Class 11 — Thermal Properties of Matter

Chapter Overview & Weightage

Thermal Properties of Matter is a 4-5 mark chapter in Class 11 boards, but its concepts feed directly into Thermodynamics (next chapter) and Kinetic Theory (also Class 11). Master this and the next two chapters become much smoother.

Year	Marks Asked	Question Type
2024	5	Numerical on heat conduction + theory
2023	4	Calorimetry + thermal expansion
2022	5	Stefan’s law + radiation
2021	3	Specific heat numerical
2020	4	Newton’s law of cooling

CBSE has been alternating between conduction problems and calorimetry numericals year after year. Expect at least one of these in the 2026 paper.

Key Concepts You Must Know

Temperature scales — Celsius, Fahrenheit, Kelvin conversions
Thermal expansion — linear ( $\alpha$ ), areal ( $\beta = 2\alpha$ ), volume ( $\gamma = 3\alpha$ )
Specific heat — $c$ (for solids/liquids), $C_p$ and $C_v$ (for gases)
Latent heat — $L_f$ (fusion), $L_v$ (vaporization)
Calorimetry — principle of mixtures
Heat transfer — conduction (Fourier), convection, radiation (Stefan’s law)
Newton’s law of cooling — exponential approach to ambient temperature
Black body radiation — Wien’s displacement, Stefan-Boltzmann

Important Formulas

L = L_0(1 + \alpha \Delta T), \quad V = V_0(1 + \gamma \Delta T)

Use when finding new dimensions after heating/cooling. For a metal rod heated from $20°\text{C}$ to $120°\text{C}$ , plug $\Delta T = 100$ .

Q = mc \Delta T

Use when calculating heat to raise temperature of a substance without state change.

Q = mL

Use during phase changes — temperature stays constant while $Q$ goes into breaking molecular bonds.

\frac{Q}{t} = -kA\frac{dT}{dx}

For steady-state through a slab: $\dfrac{Q}{t} = \dfrac{kA(T_1 - T_2)}{L}$ .

P = \sigma \epsilon A T^4

For net radiation between body at $T$ and surroundings at $T_0$ : $P_{net} = \sigma \epsilon A (T^4 - T_0^4)$ .

\frac{dT}{dt} = -k(T - T_0)

Solution: $T - T_0 = (T_i - T_0) e^{-kt}$ .

Solved Previous Year Questions

PYQ 1 (CBSE 2024)

A copper rod and an iron rod of equal length and cross-section are joined end-to-end. The free end of copper is at $100°\text{C}$ and free end of iron at $0°\text{C}$ . Find the temperature of the junction. ( $k_{Cu} = 400$ , $k_{Fe} = 80$ W/m K.)

Heat flow through both rods is equal in steady state: $\dfrac{k_{Cu} A (100 - T)}{L} = \dfrac{k_{Fe} A (T - 0)}{L}$ .

$400(100 - T) = 80T \implies 40000 - 400T = 80T \implies T = 40000/480 = 83.3°\text{C}$ .

Answer: $T \approx \mathbf{83.3°\text{C}}$ .

PYQ 2 (CBSE 2023)

$50 \text{ g}$ of ice at $0°\text{C}$ is added to $200 \text{ g}$ water at $30°\text{C}$ . Find final temperature. ( $L_f = 80 \text{ cal/g}$ , $c = 1 \text{ cal/g}°\text{C}$ .)

Heat released by water cooling to $0°\text{C}$ : $200 \times 1 \times 30 = 6000 \text{ cal}$ .

Heat to melt ice: $50 \times 80 = 4000 \text{ cal}$ .

Excess heat after melting all ice: $6000 - 4000 = 2000 \text{ cal}$ .

This warms the now- $250 \text{ g}$ water: $T = 2000/(250 \times 1) = 8°\text{C}$ .

Answer: Final temperature $= \mathbf{8°\text{C}}$ .

PYQ 3 (CBSE 2022)

A black body at $T = 300 \text{ K}$ radiates power $P_1$ . If the temperature is doubled, find the new power $P_2$ . ( $\sigma = 5.67 \times 10^{-8}$ , area $1 \text{ m}^2$ .)

By Stefan’s law, $P \propto T^4$ . So $P_2/P_1 = (600/300)^4 = 16$ .

$P_1 = \sigma T^4 = 5.67 \times 10^{-8} \times (300)^4 = 459.3 \text{ W}$ . So $P_2 = 7349 \text{ W}$ .

Answer: $P_2 = 16 P_1 = \mathbf{7349 \text{ W}}$ .

Difficulty Distribution

Easy (1-2 marks): Definitions, unit conversions, simple plug-ins.
Medium (3 marks): Calorimetry mixtures, conduction in single rods, expansion problems.
Hard (5 marks): Composite walls (series/parallel conduction), cooling curves, radiation in cavities, blackbody questions.

About 60% of marks come from medium and 30% from easy. Prep accordingly.

Expert Strategy

Topper’s approach: Memorize the four big formulas (heat equation, latent heat, Fourier, Stefan) cold. CBSE problems are mostly direct applications — recognize which formula applies, plug in. Don’t get distracted by Wien’s displacement or convection unless explicitly asked.

For conduction in series, treat each material like a resistor: total thermal resistance = sum of individual resistances. $R_{thermal} = L/(kA)$ . This trick handles 90% of composite-wall problems in 3 lines.

Common Traps

Trap 1: Forgetting that $L_f$ is needed for $0°\text{C}$ ice → $0°\text{C}$ water transition. Many students just use $mc\Delta T$ — wrong.

Trap 2: Using $\alpha$ for volume expansion. Volume expansion uses $\gamma = 3\alpha$ , not $\alpha$ .

Trap 3: In Stefan’s law, students often forget the fourth power and write $T^2$ or linear. $T^4$ — engrave it.

Trap 4: Newton’s law of cooling assumes small temperature differences. For very hot bodies cooling to room temperature, use Stefan’s law.

Trap 5: Mixing units of specific heat (cal/g vs J/kg). $1 \text{ cal/g}°\text{C} = 4184 \text{ J/kg K}$ . Always check.