetry and latent heat model.

Model chosenTest whether available heat can bring ice to 0 °C and melt it.

Processed solution

  1. Heat to warm ice to 0 °C: 50×0.5×10=250 cal.
  2. Heat to melt all ice: 50×80=4000 cal; total needed before warming meltwater: 4250 cal.
  3. Heat available cooling water to 0 °C: 100×1×50=5000 cal.
  4. Surplus 750 cal warms 150 g water: ΔT=750/150=5 °C.
  5. Final: all liquid water at 5 °C.

Answer150 g water at 5 °C

Takeaway: Phase checkpoints prevent solving a single temperature equation blindly.

Reusable models

Common question families

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.

01

Linear/area/volume expansion

Looks likeGap closing, apparent expansion, or bimetallic

Fast modelΔL=LαΔT; γ≈3α; apparent = true − vessel.

Same solve path

  1. Identify constrained vs free expansion.
  2. Apply the matching expansion law.
  3. Include vessel expansion if liquid-in-container.
  4. Solve for T or gap.

Rough skeleton

  • α/γ
  • Δ size
  • T

Why faster

Recognition fixes the model before arithmetic begins.

Refuse this

Do not start blind expansion or casework before identifying the governing model.

02

Calorimetry and latent heat

Looks likeMixture to equilibrium temperature/phase

Fast modelΣQ=0 with mcΔT and mL terms; test phase feasibility.

Same solve path

  1. Guess final phase.
  2. Write heat gains/losses.
  3. Set ΣQ=0.
  4. Reject inconsistent phase roots.

Rough skeleton

  • phase guess
  • ΣQ=0
  • T_f

Why faster

Recognition fixes the model before arithmetic begins.

Refuse this

Do not start blind expansion or casework before identifying the governing model.

03

Heat capacity of solids/liquids

Looks likeSpecific heat from mixing or electrical heating

Fast modelQ = mcΔT = VIt or power×time when heated electrically.

Same solve path

  1. Identify heat source and sink.
  2. Equate energy accounting.
  3. Solve c or ΔT.
  4. Watch units (cal vs J).

Rough skeleton

  • energy in
  • mcΔT
  • c

Why faster

Recognition fixes the model before arithmetic begins.

Refuse this

Do not start blind expansion or casework before identifying the governing model.

04

Thermal stress

Looks likeRod fixed between walls heated

Fast modelIf expansion prevented, stress = Y α ΔT.

Same solve path

  1. Compute free ΔL.
  2. Set mechanical compression equal to free expansion.
  3. Use Y to find force/stress.
  4. Check buckling not asked.

Rough skeleton

  • free ΔL
  • constraint
  • stress

Why faster

Recognition fixes the model before arithmetic begins.

Refuse this

Do not start blind expansion or casework before identifying the governing model.

Hall timing

60–90s process

  1. 0–15s
    Classify: solid/liquid expansion, calorimetry/phase change, 1D conduction network, or Newton cooling.

    Underline given/asked quantities, free/closed surface labels, idealisations and the exact target. Reject any formula whose assumptions are already violated.

  2. 15–35s
    Write ΔL/ΔV formulas, ΣQ=0 heat ledger, H=KAΔT/x (or thermal R), or ln cooling integral.

    Write the governing relation symbolically before substitution; define a control volume, free body, reference level, or thermodynamic path if the stem mixes regimes.

  3. 35–75s
    Track which body expands, whether phase change completes, and series vs parallel for slabs.

    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.

  4. 75–90s
    Check final T between extremes, energy sign (lost vs gained), and that radiation Stefan law was not forced unless needed.

    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

Quick formula bank

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

Mental bank

  • ΔL=αLΔT; γ≈3α
  • Apparent γ: liquid minus vessel
  • Q=mcΔT; Q=mL at phase change
  • Heat lost = heat gained (ideal)
  • H=KAΔT/x steady conduction
  • Series: same H; parallel: same ΔT
  • Newton: rate ∝ excess temperature
  • Hole expands with the plate
  • γ≈3α; apparent γ = γ_liq − γ_vessel
  • Heat lost = heat gained (ideal calorimeter)
  • Series slabs: same H; parallel: same ΔT
  • ΔT in K or °C is fine; absolute T only when required

Make it automatic

Practice · checklist

Daily

  • One expansion, one calorimetry (with L), one conduction composite.
  • One Newton-cooling log practice.

Weekly

  • Mixed thermal-properties timed set.
  • Rework errors by rewriting the heat ledger or R-network from scratch.

100% checklist

  • Expansion applied to the correct object
  • α/γ relation consistent
  • Calorimetry includes latent heat when needed
  • Final phase hypothesis verified
  • Conduction steady-state assumptions stated
  • R_eq built correctly for series/parallel
  • Newton integrated, not linearised blindly
  • Units: K vs °C differences OK for ΔT
  • Expansion applied to the correct object
  • Calorimetry includes latent heat when needed
  • Conduction network (series/parallel) built correctly
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