Class 10 Physics — Chapter 11: Thermal Expansion and Change of State

Board: Federal Board (FBISE)

SECTION I: MULTIPLE CHOICE QUESTIONS (MCQs)

1. During a hot summer day, a metal bridge might expand slightly. This expansion is caused by:

A. The bridge rusting and weakening
B. The metal atoms in the bridge vibrating more intensely
C. The weight of cars driving over the bridge
D. A decrease in the air pressure around the bridge

Correct Answer: B. The metal atoms in the bridge vibrating more intensely.

2. Fog forms on a cold window pane in the morning. Which change of state is occurring?

A. Melting
B. Boiling
C. Condensation
D. Deposition

Correct Answer: C. Condensation.

3. Which process involves the change of state from a gas to a solid without passing through the liquid phase?

A. Deposition
B. Melting
C. Freezing
D. Sublimation

Correct Answer: A. Deposition.

4. Boiling point of water is:

A. \(212^\circ C\)
B. \(212^\circ F\)
C. \(100\,K\)
D. \(373^\circ C\)

Correct Answer: B. \(212^\circ F\).

5. \(J\,kg^{-1}K^{-1}\) is the unit of:

A. Specific heat capacity
B. Heat capacity
C. Latent heat of fusion
D. Heat energy

Correct Answer: A. Specific heat capacity.

6. Evaporation takes place from:

A. Surface
B. Bottom
C. Center
D. Any location

Correct Answer: A. Surface.

7. Relation between linear and volume expansion of solids is:

A. \(\beta=\frac{\alpha}{3}\)
B. \(\beta=1.5\alpha\)
C. \(\alpha=\frac{\beta}{3}\)
D. \(\alpha=3\beta\)

Correct Answer: C. \(\alpha=\frac{\beta}{3}\).

8. Heat added to a substance at its melting point is used to:

A. Increase the kinetic energy of particles
B. Decrease the kinetic energy of particles
C. Increase the attraction between particles
D. Decrease the attraction between particles

Correct Answer: D. Decrease the attraction between particles.

9. \(336\,J/g\) is the latent heat of fusion of a material. How much heat is required to melt 10 g of the material at its melting point?

A. 336 J
B. 3360 J
C. 33600 J
D. \(3.36\times10^5\) J

Correct Answer: B. 3360 J.

Calculation:

10. Which of the following factors increases the rate of evaporation?

A. Decrease in temperature
B. Increase in humidity
C. Increase in wind speed
D. Decrease in surface area

Correct Answer: C. Increase in wind speed.

11. What is the value of \(\alpha\) for a solid if its \(\beta\) is \(9\times10^{-5}\,K^{-1}\)?

A. \(3\times10^{-5}\,K^{-1}\)
B. \(4.5\times10^{-5}\,K^{-1}\)
C. \(9\times10^{-5}\,K^{-1}\)
D. \(27\times10^{-5}\,K^{-1}\)

Correct Answer: A. \(3\times10^{-5}\,K^{-1}\).

12. The process that involves the latent heat of vaporization is:

A. Melting of ice
B. Freezing of water
C. Evaporation
D. Condensation of steam

Correct Answer: D. Condensation of steam (or evaporation).

13. The sum and difference of the coefficients of real and apparent expansion of a liquid are in the ratio 2:1. The ratio of the coefficient of real expansion and apparent expansion must be:

A. 1:1
B. 2:1
C. 2:3
D. 3:1

Correct Answer: D. 3:1.

14. Latent heat refers to the energy absorbed or released by a substance during a change of state, but with no change in temperature. What does “latent” mean in this context?

A. Constant
B. Visible
C. Hidden
D. Transparent

Correct Answer: C. Hidden.

SECTION II: CONSTRUCTED RESPONSE QUESTIONS

QII.1. Look at the graphs for heating ice.

(a) Explain why the temperature does not change at these two stages.

The two horizontal sections represent phase changes (melting and boiling). During these stages, the added heat energy is entirely used as latent heat to overcome intermolecular forces and change the state of the substance rather than increasing the kinetic energy of particles. Therefore, the temperature remains constant.

(b) Explain why the temperature and energy trends are not the same for the same time intervals.

Temperature measures the average kinetic energy of particles, while energy accounts for the total heat supplied. During phase transitions, energy increases continuously while temperature remains constant. Moreover, different phases (ice, water, and steam) possess different specific heat capacities.

QII.2. A heater supplies energy at a constant rate to 100 g of a substance (\(P=250\,W\)).

(a) Determine the melting and boiling points.

• Melting point = \(-10^\circ C\)

• Boiling point = \(30^\circ C\)

(b) Determine the melting and vaporization times.

• Melting duration = 3 minutes = 180 s

• Vaporization duration = 13 minutes = 780 s

(c) Calculate the temperature increase in the liquid phase.

(d) Calculate the latent heat of vaporization (\(H_v\)).

Given:

Heat supplied:

Mass:

Specific latent heat of vaporization:

SECTION III: SHORT RESPONSE QUESTIONS

QIII.1. Why do dew-drops form on leaves and grass on a spring morning?

Leaves and grass radiate heat and cool down at night. When moist morning air touches these cold surfaces, water vapour cools below its dew point and condenses into liquid droplets called dew-drops.

QIII.2. Explain the effect of pressure and temperature variation on sublimation and deposition.

Sublimation is favoured by low pressure and high temperature. Deposition is favoured by high pressure and low temperature.

QIII.3. Why do vapours form on the handle and cylinder of a fire extinguisher when discharged?

Rapid expansion of compressed gas causes an adiabatic temperature drop. The cold surface cools the surrounding moist air below its dew point, causing water vapour to condense.

QIII.4. How does sweating help to cool our body down during exercise?

Sweat absorbs body heat as latent heat of vaporization and evaporates into the atmosphere, carrying away thermal energy and cooling the skin.

QIII.5. Explain the heating behaviour of Metal X and Metal Y.

(I) Temperature-time graph of Metal X

The temperature-time graph rises linearly, flattens at \(250^\circ C\) (melting plateau), and then rises again to \(400^\circ C\).

(II) Comparison of Metal Y with Metal X

Metal Y has a greater latent heat of fusion, so its horizontal melting plateau will be longer than that of Metal X, while the temperature-rise slopes remain identical.

QIII.6. Explain the pressure change in a car tyre during a long drive on a hot day.

Friction and high ambient temperature heat the trapped air. Increased temperature raises molecular kinetic energy and collision frequency, increasing tyre pressure.

QIII.7. How can cracks in sidewalks be prevented?

Expansion joints (small gaps) are left between concrete slabs to provide room for thermal expansion during hot weather, avoiding destructive internal thermal stresses.

QIII.8. Why is a pot of hot water more effective than a heat lamp for melting snow?

A pot of hot water is more effective because water has a high specific heat capacity and transfers heat directly through conduction and phase change, whereas snow reflects thermal radiation from lamps.

QIII.9. Explain transpiration and water transport in plants.

Evaporation from leaves creates a transpiration pull (negative pressure) that draws water and nutrients upward from roots through xylem vessels.

QIII.10. Why does ice cool drinks more effectively than cold water?

Ice absorbs sensible heat plus a large amount of thermal energy as latent heat of fusion (\(3.36\times10^5\,J/kg\)) while melting at \(0^\circ C\).

QIII.11. What are the challenges of superconductivity?

• It requires expensive cryogenic equipment, such as liquid helium or nitrogen.

• Complex thermal insulation is needed.

• Refrigeration can consume considerable energy.

• Some superconducting materials are brittle at low temperatures.

SECTION IV: LONG RESPONSE QUESTIONS

Question 1. Define latent heat. Differentiate between latent heat and specific latent heat of fusion. Write their formulae.

Latent Heat

Latent heat is the thermal energy absorbed or released during a phase change at constant temperature without altering the kinetic energy of particles.

Difference between Latent Heat of Fusion and Specific Latent Heat of Fusion

Question 2. Differentiate between latent heat of vaporization and specific latent heat of vaporization. Give their formulae and units.

Difference between Latent Heat of Vaporization and Specific Latent Heat of Vaporization

Question 3. What is evaporation? Differentiate between boiling and evaporation. On what factors does evaporation depend?

Evaporation

Evaporation is the spontaneous process in which a liquid changes into gas at any temperature below its boiling point. It occurs exclusively at the surface and causes cooling.

Difference between Boiling and Evaporation

Factors Affecting Evaporation

1. Surface area

2. Temperature

3. Humidity

4. Wind speed

5. Nature of the liquid

Question 4. What are linear and volume thermal expansion of solids? Discuss qualitatively the factors upon which these thermal expansions depend.

Linear Expansion

Linear expansion is the change in length along one dimension when the temperature of a solid rises.

Volume Expansion

Volume expansion is the change in the total three-dimensional volume of a solid when its temperature rises.

For solids:

Factors Affecting Thermal Expansion

1. Initial Dimensions (\(L_0\) or \(V_0\)): Greater initial size results in proportionally larger expansion.

2. Temperature Change (\(\Delta T\)): A higher temperature rise increases atomic vibrations and expansion.

3. Nature of Material: Different materials have different coefficients (\(\alpha\) or \(\beta\)) based on the strength of their interatomic bonds.

Question 5. What are the uses of thermal expansion in our daily life? Give examples.

Applications of Thermal Expansion

1. Bimetallic Strips: Used in thermostats for automatic temperature control in electric irons and refrigerators.

2. Riveting: Hot rivets contract upon cooling and hold steel plates tightly together.

3. Metal Tyres: Heated rims shrink tightly onto wooden or metal wheels upon cooling.

4. Thermometers: Expansion of liquid inside capillary tubes is used to measure temperature.

5. Jammed Lids: Warming a metal cap makes it expand and loosen from a glass bottle.

Question 6. Explain thermal expansion of liquids in detail.

Concept

Liquids expand in volume only and require a container. Both the container and the liquid expand simultaneously when heated.

Real and Apparent Expansion

• Apparent Expansion (\(\Delta V_a\)): The observed expansion of a liquid without considering the expansion of its container.

• Real Expansion (\(\Delta V_r\)): The actual total expansion of the liquid.

The relationship is:

Where:

• \(\Delta V_r\) = Real expansion of liquid

• \(\Delta V_a\) = Apparent expansion of liquid

• \(\Delta V_g\) = Expansion of the vessel

Anomalous Expansion of Water

Water contracts when heated from \(0^\circ C\) to \(4^\circ C\), achieving maximum density at \(4^\circ C\). This property allows aquatic life to survive during winter beneath the ice.

Question 7. Discuss the application of bimetallic strips in temperature control devices like thermostats. Explain the principle of thermal expansion that allows the bimetallic strip to function, and illustrate how the differing expansion rates of the two metals are utilized in practical applications.

Principle

A bimetallic strip consists of two bonded strips of metals with different rates of thermal expansion. For example, brass expands more than iron. When heated, the strip bends into an arc because of unequal expansion.

Thermostat Operation

• Heating/Overheating: The strip bends away from the electrical contact, breaking the circuit and turning the power OFF.

• Cooling: The strip cools, straightens, re-establishes contact, and turns the power back ON.

Practical Uses

• Electric irons

• Refrigerators

• Air conditioners

• Fire alarm buzzers

Question 8. What is superconductivity? Explain the phenomenon in detail. What is its scope in the future world?

Definition

Superconductivity is a state in which certain materials exhibit zero electrical resistance and expel magnetic fields completely below a critical temperature (\(T_c\)).

Detailed Phenomenon

1. Zero Resistance: Continuous electrical current flows without heat loss.

2. Meissner Effect: Complete expulsion of internal magnetic fields enables magnetic levitation.

3. BCS Theory: Electrons form bound pairs called Cooper pairs, which move smoothly without lattice scattering.

Future Scope of Superconductivity

1. Lossless power transmission grids.

2. Frictionless Maglev trains.

3. High-resolution medical MRI machines.

4. Ultrafast quantum computers.

5. Development of room-temperature superconductors.

SECTION V: NUMERICAL RESPONSE QUESTIONS

Question 1. Consider a steel bar of length 1.5 m at \(10^\circ C\). It is heated to raise its temperature to \(100^\circ C\). Calculate:

(a) Increase in length
(b) Final length at \(100^\circ C\)

Given coefficient of linear thermal expansion of steel:

Given Data

• Original length: \(L_0=1.5\,m\)

• Initial temperature: \(T_1=10^\circ C\)

• Final temperature: \(T_2=100^\circ C\)

• Coefficient of linear expansion: \(\alpha=1.2\times10^{-5}\,K^{-1}\)

Change in temperature:

Solution

(a) Increase in Length (\(\Delta L\))

Using the linear thermal expansion formula:

Substituting the values:

Converting metres into millimetres:

(b) Final Length (\(L\))

Answer:

• (a) Increase in length = \(1.62\,mm\)

• (b) Final length = \(1.50162\,m\) (approximately \(1.5\,m\))

Question 2. A solid cube of side length 10 cm at \(25^\circ C\) is heated. What will be the increase in its volume at \(125^\circ C\) if its coefficient of linear thermal expansion is \(\alpha=9\times10^{-6}\,K^{-1}\)?

Given Data

• Side length of cube: \(l=10\,cm\)

• Initial volume:

• Initial temperature: \(T_1=25^\circ C\)

• Final temperature: \(T_2=125^\circ C\)

• Coefficient of linear expansion:

Change in temperature:

Coefficient of volumetric expansion:

Solution

Using the volume thermal expansion formula:

Substituting the values:

Answer: Increase in volume = \(2.7\,cm^3\).

Question 3. A steel railroad track segment is 10 metres long at a cool morning temperature of \(15^\circ C\). The coefficient of linear expansion for steel is \(1.2\times10^{-5}\) per \(^{\circ}C\). Later in the day, the temperature rises to \(30^\circ C\). How much will the steel track segment expand in length?

Given Data

• Original length: \(L_0=10\,m\)

• Initial temperature: \(T_1=15^\circ C\)

• Final temperature: \(T_2=30^\circ C\)

• Coefficient of linear expansion:

Change in temperature:

Solution

Using the expansion formula:

Substituting the values:

Converting metres into millimetres:

Answer: Expansion in length = \(1.8\,mm\).

Question 4. A 2-litre (\(2000\,cm^3\)) glass bottle is filled completely with orange juice at a room temperature of \(20^\circ C\). The coefficient of volumetric expansion for orange juice is \(5\times10^{-4}\) per \(^{\circ}C\). If the bottle is left in a hot car where the temperature reaches \(40^\circ C\), what volume of orange juice will overflow? (Expansion of the glass bottle is negligible.)

Given Data

• Initial volume: \(V_0=2000\,cm^3\)

• Initial temperature: \(T_1=20^\circ C\)

• Final temperature: \(T_2=40^\circ C\)

• Coefficient of volumetric expansion:

Change in temperature:

Solution

Since the expansion of the glass bottle is negligible, the volume of juice that overflows equals the increase in the volume of the orange juice.

Using:

Substituting the values:

Note: The printed reference answer of \(2\,cm^3\) in the textbook key appears to contain a calculation error. Using the given values gives \(20\,cm^3\).

Answer: Volume of orange juice overflowing = \(20\,cm^3\).

Question 5. How much heat is required to change 15 kg of ice into water at its melting point?

Given Data

• Mass of ice: \(m=15\,kg\)

• Specific latent heat of fusion of ice:

Solution

Using the latent heat formula for melting:

Substituting the values:

Answer: Heat required = \(4.95\times10^6\,J\).

Question 6. How much heat is required to change 7 kg of water into steam at its boiling point?

Given Data

• Mass of water: \(m=7\,kg\)

• Specific latent heat of vaporization of water:

Solution

Using the latent heat formula for vaporization:

Substituting the values:

Answer: Heat required = \(1.582\times10^7\,J\) (approximately \(1.58\times10^7\,J\)).

Question 7. Four kilograms of ice has a temperature of \(-20^\circ C\). It is heated to convert into steam. Its final temperature is \(120^\circ C\). Calculate the total amount of heat energy involved in this conversion of ice into steam.

Given:

• Specific heat of ice = \(2100\,J\,kg^{-1}K^{-1}\)

• Specific heat of water = \(4200\,J\,kg^{-1}K^{-1}\)

• Specific heat of steam = \(2000\,J\,kg^{-1}K^{-1}\)

• Latent heat of fusion of ice = \(3.3\times10^5\,J\,kg^{-1}\)

• Latent heat of vaporization of water = \(2.26\times10^6\,J\,kg^{-1}\)

Given Data

Solution: Five-Step Calculation

Step 1: Heat required to raise the temperature of ice from \(-20^\circ C\) to \(0^\circ C\) (\(Q_1\))

Using:

Step 2: Heat required to melt ice into water at \(0^\circ C\) (\(Q_2\))

Step 3: Heat required to raise the temperature of water from \(0^\circ C\) to \(100^\circ C\) (\(Q_3\))

Step 4: Heat required to convert water into steam at \(100^\circ C\) (\(Q_4\))

Step 5: Heat required to raise the temperature of steam from \(100^\circ C\) to \(120^\circ C\) (\(Q_5\))

Total Heat Required (\(Q_{\text{total}}\))

Answer: Total heat energy required = \(1.2368\times10^7\,J\) (approximately \(1.236\times10^7\,J\)).

Notes by Sir Dilawar
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