Thermal Properties of Matter Class 11 Physics Notes

The three common temperature scales are Celsius, Fahrenheit and Kelvin. They are related by C/5 = (F − 32)/9 = (K − 273.15)/5. The Kelvin scale is the absolute thermometric scale; its zero is absolute zero, the lowest possible temperature (−273.15 °C), at which molecular motion is minimal.

• Boiling point of water: 100 °C = 212 °F = 373.15 K.
• Freezing point of water: 0 °C = 32 °F = 273.15 K.
• A change of 1 K equals a change of 1 °C; a change of 1 °F equals 5/9 K.

MCQ Questions

1 Mark Questions

1. 1
   Distinguish between heat and temperature.
2. 2
   State the SI units of heat and temperature.
3. 3
   What is absolute zero?

2 Mark Questions

1. 1
   Convert 98.6 °F (normal body temperature) to the Celsius scale.
2. 2
   Write the relation between the Celsius, Fahrenheit and Kelvin scales and define each.
3. 3
   Convert 300 K to the Celsius and Fahrenheit scales.

3 Mark Questions

1. 1
   Explain the need for an absolute (Kelvin) scale of temperature and write its relation with the Celsius scale.
2. 2
   At what temperature do the Celsius and Fahrenheit scales read the same numerical value? Derive your answer.

The volume expansion of a liquid is described by γ_l (its coefficient of volume expansion). Since a liquid is always held in a container that also expands, the apparent expansion observed is slightly less than the real expansion. Water behaves oddly: it contracts on heating from 0 °C to 4 °C (its density is maximum at 4 °C).

• Steel and concrete in bridges and railway tracks expand on hot days — expansion joints allow for this.
• A bimetallic strip curves on heating because the two metals expand by different amounts; it is used in thermostats.
• Water expands on freezing — the reason pipes burst in winter.

MCQ Questions

1 Mark Questions

1. 1
   Define the coefficient of linear expansion.
2. 2
   Write the relations between α, β and γ for a solid.
3. 3
   At what temperature is the density of water maximum?

2 Mark Questions

1. 1
   A steel rod of length 1 m and coefficient of linear expansion 1.1 × 10⁻⁵ K⁻¹ is heated from 20 °C to 120 °C. Find its increase in length.
2. 2
   Why are gaps left between successive sections of railway tracks?
3. 3
   Show that for a solid β = 2α and γ = 3α.

3 Mark Questions

1. 1
   Define α, β and γ for a solid, and derive the relations β = 2α and γ = 3α.
2. 2
   A copper plate has a hole of diameter 1 cm at 20 °C. Find the new diameter of the hole when the plate is heated to 220 °C. (α = 1.7 × 10⁻⁵ K⁻¹.)

Calorimetry is the measurement of heat. In a calorimeter, the principle of the method of mixtures states that the heat lost by hotter bodies equals the heat gained by colder ones (assuming no heat loss to the surroundings). Water's high specific heat (≈ 4200 J kg⁻¹ K⁻¹) makes it an ideal coolant and a climate regulator.

• Heat lost = heat gained in an ideal calorimeter.
• Water's high specific heat stabilises coastal climates and cools engines.
• Sand and land heat and cool faster than water because their specific heat is far smaller.

MCQ Questions

1 Mark Questions

1. 1
   Define specific heat capacity. Write its SI unit.
2. 2
   Write the expression Q = mcΔT and identify each symbol.
3. 3
   Why is water used as a coolant?

2 Mark Questions

1. 1
   How much heat is required to raise the temperature of 500 g of water from 20 °C to 40 °C? (c = 4200 J kg⁻¹ K⁻¹.)
2. 2
   State the principle of the method of mixtures and describe how a calorimeter is used.
3. 3
   A block of iron of mass 200 g at 100 °C is dropped into 200 g of water at 20 °C in a calorimeter. Explain why the final temperature is not 60 °C.

3 Mark Questions

1. 1
   Define specific heat capacity and heat capacity, and state their SI units. Explain the meaning of the method of mixtures.
2. 2
   A piece of metal of mass 100 g at 100 °C is placed in 200 g of water at 20 °C in a calorimeter of negligible heat capacity. If the final temperature is 25 °C, find the specific heat of the metal. (c_water = 4200 J kg⁻¹ K⁻¹.)

During a change of state the temperature stays constant while heat is absorbed (melting, boiling, sublimation) or released (freezing, condensation, deposition). The latent heat of vaporisation of water is about 2.26 × 10⁶ J kg⁻¹ — over six times its heat of fusion — which is why steam burns are so damaging.

• Ice at 0 °C absorbs 3.34 × 10⁵ J per kg to melt to water at 0 °C.
• Water at 100 °C absorbs 2.26 × 10⁶ J per kg to become steam at 100 °C.
• Perspiration cools the body because the sweat evaporates, taking latent heat from the skin.

MCQ Questions

1 Mark Questions

1. 1
   Define latent heat.
2. 2
   Write the expression Q = mL and identify each symbol.
3. 3
   Why is welding done so that heat is applied during melting and boiling?

2 Mark Questions

1. 1
   How much heat is needed to convert 100 g of ice at 0 °C to water at 0 °C? (L_f = 3.34 × 10⁵ J kg⁻¹.)
2. 2
   Explain why steam at 100 °C causes more severe burns than water at 100 °C.
3. 3
   State the latent heat of fusion and vaporisation of water.

3 Mark Questions

1. 1
   Define latent heat of fusion and vaporisation, and explain why temperature stays constant during a change of state.
2. 2
   Find the heat required to convert 200 g of ice at −10 °C to steam at 100 °C. (c_ice = 2100, c_water = 4200, L_f = 3.34×10⁵, L_v = 2.26×10⁶ J kg⁻¹, all in J kg⁻¹ K⁻¹.)

Metals are good conductors (high k); air and insulating materials like glass wool and wood are poor conductors (low k). Convection is heat transfer by the bulk motion of a fluid — warm fluid rises and cool fluid sinks, setting up currents. Radiation is the emission of energy in the form of electromagnetic waves; it needs no medium and can travel through vacuum (solar heat).

• Thermal conductivity k has SI unit W m⁻¹ K⁻¹.
• Convection explains land and sea breezes and the circulation of hot water in a geyser.
• Radiation is the only mode of heat transfer that can travel through a vacuum.

MCQ Questions

1 Mark Questions

1. 1
   Define thermal conductivity.
2. 2
   Name the three modes of heat transfer.
3. 3
   Which mode of heat transfer can operate in a vacuum?

2 Mark Questions

1. 1
   A metal rod of length 0.5 m and cross-section 10⁻⁴ m² has a temperature difference of 100 °C across its ends. If k = 200 W m⁻¹ K⁻¹, find the rate of heat flow.
2. 2
   Explain how convection produces a sea breeze.
3. 3
   Why are good insulators used in building walls? Distinguish between conductors and insulators.

3 Mark Questions

1. 1
   Explain the three modes of heat transfer — conduction, convection and radiation — giving one example of each.
2. 2
   A window pane is 1 cm thick, 1 m × 1 m in area, with a temperature difference of 20 °C between its faces. Find the heat conducted per second. (k_glass = 0.8 W m⁻¹ K⁻¹.)

Good absorbers are also good emitters; dark surfaces absorb and radiate heat well, while shiny (polished) surfaces reflect radiation and radiate poorly. This is why radiators are painted black and solar collectors use dark surfaces.

• The rate of radiation depends on T⁴, so a tiny rise in temperature greatly increases radiated power.
• Thermometers and kettles are often polished to reduce heat loss by radiation.
• A black body is the best absorber and the best emitter of radiation.

MCQ Questions

1 Mark Questions

1. 1
   State the Stefan-Boltzmann law.
2. 2
   Define a black body.
3. 3
   State Newton's law of cooling.

2 Mark Questions

1. 1
   A body of surface area 0.1 m² at temperature 500 K radiates as a black body. Find the power radiated. (σ = 5.67 × 10⁻⁸ W m⁻² K⁻⁴.)
2. 2
   Why are radiators painted black while vacuum flasks are silvery?
3. 3
   A body cools from 80 °C to 70 °C in 5 minutes when the room is at 20 °C. Estimate how long it takes to cool from 70 °C to 60 °C using Newton's law of cooling.

3 Mark Questions

1. 1
   State and explain the Stefan-Boltzmann law and Newton's law of cooling, contrasting their temperature dependences.
2. 2
   A black-body sphere of radius 5 cm at 1000 K radiates energy. Find the rate of energy radiated. (σ = 5.67 × 10⁻⁸ W m⁻² K⁻⁴.)

Exercises (NCERT Q10.1–Q10.20)

• 10.1) The triple points of neon and carbon dioxide are 24.57 K and 216.55 K respectively. Express these temperatures on the Celsius and Fahrenheit scales.
• 10.2) Two absolute scales A and B have triple points of water defined to be 200 A and 350 B. What is the relation between T_A and T_B?
• 10.3) The electrical resistance in ohms of a certain thermometer varies with temperature according to the approximate law: R = R₀[1 + α(T − T₀)]. The resistance is 101.6 Ω at the triple-point of water 273.16 K, and 165.5 Ω at the normal melting point of lead (600.5 K). What is the temperature when the resistance is 123.4 Ω?
• 10.4) Answer the following: (a) The triple-point of water is a standard fixed point in modern thermometry. Why? What is wrong in taking the melting point of ice and the boiling point of water as standard fixed points (as was originally done in the Celsius scale)? (b) There were two fixed points in the original Celsius scale as mentioned above which were assigned the number 0 °C and 100 °C respectively. On the absolute scale, one of the fixed points is the triple-point of water, which on the Kelvin absolute scale is assigned the number 273.16 K. What is the other fixed point on this (Kelvin) scale? (c) The absolute temperature (Kelvin scale) T is related to the temperature t_c on the Celsius scale by t_c = T − 273.15. Why do we have 273.15 in this relation, and not 273.16? (d) What is the temperature of the triple-point of water on an absolute scale whose unit interval size is equal to that of the Fahrenheit scale?
• 10.5) Two ideal gas thermometers A and B use oxygen and hydrogen respectively. The following observations are made: (temperature, P_A, P_B) triple-point of water: 1.250 × 10⁵ Pa, 0.200 × 10⁵ Pa; normal melting point of sulphur: 1.797 × 10⁵ Pa, 0.287 × 10⁵ Pa. (a) What is the absolute temperature of normal melting point of sulphur as read by thermometers A and B? (b) What do you think is the reason behind the slight difference in answers of thermometers A and B? (The thermometers are not faulty). What further procedure is needed in the experiment to reduce the discrepancy between the two readings?
• 10.6) A steel tape 1 m long is correctly calibrated for a temperature of 27.0 °C. The length of a steel rod measured by this tape is found to be 63.0 cm on a hot day when the temperature is 45.0 °C. What is the actual length of the steel rod on that day? What is the length of the same steel rod on a day when the temperature is 27.0 °C? Coefficient of linear expansion of steel = 1.20 × 10⁻⁵ K⁻¹.
• 10.7) A large steel wheel is to be fitted on to a shaft of the same material. At 27 °C, the outer diameter of the shaft is 8.70 cm and the diameter of the central hole in the wheel is 8.69 cm. The shaft is cooled using 'dry ice'. At what temperature of the shaft does the wheel slip on the shaft? Assume coefficient of linear expansion of the steel to be constant over the required temperature range: α_steel = 1.20 × 10⁻⁵ K⁻¹.
• 10.8) A hole is drilled in a copper sheet. The diameter of the hole is 4.24 cm at 27.0 °C. What is the change in the diameter of the hole when the sheet is heated to 227 °C? Coefficient of linear expansion of copper = 1.70 × 10⁻⁵ K⁻¹.
• 10.9) A brass wire 1.8 m long at 27 °C is held taut with little tension between two rigid supports. If the wire is cooled to a temperature of −39 °C, what is the tension developed in the wire, if its diameter is 2.0 mm? Co-efficient of linear expansion of brass = 2.0 × 10⁻⁵ K⁻¹; Young's modulus of brass = 0.91 × 10¹¹ Pa.
• 10.10) A brass rod of length 50 cm and diameter 3.0 mm is joined to a steel rod of the same length and diameter. What is the change in length of the combined rod at 250 °C, if the original lengths are at 40.0 °C? Is there a 'thermal stress' developed at the junction? The ends of the rod are free to expand (Co-efficient of linear expansion of brass = 2.0 × 10⁻⁵ K⁻¹, steel = 1.2 × 10⁻⁵ K⁻¹).
• 10.11) The coefficient of volume expansion of glycerine is 49 × 10⁻⁵ K⁻¹. What is the fractional change in its density for a 30 °C rise in temperature?
• 10.12) A 10 kW drilling machine is used to drill a bore in a small aluminium block of mass 8.0 kg. How much is the rise in temperature of the block in 2.5 minutes, assuming 50% of power is used up in heating the machine itself or lost to the surroundings. Specific heat of aluminium = 0.91 J g⁻¹ K⁻¹.
• 10.13) A copper block of mass 2.5 kg is heated in a furnace to a temperature of 500 °C and then placed on a large ice block. What is the maximum amount of ice that can melt? (Specific heat of copper = 0.39 J g⁻¹ K⁻¹; heat of fusion of water = 335 J g⁻¹).
• 10.14) In an experiment on the specific heat of a metal, a 0.20 kg block of the metal at 150 °C is dropped in a copper calorimeter (of water equivalent 0.025 kg) containing 150 cm³ of water at 27 °C. The final temperature is 40 °C. Compute the specific heat of the metal. If heat losses to the surroundings are not negligible, is your answer greater or smaller than the actual value for specific heat of the metal?
• 10.15) Given below are observations on molar specific heats at room temperature of some common gases. Gas, molar specific heat (C_v in cal mol⁻¹ K⁻¹): Hydrogen 4.87, Nitrogen 4.97, Oxygen 5.02, Nitric oxide 4.99, Carbon monoxide 5.01, Chlorine 6.17. The measured molar specific heats of these gases are markedly different from those for monatomic gases. Typically, molar specific heat of a monatomic gas is 2.92 cal/mol K. Explain this difference. What can you infer from the somewhat larger (than the rest) value for chlorine?
• 10.16) A child running a temperature of 101 °F is given an antipyrin (i.e. a medicine that lowers fever) which causes an increase in the rate of evaporation of sweat from his body. If the fever is brought down to 98 °F in 20 minutes, what is the average rate of extra evaporation caused, by the drug. Assume the evaporation mechanism to be the only way by which heat is lost. The mass of the child is 30 kg. The specific heat of human body is approximately the same as that of water, and latent heat of evaporation of water at that temperature is about 580 cal g⁻¹.
• 10.17) A 'thermacole' icebox is a cheap and an efficient method for storing small quantities of cooked food in summer in particular. A cubical icebox of side 30 cm has a thickness of 5.0 cm. If 4.0 kg of ice is put in the box, estimate the amount of ice remaining after 6 h. The outside temperature is 45 °C, and co-efficient of thermal conductivity of thermacole is 0.01 J s⁻¹ m⁻¹ K⁻¹. [Heat of fusion of water = 335 × 10³ J kg⁻¹].
• 10.18) A brass boiler has a base area of 0.15 m² and thickness 1.0 cm. It boils water at the rate of 6.0 kg/min when placed on a gas stove. Estimate the temperature of the part of the flame in contact with the boiler. Thermal conductivity of brass = 109 J s⁻¹ m⁻¹ K⁻¹; Heat of vaporisation of water = 2256 × 10³ J kg⁻¹.
• 10.19) Explain why: (a) a body with large reflectivity is a poor emitter (b) a brass tumbler feels much colder than a wooden tray on a chilly day (c) an optical pyrometer (for measuring high temperatures) calibrated for an ideal black body radiation gives too low a value for the temperature of a red hot iron piece in the open, but gives a correct value for the temperature when the same piece is in the furnace (d) the earth without its atmosphere would be inhospitably cold (e) heating systems based on circulation of steam are more efficient in warming a building than those based on circulation of hot water.
• 10.20) A body cools from 80 °C to 50 °C in 5 minutes. Calculate the time it takes to cool from 60 °C to 30 °C. The temperature of the surroundings is 20 °C.

Answers at a glance

1. 1
   Q10.1 → Neon: −248.58 °C, −415.44 °F; carbon dioxide: −56.60 °C, −69.88 °F.
2. 2
   Q10.2 → T_A = (4/7) T_B, i.e. T_A : T_B = 4 : 7.
3. 3
   Q10.3 → The temperature is about 385 K.
4. 4
   Q10.4 → (a) the triple point is unique, ice/steam points vary with pressure (b) absolute zero, 0 K (c) 0 °C is at 273.15 K, the melting point, not the triple point (d) 491.7.
5. 5
   Q10.5 → (a) A reads 392.69 K, B reads 391.98 K (b) non-ideal gas behaviour; use low pressures and extrapolate to zero pressure.
6. 6
   Q10.6 → Actual length at 45 °C ≈ 63.014 cm; length at 27 °C = 63.0 cm.
7. 7
   Q10.7 → The wheel slips on when the shaft cools to about −69 °C.
8. 8
   Q10.8 → The hole diameter increases by about 0.0144 cm (1.44 × 10⁻² cm).
9. 9
   Q10.9 → A tension of 3.8 × 10² N develops in the wire.
10. 10
    Q10.10 → Combined change in length ≈ 0.35 cm; no thermal stress since the ends are free.
11. 11
    Q10.11 → Density decreases by a fraction 1.47 × 10⁻² (1.47%).
12. 12
    Q10.12 → The block temperature rises by 103 °C.
13. 13
    Q10.13 → About 1.45 kg of ice can melt.
14. 14
    Q10.14 → c ≈ 0.43 × 10³ J kg⁻¹ K⁻¹; with heat losses the computed value is smaller than the actual one.
15. 15
    Q10.15 → Diatomic gases store extra energy in rotational (≈5/2 R) and for chlorine also vibrational modes; chlorine's large value shows its vibrations are active at room temperature.
16. 16
    Q10.16 → The average extra evaporation rate is 4.3 g min⁻¹.
17. 17
    Q10.17 → About 3.7 kg of ice remains after 6 hours.
18. 18
    Q10.18 → The flame part in contact with the boiler is at about 238 °C.
19. 19
    Q10.19 → (a) reflectors absorb (and so emit) little (b) brass conducts heat from the hand, wood does not (c) open-air iron is a poor radiator, furnace iron approaches a black body (d) the atmosphere traps heat (e) steam releases latent heat on condensing.
20. 20
    Q10.20 → It takes 10 minutes to cool from 60 °C to 30 °C.

MCQ Questions

1 Mark Questions

1. 1
   Define specific heat capacity and give its SI unit.
2. 2
   Define latent heat of fusion and latent heat of vaporisation.
3. 3
   Define the coefficient of linear expansion of a solid.
4. 4
   State Newton's law of cooling.

2 Mark Questions

1. 1
   A copper rod of length 1 m is heated from 20°C to 100°C. If the coefficient of linear expansion is 1.7 × 10⁻⁵ K⁻¹, find the increase in length. (Ans: Δl = αlΔT = 1.36 mm)
2. 2
   How much heat is needed to raise the temperature of 200 g of water from 25°C to 75°C? (c = 4.18 × 10³ J/kg K) (Ans: Q = mcΔT = 4.18 × 10⁴ J)
3. 3
   5 kg of water at 60°C is mixed with 5 kg of water at 20°C. Find the final temperature assuming no heat loss. (Ans: 40°C)

3 Mark Questions

1. 1
   State and explain the law of thermal conduction (Fourier's law) and derive the heat-current formula for a rod of length l and area A. (Ans: H = kA(θ₁ − θ₂)/l)
2. 2
   Explain the principle of calorimetry and describe how the specific heat of a solid is measured by the method of mixtures.
3. 3
   State Stefan's law of black body radiation and explain the Newton's law of cooling as its consequence. (Ans: E ∝ T⁴)

5 Mark Questions

1. 1
   A copper calorimeter of mass 100 g contains 150 g of water at 25°C. Steam at 100°C is passed until the temperature reaches 30°C. Find the mass of steam condensed (L = 2.26 × 10⁶ J/kg, c = 4180 J/kg K).
2. 2
   Explain heat transfer by conduction, convection and radiation with examples, describe the green-house effect, and state Stefan's law and Wien's displacement law.