Thermal Properties of Matter Class 11: Notes, Calorimetry and Numericals

What Thermal Properties of Matter is about

Weightage: This chapter is part of Unit VII, Properties of Bulk Matter. The syllabus groups Unit VII with Unit VIII, Thermodynamics and Unit IX, Behaviour of Perfect Gases and Kinetic Theory of Gases: together they carry 20 of the 70 theory marks in the school annual exam.Source: CBSE Physics (042) syllabus 2026-27, Class XI course structure, Unit VII Properties of Bulk Matter

Key concepts

Temperature, heat and temperature scales

NCERT section 10.2 to 10.4

Temperature measures how hot or cold a body is. Heat is energy transferred between bodies because of a temperature difference; SI unit the joule (older unit the calorie, 1 cal ≈ 4.186 J).

Scales use two fixed points (ice point and steam point): Celsius 0 and 100, Fahrenheit 32 and 212. So
$\frac{t_F-32}{180}=\frac{t_C}{100}$, i.e. $t_F=\frac{9}{5}{t}_C+32$.

Ideal-gas equation and absolute temperature: for a fixed amount of a low-density gas, $PV=\mu RT$. At constant volume, pressure falls linearly with temperature; extending the line to zero pressure gives absolute zero, −273.15 °C. The Kelvin scale starts there: $T=t_C+273.15$. A change of 1 K equals a change of 1 °C.

Worked example

Normal body temperature is 98.6 °F. Express it in °C and in K. [1 mark]

Try it first, then show the solutionSolution

1. $t_C=\frac{5}{9}(98.6-32)=\frac{5}{9}\times 66.6=37°C$
2. $T=37+273.15=310.15K$

Answer: 37 °C; 310.15 K

Thermal expansion of solids

NCERT section 10.5

Most solids expand on heating because their atoms vibrate more and move slightly farther apart.

• Linear expansion: $\frac{\Delta l}{l}=\alpha \Delta T$, α = coefficient of linear expansion (K${}^{-1}$).
• Area expansion: $\frac{\Delta A}{A}=\beta \Delta T$, with $\beta =2\alpha$.
• Volume expansion: $\frac{\Delta V}{V}=\gamma \Delta T$, with $\gamma =3\alpha$ for an isotropic solid.

Why γ = 3α: a cube of side l becomes $l(1+\alpha \Delta T)$, so its volume becomes $l^3(1+\alpha \Delta T{)}^3\approx l^3(1+3\alpha \Delta T)$, neglecting tiny squared terms.

Metals expand more than glass or invar. Uses and effects: gaps in railway tracks and bridges, fitting iron rims on cart wheels by heating, bimetallic strips in thermostats. A hole in a plate expands as if it were made of the same material.

Worked example

A steel rail 10 m long is laid at 10 °C. How much longer is it at 50 °C? (α = $1.2\times 10^{-5}$ K${}^{-1}$) [1 mark]

Try it first, then show the solutionSolution

1. $\Delta l=l\alpha \Delta T=10\times 1.2\times 10^{-5}\times 40$
2. $\Delta l=4.8\times 10^{-3}m=4.8mm$

Answer: 4.8 mm

Expansion of liquids and gases; anomalous expansion of water

NCERT section 10.5

Liquids and gases have no fixed shape, so only volume expansion matters. Liquids generally expand more than solids; gases expand far more.

For an ideal gas at constant pressure, $PV=\mu RT$ gives $\frac{\Delta V}{V}=\frac{\Delta T}{T}$, so $\gamma =\frac{1}{T}$: about $3.3\times 10^{-3}$ K${}^{-1}$ at room temperature, much larger than for solids and liquids.

Anomalous expansion of water: from 0 °C to 4 °C water contracts on heating; above 4 °C it expands normally. So water has its maximum density at 4 °C.

Consequence: in winter, as a lake cools, water at 4 °C sinks to the bottom. The surface cools further and freezes first, and the ice (less dense) floats, insulating the water below. Aquatic life survives at the bottom.

Worked example

Find the coefficient of volume expansion of an ideal gas at constant pressure at 27 °C. [1 mark]

Try it first, then show the solutionSolution

1. $\gamma =\frac{1}{T}$ with T = 300 K
2. $\gamma =\frac{1}{300}\approx 3.3\times 10^{-3}{K}^{-1}$

Answer: About $3.3\times 10^{-3}$ K${}^{-1}$

Thermal stress

NCERT section 10.5 (Example 10.2)

If a rod is clamped so that it cannot expand, heating it sets up a compressive stress. The strain it would have had, $\alpha \Delta T$, is prevented, so by Hooke's law:
$\text{thermal stress}=\frac{F}{A}=Y\alpha \Delta T$

This is why railway tracks, bridges and concrete roads have expansion gaps; without them they buckle in summer. The same idea is used deliberately when a heated iron ring is fitted on a wheel: as it cools it tightens strongly.

Worked example

A steel rod is clamped between two rigid walls and heated by 50 K. Find the thermal stress. ($Y=2\times 10^{11}$ Pa, α = $1.2\times 10^{-5}$ K${}^{-1}$) [1 mark]

Try it first, then show the solutionSolution

1. Stress $=Y\alpha \Delta T=2\times 10^{11}\times 1.2\times 10^{-5}\times 50$
2. Stress $=1.2\times 10^{8}Pa$ (compressive)

Answer: $1.2\times 10^8$ Pa

Specific heat capacity, molar specific heat, Cp and Cv

NCERT section 10.6

The heat needed to raise the temperature of a body depends on its mass, the temperature rise and the substance:
$Q=mc\Delta T$
where c is the specific heat capacity (J kg${}^{-1}$ K${}^{-1}$). The heat capacity of a body is $S=mc$.

Molar specific heat C is the heat for one mole: $Q=\mu C\Delta T$.

For gases, the heat needed depends on the conditions: at constant volume ($C_v$) all the heat raises the internal energy; at constant pressure ($C_p$) the gas also does work as it expands, so $C_p>C_v$ (for an ideal gas $C_p-C_v=R$, shown in Thermodynamics).

Water has a very high specific heat (4186 J kg${}^{-1}$ K${}^{-1}$): it heats and cools slowly. That is why it is used in car radiators and hot-water bottles, and why coastal places have milder climates and sea breezes.

Worked example

How much heat is needed to warm 2 kg of water from 20 °C to 80 °C? (c = 4186 J kg${}^{-1}$ K${}^{-1}$) [1 mark]

Try it first, then show the solutionSolution

1. $Q=mc\Delta T=2\times 4186\times 60$
2. $Q=502320J\approx 5.0\times 10^{5}J$

Answer: About $5.0\times 10^5$ J

Calorimetry

NCERT section 10.7

Calorimetry means measuring heat. In an isolated system (no heat lost to the surroundings), when hot and cold bodies are mixed:
$\text{heat lost by hot bodies}=\text{heat gained by cold bodies}$

A calorimeter is a metal vessel (often copper) with a stirrer, kept in an insulating jacket. Its own heat capacity must be included in the balance.

Method of mixtures: drop a hot metal block into water in a calorimeter, record the final steady temperature, and solve the heat balance for the unknown specific heat.

Worked example

A 0.25 kg metal block at 120 °C is dropped into 0.2 kg of water at 25 °C. The final temperature is 35 °C. Neglecting heat losses and the calorimeter, find the specific heat of the metal. [2 marks]

Try it first, then show the solutionSolution

1. Heat gained by water $=0.2\times 4186\times 10=8372J$
2. Heat lost by metal $=0.25\times c\times 85$; equate: $c=\frac{8372}{21.25}\approx 394Jk{g}^{-1}{K}^{-1}$

Answer: About 394 J kg${}^{-1}$ K${}^{-1}$ (close to copper)

Change of state and latent heat

NCERT section 10.8 and 10.8.1

Matter changes state (solid ↔ liquid ↔ gas) at fixed temperatures for a given pressure: melting point and boiling point. During the change, heat is absorbed or released without any change of temperature; it breaks or forms bonds between molecules.

Latent heat: $Q=mL$. For water, latent heat of fusion $L_f=3.33\times 10^5$ J kg${}^{-1}$ and of vaporisation $L_v=22.6\times 10^5$ J kg${}^{-1}$. Steam at 100 °C scalds worse than water at 100 °C because it also releases $L_v$.

Effect of pressure: for water, more pressure lowers the melting point (regelation: a weighted wire passes through ice, which refreezes behind it). More pressure raises the boiling point (a pressure cooker cooks faster); at hill stations water boils below 100 °C. Sublimation is a direct solid-to-gas change (dry ice, naphthalene). The triple point of water (273.16 K, 0.006 atm) is where all three phases coexist.

Worked example

How much heat turns 1 kg of ice at −10 °C into steam at 100 °C? ($c_{ice}$ = 2100, $c_{water}$ = 4186 J kg${}^{-1}$ K${}^{-1}$, $L_f=3.33\times 10^5$, $L_v=22.56\times 10^5$ J kg${}^{-1}$) [3 marks]

Try it first, then show the solutionSolution

1. Ice −10 → 0 °C: $1\times 2100\times 10=21000J$; melting: 333 000 J
2. Water 0 → 100 °C: $1\times 4186\times 100=418600J$; boiling: 2 256 000 J
3. Total $\approx 3.03\times 10^{6}J$ (three-quarters of it is the latent heat of vaporisation)

Answer: About $3.0\times 10^6$ J

Conduction and thermal conductivity

NCERT section 10.9 and 10.9.1

Heat travels by conduction (through a material, particle to particle, without the material moving), convection (by movement of the fluid itself) and radiation (electromagnetic waves, no medium needed).

Conduction: for a bar of length L and cross-section A with ends at $T_C$ and $T_D$, in the steady state the heat current is
$H=KA\frac{T_C-T_D}{L}$
where K is the thermal conductivity (W m${}^{-1}$ K${}^{-1}$). Metals have high K (copper about 400); wood, air, glass wool and thermocole have low K (insulators).

A metal at room temperature feels colder than wood because it conducts heat away from your hand faster. Cooking pots have copper bottoms and wooden or plastic handles. For slabs in series, the same H flows through each, which fixes the temperature at the junction.

Worked example

A glass window of area 1 m${}^2$ and thickness 4 mm has inside and outside surfaces at 20 °C and 10 °C. Find the rate of heat flow through it. (K = 0.8 W m${}^{-1}$ K${}^{-1}$) [1 mark]

Try it first, then show the solutionSolution

1. $H=KA\frac{\Delta T}{L}=0.8\times 1\times \frac{10}{0.004}$
2. H = 2000 W

Answer: 2000 W (2 kW)

Convection, radiation and blackbody radiation (qualitative)

NCERT section 10.9.2 to 10.9.4

Convection: warmer fluid is less dense, rises, and cooler fluid sinks to take its place (natural convection), as in sea and land breezes and trade winds. A fan or pump gives forced convection.

Radiation: heat carried by electromagnetic waves at the speed of light, through a vacuum too (heat from the Sun). Dark, rough surfaces absorb and emit well; shiny, light surfaces reflect. That is why we wear light clothes in summer and why a thermos flask has silvered walls.

Blackbody: an ideal body that absorbs all radiation falling on it; it is also the best emitter. Its spectrum is continuous, with a peak.

• Wien's displacement law: the wavelength of maximum emission falls as temperature rises: ${\lambda }_{m}T=b$, with $b\approx 2.9\times 10^{-3}$ m K. A heated iron rod glows dull red, then orange, then white. The Sun (${\lambda }_m\approx 500$ nm) has a surface near 5800 K.
• Stefan's law: the energy radiated per second by a blackbody grows as the fourth power of its absolute temperature: $H=\sigma A{T}^4$ (for other bodies $H=e\sigma A{T}^4$, with emissivity e < 1). σ ≈ $5.67\times 10^{-8}$ W m${}^{-2}$ K${}^{-4}$.

The syllabus asks for these laws as qualitative ideas.

Worked example

The absolute temperature of a blackbody is doubled. What happens to (a) the power it radiates, (b) its wavelength of maximum emission? [2 marks]

Try it first, then show the solutionSolution

1. (a) Stefan's law, $H\propto T^4$: power becomes $2^4=16$ times
2. (b) Wien's law, ${\lambda }_m\propto \frac{1}{T}$: it halves (the colour shifts towards blue)

Answer: (a) 16 times (b) halved

Physics in real life: Thermal Properties of Matter

Each concept, met in an everyday situation. Read the situation, try the problem, then check the solution. The one-line hook is what to remember.

Topics in this chapter

• Calorimetry, Specific Heat and Latent Heat
• Thermal Expansion and Heat Conduction

Thermal Properties of Matter formula sheet

Temperature scales

$t_F=\frac{9}{5}{t}_C+32,T=t_C+273.15$

Thermal expansion

$\frac{\Delta l}{l}=\alpha \Delta T,\frac{\Delta A}{A}=\beta \Delta T,\frac{\Delta V}{V}=\gamma \Delta T$

Relations between coefficients

$\beta =2\alpha ,\gamma =3\alpha ,{\gamma }_{gas}=\frac{1}{T}$

Thermal stress

$\frac{F}{A}=Y\alpha \Delta T$

Heat and specific heat

$Q=mc\Delta T,Q=\mu C\Delta T$

Calorimetry

$\text{heat lost}=\text{heat gained}$

Latent heat

$Q=mL$

Conduction

$H=KA\frac{T_C-T_D}{L}$

Wien's displacement law

${\lambda }_{m}T=b\approx 2.9\times 10^{-3}mK$

Stefan's law

$H=e\sigma A{T}^4,\sigma \approx 5.67\times 10^{-8}W{m}^{-2}{K}^{-4}$

How the school exam asks Thermal Properties of Matter

The question patterns to expect, and the method that works for each.

Tricks to remember Thermal Properties of Matter

Short memory aids. Say each one aloud once, then use it on a question the same day.

• 1, 2, 3 for α, β, γ

  Length α, area 2α, volume 3α: one, two, three dimensions.

  Use it when: Expansion relations.

• Water's odd four

  Water is densest at 4 °C, so lakes freeze top-down and fish survive below.

  Use it when: Anomalous expansion questions.

• Hotter is bluer and much brighter

  Wien: ${\lambda }_m\propto 1/T$ (colour shifts to blue). Stefan: $H\propto T^4$ (double T, 16 times the power).

  Use it when: Radiation MCQs.

• Lost = gained

  Every calorimetry problem is one equation: heat lost by the hot side = heat gained by the cold side.

  Use it when: Mixtures.

• −40 is the meeting point

  −40 °C = −40 °F.

  Use it when: Scale-conversion MCQs.

Thermal Properties of Matter: exam-level solved questions

Ordered from exam level to HOTS. Cover the solution, write your own, then compare step by step.

Case-study practice (Section E style)

Read the situation, then answer every part. In a school exam set on the board pattern this is a 4-mark question split into 1 + 1 + 1 + 1 marks.

Where the marks are

How a typical answer is split into step marks. Show every step: a right final answer alone rarely earns full marks.

Where students lose marks in Thermal Properties of Matter

The slips examiners see most often, and what to write instead.

• ✗Mistake: Assuming all the ice melts

  Not checking the heat available.

  ✓Do this: First compare the heat needed to melt all the ice with the heat the warm water can give while cooling to 0 °C. If it is less, the final temperature is 0 °C with some ice left.

  Usually costs: Whole numerical.

• ✗Mistake: Adding 273 to temperature differences

  Converting everything to kelvin.

  ✓Do this: A temperature change is the same in °C and K; add 273.15 only to actual temperatures (as in Wien and Stefan laws).

  Usually costs: 1 mark.

• ✗Mistake: Using Celsius in Stefan's or Wien's law

  Forgetting absolute temperature.

  ✓Do this: Always use kelvin in $T^4$ and ${\lambda }_{m}T$.

  Usually costs: 1-2 marks.

• ✗Mistake: Writing Newton's law of cooling or the greenhouse effect in detail

  Old notes.

  ✓Do this: The greenhouse effect was removed and Newton's law of cooling is not named in the 2026-27 CBSE content; focus on the listed topics.

  Usually costs: Time.

• ✗Mistake: Confusing heat and temperature

  Everyday language.

  ✓Do this: Temperature is a state (how hot); heat is energy in transit because of a temperature difference.

  Usually costs: 1 mark in definitions.

NCERT exercise guide: Thermal Properties of Matter

What each exercise in the NCERT chapter tests, how to approach it, and a question of the same kind solved step by step. Questions here are written in our own words.

Practice questions on Thermal Properties of Matter

Write each answer on paper first. Open the hint only if you are stuck, and the answer only when you have finished.

1. Q1 · 1 mark · MCQExam level

   The SI unit of thermal conductivity is:
   (a) W m${}^{-1}$ K${}^{-1}$
   (b) J kg${}^{-1}$ K${}^{-1}$
   (c) W m${}^{-2}$ K${}^{-4}$
   (d) J K${}^{-1}$

   Hint

   K = HL/(AΔT).

   Answer

   (a) W m${}^{-1}$ K${}^{-1}$

2. Q2 · 1 mark · MCQExam level

   When the temperature of a blackbody increases, its wavelength of maximum emission:
   (a) increases
   (b) decreases
   (c) stays the same
   (d) first increases then decreases

   Hint

   Wien's law.

   Answer

   (b) decreases

3. Q3 · 1 mark · Assertion-reasonExam level

   Assertion (A): A piece of metal feels colder than a piece of wood at the same temperature.
   Reason (R): Metals are good conductors of heat.
   (a) Both true, R explains A. (b) Both true, R does not explain A. (c) A true, R false. (d) A false, R true.

   Hint

   Rate of heat flow from the hand.

   Answer

   (a)

4. Q4 · 2 marks · Very short answerExam level

   Explain why a lake freezes from the top and how this helps aquatic life.

   Hint

   Maximum density at 4 °C.

   Answer

   As the surface water cools to 4 °C it becomes densest and sinks; below 4 °C it becomes lighter and stays on top, where it freezes. The ice floats and insulates the water below, which stays near 4 °C, so fish survive.

5. Q5 · 1 mark · Very short answerHarder exam level

   Express 300 K on the Fahrenheit scale.

   Hint

   Convert to °C first.

   Answer

   300 K = 26.85 °C; $t_F=\frac{9}{5}(26.85)+32\approx 80.3$ °F.

6. Q6 · 2 marks · Very short answerHarder exam level

   How much heat is needed to turn 100 g of ice at 0 °C into water at 50 °C? ($L_f$ = 333 J g${}^{-1}$, c = 4.186 J g${}^{-1}$ K${}^{-1}$)

   Hint

   Melt, then warm.

   Answer

   $100\times 333+100\times 4.186\times 50=33300+20930=54230$ J.

7. Q7 · 2 marks · Very short answerHarder exam level

   A 500 W heater warms 2 kg of a liquid by 10 K in 100 s, with no heat lost. Find the specific heat of the liquid.

   Hint

   Q = Pt.

   Answer

   $Q=500\times 100=5\times 10^4$ J; $c=\frac{5\times 10^4}{2\times 10}=2500$ J kg${}^{-1}$ K${}^{-1}$.

8. Q8 · 2 marks · Very short answerHarder exam level

   A metal sheet has a circular hole of area 10.00 cm${}^2$ at 20 °C. Find its area at 120 °C. (α = $2\times 10^{-5}$ K${}^{-1}$)

   Hint

   β = 2α; the hole expands like the metal.

   Answer

   $\Delta A=A\times 2\alpha \Delta T=10\times 4\times 10^{-5}\times 100=0.04$ cm${}^2$, so the area becomes 10.04 cm${}^2$.

9. Q9 · 2 marks · Very short answerHarder exam level

   Why does food cook faster in a pressure cooker, and why is it hard to cook rice in an open pot on a high mountain?

   Hint

   Boiling point and pressure.

   Answer

   Higher pressure raises the boiling point of water (to about 120 °C in a cooker), so food cooks at a higher temperature. On a mountain the air pressure is lower, so water boils below 100 °C and food cooks slowly.

10. Q10 · 2 marks · Very short answerHOTS / competency

    The surface temperature of a star is twice that of the Sun and its radius is the same. Compare (a) the power it radiates, (b) its peak wavelength with the Sun's (about 500 nm).

    Hint

    $H\propto R^2{T}^4$, ${\lambda }_m\propto 1/T$.

    Answer

    (a) 16 times the Sun's power. (b) Half the wavelength: about 250 nm, in the ultraviolet, so the star looks bluish-white.

11. Q11 · 3 marks · Short answerHOTS / competency

    Steam at 100 °C is passed into 1 kg of water at 20 °C until the temperature reaches 80 °C. How much steam condenses? ($L_v=2.26\times 10^6$ J kg${}^{-1}$, c = 4186 J kg${}^{-1}$ K${}^{-1}$)

    Hint

    Steam gives latent heat, then cools from 100 to 80 °C.

    Answer

    Heat gained by water $=1\times 4186\times 60=251160$ J. Each kg of steam gives $2.26\times 10^6+4186\times 20=2343720$ J. Mass $=\frac{251160}{2343720}\approx 0.107$ kg, about 107 g.

Test your recall

Answer in your head or on paper first, then open the card. Pulling an answer out of memory makes it stick far better than re-reading.

1. 1.Write the relation between α, β and γ.Show answer

   β = 2α, γ = 3α.

2. 2.At what temperature is water densest?Show answer

   4 °C.

3. 3.Define specific heat capacity.Show answer

   The heat needed to raise the temperature of 1 kg of a substance by 1 K.

4. 4.State the principle of calorimetry.Show answer

   In an isolated system, heat lost by the hot bodies equals heat gained by the cold bodies.

5. 5.Why does steam cause worse burns than boiling water?Show answer

   Steam gives out its latent heat of vaporisation as it condenses, in addition to the heat from cooling.

6. 6.Write the heat current through a rod.Show answer

   $H=KA(T_C-T_D)/L$.

7. 7.State Wien's displacement law.Show answer

   ${\lambda }_{m}T$ is constant: the peak wavelength of a blackbody is inversely proportional to its absolute temperature.

8. 8.How does the power radiated by a blackbody depend on temperature?Show answer

   As $T^4$ (Stefan's law).

Quick revision checklist

The night before the exam: can you do each of these without looking?

• ☐Can you convert 50 °C to °F and K?
• ☐Can you explain why absolute zero is −273.15 °C?
• ☐Can you show γ = 3α?
• ☐Can you explain why lakes freeze from the top?
• ☐Can you find a thermal stress?
• ☐Can you solve an ice-water mixture problem?
• ☐Can you find the total heat to turn ice into steam?
• ☐Can you find the junction temperature of two slabs?
• ☐Can you explain sea breezes by convection?
• ☐Can you state Wien's and Stefan's laws and use them for ratios?

Thermal Properties of Matter: frequently asked questions