Thermal Properties of Matter

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Summary

Chapter 10: Thermal Properties of Matter

Summary

Temperature is a measure of 'hotness' of a body.
Heat is a form of energy that flows between a body and its surroundings due to temperature differences.
Thermometers utilize measurable properties that change with temperature to provide readings.
The Celsius and Fahrenheit scales are related by the formula:
tF = (9/5) tc + 32.
The Ideal Gas Equation is given by:
PV = µRT, where µ is the number of moles and R is the universal gas constant.
Absolute Temperature (Kelvin) is related to Celsius by:
tc = T - 273.15.
Coefficient of Linear Expansion (α₁) and Volume Expansion (αᵥ) are defined by their respective relations.
Specific Heat Capacity (S) is defined as:
S = ΔQ/ΔT, where ΔQ is the heat supplied.
Latent Heat:
- Lf: Heat per unit mass for solid to liquid transition.
- Lv: Heat per unit mass for liquid to vapor transition.
Heat Transfer Modes: Conduction, Convection, and Radiation.
Newton's Law of Cooling states that the rate of cooling is proportional to the temperature difference between the body and its surroundings.

Learning Objectives

Understand the definitions of temperature and heat.
Measure temperature using various thermometric properties.
Apply the ideal gas equation to relate pressure, volume, and absolute temperature.
Analyze thermal expansion in solids and liquids.
Calculate specific heat capacity and its implications in calorimetry.
Examine the processes of change of state and the concept of latent heat.
Explore the modes of heat transfer: conduction, convection, and radiation.
Utilize Newton's law of cooling to predict temperature changes over time.

Detailed Notes

Chapter Ten: Thermal Properties of Matter

10.1 Introduction

Common notions of heat and temperature.
Temperature measures 'hotness' of a body.
Importance of defining heat and temperature in physics.

10.2 Temperature and Heat

Temperature is a relative measure of hotness or coldness.
Heat transfer occurs until temperatures equalize.

10.3 Measurement of Temperature

Thermometers use measurable properties that change with temperature.
Different thermometers lead to different temperature scales.

10.4 Ideal-Gas Equation and Absolute Temperature

Ideal gas equation: PV = µRT
- Where µ is the number of moles and R is the universal gas constant.
Absolute temperature scale: T = tc + 273.15

10.5 Thermal Expansion

Coefficient of linear expansion (α₁) and volume expansion (αᵥ):
- αᵥ = 3α₁

10.6 Specific Heat Capacity

Specific heat capacity (S): S = ΔQ / ΔT
- Where ΔQ is the heat supplied and ΔT is the change in temperature.

10.7 Calorimetry

Heat transfer calculations in calorimetry experiments.

10.8 Change of State

Latent heat of fusion (Lf) and vaporization (Lv):
- Lf: heat per unit mass for solid to liquid transition.
- Lv: heat per unit mass for liquid to vapor transition.

10.9 Heat Transfer

Three modes of heat transfer: conduction, convection, radiation.
Conduction: heat transfer through molecular collisions.

10.10 Newton's Law of Cooling

Rate of cooling is proportional to the temperature difference:
- Rate = K(T₂ - T₁)
- Where T₁ is the temperature of the surroundings and T₂ is the temperature of the body.

Summary

Heat is energy that flows due to temperature differences.
Thermometers utilize measurable properties to define temperature scales.
The Celsius and Fahrenheit scales have specific relationships.
The ideal gas equation relates pressure, volume, and temperature.
The absolute temperature scale has a unique zero point.
Coefficients of expansion define how materials change with temperature.

Points to Ponder

The triple point of water is a standard fixed point in thermometry.
Heat transfer requires a temperature difference.
Convection involves fluid movement due to temperature differences.

Exam Tips & Common Mistakes

Common Mistakes and Exam Tips

Common Pitfalls

Misunderstanding Temperature vs. Heat: Students often confuse temperature (a measure of hotness) with heat (energy transfer due to temperature difference). Ensure clarity on definitions.
Ignoring Units: When solving problems involving specific heat capacity or thermal expansion, neglecting units can lead to incorrect answers. Always check that units are consistent.
Not Considering Surroundings: In calorimetry problems, failing to account for heat exchange with the surroundings can skew results. Remember that heat transfer occurs until thermal equilibrium is reached.
Assuming Linear Expansion is Always Applicable: The coefficient of linear expansion is only valid within certain temperature ranges. Be cautious when applying it outside these limits.

Tips for Success

Understand Key Concepts: Focus on grasping the fundamental principles of heat transfer, such as conduction, convection, and radiation, rather than just memorizing formulas.
Practice with Real-World Examples: Relate concepts to everyday situations (e.g., why ice melts faster in warm water) to enhance understanding and retention.
Use Diagrams: When applicable, sketch diagrams to visualize problems, especially in calorimetry and thermal expansion scenarios.
Review Formulas Regularly: Create a summary sheet of essential formulas and definitions, including units, to reinforce memory and ensure quick recall during exams.

Practice & Assessment

Multiple Choice Questions

9750 J

19500 J

7800 J

15000 J

Correct Answer: A

Solution:

The heat required

Q

can be calculated using the formula

Q = mc\Delta T

, where

m = 500 \text{ g}

c = 0.39 \text{ J g}^{-1} \text{ K}^{-1}

, and

\Delta T = 75 - 25 = 50 \text{ °C}

. Thus,

Q = 500 \times 0.39 \times 50 = 9750 \text{ J}

0.39 J/g°C

0.50 J/g°C

0.45 J/g°C

0.35 J/g°C

Correct Answer: A

Solution:

Using the principle of calorimetry, heat lost by copper = heat gained by water.

m_c c_c (T_i - T_f) = m_w c_w (T_f - T_i)

where

m_c = 500 \text{ g}

T_i = 100°C

T_f = 30°C

m_w = 200 \text{ g}

c_w = 4.18 \text{ J/g°C}

, and

T_i = 25°C

. Solving,

500 c_c (100 - 30) = 200 \times 4.18 \times (30 - 25)

c_c = \frac{200 \times 4.18 \times 5}{500 \times 70} = 0.39 \text{ J/g°C}

It is independent of pressure.

It is the temperature at which solid and liquid states coexist in equilibrium.

It is always higher than the boiling point.

It decreases with an increase in pressure.

Correct Answer: B

Solution:

The melting point is defined as the temperature at which the solid and liquid states of a substance are in thermal equilibrium.

1.0 minute

0.7 minute

1.5 minutes

2.0 minutes

Correct Answer: B

Solution:

According to Newton's Law of Cooling, the rate of cooling is proportional to the temperature difference. For the first case,

\Delta T = 94 - 86 = 8 \text{ °C}

in 2 minutes. For the second case,

\Delta T = 71 - 69 = 2 \text{ °C}

. Using the proportionality,

\frac{8}{2} = \frac{2}{t}

, solving gives

t = 0.7 \text{ minutes}

10 °C

20 °C

30 °C

40 °C

Correct Answer: B

Solution:

The energy used for heating is

0.5 \times 10 \times 2.5 \times 60 \times 1000 = 750,000 \text{ J}

. The rise in temperature is

\Delta T = \frac{750,000}{8,000 \times 0.91} \approx 20 \text{ °C}

Heat is transferred through molecular collisions without any flow of matter.

Heat is transferred by the bulk movement of a fluid due to temperature differences.

Heat is transferred through electromagnetic waves without the need for a medium.

Heat is transferred by the direct contact between two surfaces.

Correct Answer: B

Solution:

Convection involves the bulk movement of a fluid (liquid or gas) due to temperature differences, leading to the transfer of heat. This is different from conduction, which involves molecular collisions, and radiation, which involves electromagnetic waves.

1.45 kg

2.5 kg

3.0 kg

0.5 kg

Correct Answer: A

Solution:

Calculate the heat lost by the copper block and use it to find the mass of ice melted using the heat of fusion.

1.001 meters

1.002 meters

1.003 meters

1.004 meters

Correct Answer: A

Solution:

The change in length due to thermal expansion is given by

\Delta L = L_0 \alpha \Delta T

. Here,

L_0 = 1 \text{ m}

\alpha = 1.20 \times 10^{-5} \text{ K}^{-1}

, and

\Delta T = 45 - 27 = 18 \text{ K}

. Thus,

\Delta L = 1 \times 1.20 \times 10^{-5} \times 18 = 0.000216 \text{ m}

. The actual length of the rod is

1 + 0.000216 = 1.000216 \text{ m}

, which rounds to 1.001 meters.

392.7 K

392.9 K

393.1 K

393.3 K

Correct Answer: B

Solution:

The absolute temperature

T

is given by

T = T_3 \times \frac{P}{P_3}

, where

T_3 = 273.16 \text{ K}

is the triple-point temperature,

P_3 = 1.250 \times 10^5 \text{ Pa}

is the pressure at the triple-point, and

P = 1.797 \times 10^5 \text{ Pa}

is the pressure at the normal melting point of sulphur.

T = 273.16 \times \frac{1.797}{1.250} \approx 392.9 \text{ K}

Water boiling to become steam.

Iron expanding when heated.

Copper conducting electricity.

Air cooling in the evening.

Correct Answer: A

Solution:

A phase change involves a transition between different states of matter, such as water boiling to become steam.

390 J kg⁻¹ K⁻¹

420 J kg⁻¹ K⁻¹

450 J kg⁻¹ K⁻¹

480 J kg⁻¹ K⁻¹

Correct Answer: A

Solution:

Using the formula

m_1 s_1 (T_f - T_i) = (m_2 + m_3) s_w (T_f - T_i)

, where

m_1 = 0.20 \text{ kg}

s_1

is the specific heat of the metal,

T_f = 40 \text{ °C}

T_i = 150 \text{ °C}

m_2 = 0.150 \text{ kg}

m_3 = 0.025 \text{ kg}

s_w = 4.18 \times 10^3 \text{ J kg}^{-1} \text{ K}^{-1}

. Solving gives

s_1 = 390 \text{ J kg}^{-1} \text{ K}^{-1}

0.5 atm

1 atm

2 atm

4 atm

Correct Answer: A

Solution:

According to Boyle's Law,

P_1 V_1 = P_2 V_2

. Here,

P_1 = 1 \text{ atm}

V_1 = 2 \text{ L}

V_2 = 4 \text{ L}

. Solving for

P_2

P_2 = \frac{P_1 V_1}{V_2} = \frac{1 \times 2}{4} = 0.5 \text{ atm}

15.4°C

10.2°C

12.5°C

20.0°C

Correct Answer: A

Solution:

The effective power used for heating the block is 5 kW (50% of 10 kW). Energy used = Power × Time = 5000 W × 150 s = 750,000 J. The rise in temperature

\Delta T = \frac{Q}{m \cdot c} = \frac{750,000}{8000 \times 0.91} = 15.4

°C.

Solid to liquid

Liquid to gas

Gas to liquid

Liquid to solid

Correct Answer: A

Solution:

Melting is the process where a solid changes into a liquid.

It relates pressure, volume, and temperature of a gas.

It only applies to liquids.

It is used to measure the heat capacity of a substance.

It describes the process of thermal expansion.

Correct Answer: A

Solution:

The ideal gas equation connects pressure (P), volume (V), and absolute temperature (T).

-50°C

-100°C

-150°C

-200°C

Correct Answer: B

Solution:

The change in diameter required for the wheel to slip onto the shaft is 0.01 cm. Using the formula for linear expansion,

\Delta D = D \alpha \Delta T

, we have

0.01 = 8.70 \times 1.20 \times 10^{-5} \times (T - 27)

. Solving for

T

gives

T \approx -100°C

0.42 cm

0.52 cm

0.62 cm

0.72 cm

Correct Answer: A

Solution:

Change in length

\Delta L = L_0 \cdot \alpha \cdot \Delta T

. For brass,

\Delta L_1 = 50 \times 2.0 \times 10^{-5} \times (250 - 40) = 0.21

cm. For steel,

\Delta L_2 = 50 \times 1.2 \times 10^{-5} \times (250 - 40) = 0.126

cm. Total change =

0.21 + 0.126 = 0.336

cm, approximated to 0.42 cm.

The temperature increases.

The temperature decreases.

The temperature remains constant.

The temperature fluctuates.

Correct Answer: C

Solution:

During a change of state, the temperature of a substance remains constant as the heat is used to change the state.

0.39 J/g°C

0.45 J/g°C

0.35 J/g°C

0.50 J/g°C

Correct Answer: A

Solution:

Using the principle of calorimetry, heat lost by copper = heat gained by water. Let the specific heat capacity of copper be

c

. Then,

1.5 imes 1000 imes c imes (400 - 45) = 500 imes 4.18 imes (45 - 25)

. Solving for

c

, we get

c = 0.39

J/g°C.

2.5 kg

1.5 kg

3.0 kg

2.0 kg

Correct Answer: B

Solution:

The heat lost by the copper block is

Q = m c \Delta T

, where

m = 2500 \text{ g}

c = 0.39 \text{ J g}^{-1} \text{ K}^{-1}

, and

\Delta T = 500 - 0 = 500 \text{ K}

. Thus,

Q = 2500 \times 0.39 \times 500 = 487500 \text{ J}

. The amount of ice melted is

\frac{Q}{\text{heat of fusion}} = \frac{487500}{335} \approx 1454 \text{ g}

, which is approximately 1.5 kg.

1800 N

900 N

450 N

225 N

Correct Answer: A

Solution:

The change in length is

\Delta L = L_0 \alpha \Delta T

, where

L_0 = 1.8 \text{ m}

\alpha = 2.0 \times 10^{-5} \text{ K}^{-1}

, and

\Delta T = -39 - 27 = -66 \text{ K}

. Thus,

\Delta L = 1.8 \times 2.0 \times 10^{-5} \times -66 = -0.002376 \text{ m}

. The tension developed is

F = \frac{YA \Delta L}{L_0}

, where

A = \pi (0.001)^2 \text{ m}^2

and

Y = 0.91 \times 10^{11} \text{ Pa}

. Thus,

F = \frac{0.91 \times 10^{11} \times \pi \times (0.001)^2 \times 0.002376}{1.8} \approx 1800 \text{ N}

Volume

V

remains the same.

Volume

V

doubles.

Volume

V

halves.

Volume

V

quadruples.

Correct Answer: A

Solution:

According to the ideal gas equation

PV = \mu RT

, if

P

is doubled and

T

is doubled, the equation becomes

2PV = \mu R(2T)

, which simplifies to

PV = \mu RT

. Thus, the volume

V

remains the same.

Heat transfer through direct contact between molecules.

Heat transfer through electromagnetic waves.

Heat transfer through the movement of fluids due to temperature differences.

Heat transfer through a vacuum.

Correct Answer: C

Solution:

Convection involves the movement of fluid (liquid or gas) due to temperature differences within the fluid.

The liquid and vapor phases have the same molar volume.

The liquid and vapor phases are in thermal equilibrium.

The liquid and vapor phases have different densities.

The liquid and vapor phases are in chemical equilibrium.

Correct Answer: B

Solution:

In a system where a liquid is in equilibrium with its vapor, both phases must be at the same temperature and pressure due to thermal equilibrium, ensuring no net energy transfer between the phases.

0.6 mm

1.2 mm

3.0 mm

6.0 mm

Correct Answer: C

Solution:

The change in length

\Delta L

is given by

\Delta L = L_0 \alpha \Delta T

, where

L_0 = 1.5 \text{ m}

\alpha = 2.0 \times 10^{-5} \text{ K}^{-1}

, and

\Delta T = 220 - 20 = 200 \text{ K}

. Thus,

\Delta L = 1.5 \times 2.0 \times 10^{-5} \times 200 = 0.006 \text{ m} = 6.0 \text{ mm}

0.0147

0.0245

0.0343

0.0441

Correct Answer: A

Solution:

The fractional change in volume is given by

\Delta V/V = \beta \Delta T = 49 \times 10^{-5} \times 30 = 0.0147

. Since density is inversely proportional to volume, the fractional change in density is also 0.0147.

1.0 J g⁻¹ K⁻¹

1.5 J g⁻¹ K⁻¹

2.0 J g⁻¹ K⁻¹

2.5 J g⁻¹ K⁻¹

Correct Answer: A

Solution:

Using the formula

C = \frac{Q}{m \Delta T}

, where

Q = 500 \text{ J}

m = 250 \text{ g}

, and

\Delta T = 2 \text{ °C}

, we find

C = \frac{500}{250 \times 2} = 1.0 \text{ J g}^{-1} \text{ K}^{-1}

It remains at the same temperature.

It cools down further.

It warms up as heat flows from the environment to the water.

It evaporates immediately.

Correct Answer: C

Solution:

Heat transfer takes place from the environment to the water until they reach the same temperature.

Melting

Freezing

Vaporization

Sublimation

Correct Answer: B

Solution:

Freezing is the process where a liquid changes to a solid state.

0.0144 cm

0.0348 cm

0.0542 cm

0.0736 cm

Correct Answer: B

Solution:

The change in diameter is given by

\Delta D = D \alpha \Delta T = 4.24 \times 1.70 \times 10^{-5} \times 200 = 0.0348 \text{ cm}

50 J kg⁻¹ K⁻¹

25 J kg⁻¹ K⁻¹

100 J kg⁻¹ K⁻¹

10 J kg⁻¹ K⁻¹

Correct Answer: A

Solution:

Using the formula

Q = mc\Delta T

, we rearrange to find

c = \frac{Q}{m\Delta T} = \frac{500}{2 \times 5} = 50 \text{ J kg}^{-1} \text{ K}^{-1}

400 K

350 K

450 K

500 K

Correct Answer: A

Solution:

Using the relation

R = R_0 [1 + \alpha (T - T_0)]

, we find

\alpha

from the given points:

165.5 = 101.6 [1 + \alpha (600.5 - 273.16)]

. Solving gives

\alpha \approx 0.001 \text{ K}^{-1}

. For

R = 123.4

123.4 = 101.6 [1 + 0.001 (T - 273.16)]

, solving gives

T \approx 400 \text{ K}

\alpha_v = 2 \alpha_l

\alpha_v = 3 \alpha_l

\alpha_v = \alpha_l

\alpha_v = 4 \alpha_l

Correct Answer: B

Solution:

The coefficient of volume expansion

\alpha_v

is three times the coefficient of linear expansion

\alpha_l

, i.e.,

\alpha_v = 3 \alpha_l

Temperature is a measure of the amount of heat in a body.

Temperature is a measure of the 'hotness' or 'coldness' of a body.

Temperature is the same as heat.

Temperature is the energy transferred between objects.

Correct Answer: B

Solution:

Temperature is a relative measure, or indication of hotness or coldness.

1.2 x 10⁻⁵ K⁻¹

3.6 x 10⁻⁵ K⁻¹

7.2 x 10⁻⁵ K⁻¹

2.4 x 10⁻⁵ K⁻¹

Correct Answer: A

Solution:

The coefficient of volume expansion is three times the coefficient of linear expansion:

\alpha_v = 3\alpha_l

The heat required to change a substance from solid to liquid at constant temperature.

The heat required to change a substance from liquid to gas at constant temperature.

The heat required to change a substance from gas to liquid at constant temperature.

The heat required to change a substance from liquid to solid at constant temperature.

Correct Answer: A

Solution:

The latent heat of fusion is the heat required to change a substance from solid to liquid at the same temperature and pressure.

The heat required to change the temperature of a unit mass by one degree.

The heat required to change a substance from solid to liquid.

The energy transferred between two bodies at different temperatures.

The amount of heat per unit volume required to change the temperature.

Correct Answer: A

Solution:

Specific heat capacity is defined as the heat required to change the temperature of a unit mass of a substance by one degree.

Conduction

Convection

Radiation

Reflection

Correct Answer: B

Solution:

Convection involves the flow of matter within a fluid due to unequal temperatures of its parts.

Melting

Freezing

Vaporization

Sublimation

Correct Answer: C

Solution:

Vaporization is the process where a liquid changes into a gas.

63.0 cm

63.1 cm

62.9 cm

63.2 cm

Correct Answer: A

Solution:

The tape is calibrated for 27.0 °C, but the measurement is taken at 45.0 °C. Since the tape and rod expand equally, the actual length remains 63.0 cm.

It is the point where only the solid and liquid phases exist.

It is the point where the solid, liquid, and vapor phases coexist in equilibrium.

It is the point where the liquid and vapor phases coexist.

It is the point where only the vapor phase exists.

Correct Answer: B

Solution:

The triple point on a phase diagram represents the unique set of conditions at which the solid, liquid, and vapor phases of a substance coexist in equilibrium.

0.012 cm

0.024 cm

0.048 cm

0.072 cm

Correct Answer: B

Solution:

The change in length

\Delta L

can be calculated using the formula

\Delta L = L_0 \alpha \Delta T

, where

L_0 = 2 \text{ m}

\alpha = 1.20 \times 10^{-5} \text{ K}^{-1}

, and

\Delta T = 77 - 27 = 50 \text{ K}

. Therefore,

\Delta L = 2 \times 1.20 \times 10^{-5} \times 50 = 0.0012 \text{ m} = 0.012 \text{ cm}

360 N

450 N

540 N

720 N

Correct Answer: C

Solution:

Use the formula for thermal stress: Stress = YαΔT, where Y is Young's modulus, α is the coefficient of linear expansion, and ΔT is the temperature change.

The excess temperature of the body over the surroundings.

The mass of the body.

The specific heat capacity of the body.

The volume of the body.

Correct Answer: A

Solution:

Newton's Law of Cooling states that the rate of cooling of a body is proportional to the excess temperature of the body over its surroundings.

0.7 minutes

1.4 minutes

2 minutes

3 minutes

Correct Answer: A

Solution:

Using Newton's Law of Cooling,

\frac{\Delta T_1}{\Delta t_1} = K(T_{avg1} - T_{room})

and

\frac{\Delta T_2}{\Delta t_2} = K(T_{avg2} - T_{room})

. For the first case,

\Delta T_1 = 8

\Delta t_1 = 2

T_{avg1} = 90

. For the second case,

\Delta T_2 = 2

T_{avg2} = 70

. Solving gives

\Delta t_2 = 0.7 \text{ minutes}

0.4 J/g°C

0.5 J/g°C

0.6 J/g°C

0.7 J/g°C

Correct Answer: A

Solution:

Let the specific heat of the metal be

c_m

. The heat lost by the metal is

0.20 \times c_m \times (150 - 40)

. The heat gained by the water and calorimeter is

0.175 \times 4.18 \times (40 - 27)

. Equating the heat lost and gained:

0.20 \times c_m \times 110 = 0.175 \times 4.18 \times 13

. Solving for

c_m

gives

c_m = 0.4 \text{ J/g°C}

0.5 minutes

0.7 minutes

1.0 minutes

1.5 minutes

Correct Answer: B

Solution:

Using Newton's Law of Cooling, the time taken is proportional to the temperature difference. Calculate using the given data.

0.0018 m

0.0022 m

0.0036 m

0.0048 m

Correct Answer: C

Solution:

The change in length

\Delta L

is given by

\Delta L = \alpha L_0 \Delta T

. Substituting the given values,

\Delta L = 2.0 \times 10^{-5} \times 1.8 \times (27 - (-39)) = 0.0036 \text{ m}

It is the heat required to change the temperature of a unit mass by 1°C.

It is the heat required to change the state of a unit mass.

It is the heat required to change the temperature of a unit volume by 1°C.

It is the heat required to change the temperature of a unit length by 1°C.

Correct Answer: A

Solution:

Specific heat capacity is defined as the amount of heat required to raise the temperature of a unit mass of a substance by 1°C.

Heat transfer through the movement of fluids.

Heat transfer through electromagnetic waves.

Heat transfer through direct contact between molecules.

Heat transfer through a vacuum.

Correct Answer: C

Solution:

Conduction is the transfer of heat through direct contact between molecules, without any flow of matter.

T = t_c + 273.15

T = t_c + 273.16

T = t_c - 273.15

T = t_c - 273.16

Correct Answer: A

Solution:

The relation between Celsius temperature

t_c

and Kelvin temperature

T

is given by

T = t_c + 273.15

It is in the solid state.

It is in the liquid state.

It is in the vapor state.

It is at the critical point.

Correct Answer: C

Solution:

At 375°C and 219 atm, the substance is above the critical temperature and pressure, meaning it exists as a supercritical fluid, which is more similar to a vapor state.

2.00192 meters

2.0024 meters

2.0032 meters

2.004 meters

Correct Answer: A

Solution:

The change in length

\Delta L

is given by

\Delta L = L_0 \alpha \Delta T

, where

L_0 = 2 \text{ m}

\alpha = 1.20 \times 10^{-5} \text{ K}^{-1}

, and

\Delta T = 100 - 20 = 80 \text{ K}

. Thus,

\Delta L = 2 \times 1.20 \times 10^{-5} \times 80 = 0.00192 \text{ m}

. Therefore, the new length is

2 + 0.00192 = 2.00192 \text{ m}

It is the temperature and pressure at which water can exist in solid, liquid, and vapor forms simultaneously.

It is the temperature at which water boils at standard atmospheric pressure.

It is the temperature at which water freezes at standard atmospheric pressure.

It is the highest temperature at which water can exist as a liquid.

Correct Answer: A

Solution:

The triple point of water is defined as the unique set of conditions (temperature and pressure) at which water can exist simultaneously in solid, liquid, and vapor phases. This is a fundamental concept in thermodynamics.

Heat transfer does not require a temperature difference.

Heat transfer can occur without molecular collisions.

Heat transfer always involves a temperature difference.

Heat transfer is independent of the medium.

Correct Answer: C

Solution:

Heat transfer always involves a temperature difference between two systems or parts of the same system.

It is the point where solid, liquid, and vapor phases coexist in equilibrium.

It is the point where only solid and liquid phases coexist.

It is the point where only liquid and vapor phases coexist.

It is the point where only solid and vapor phases coexist.

Correct Answer: A

Solution:

The triple point is defined as the unique set of conditions at which all three phases (solid, liquid, and vapor) of a substance coexist in thermodynamic equilibrium.

The increase in volume of a substance due to an increase in temperature.

The decrease in volume of a substance due to a decrease in temperature.

The change of state from solid to liquid.

The transfer of heat from a hotter object to a cooler one.

Correct Answer: A

Solution:

Thermal expansion refers to the increase in volume of a substance as its temperature increases.

63.015 cm

63.036 cm

63.072 cm

63.090 cm

Correct Answer: B

Solution:

The actual length is calculated using the formula

L = L_0 (1 + \alpha \Delta T)

, where

\Delta T = 45 - 27 = 18

K. Thus,

L = 63.0 \times (1 + 1.20 \times 10^{-5} \times 18) = 63.036

cm.

20.9 kJ

41.8 kJ

10.45 kJ

8.36 kJ

Correct Answer: B

Solution:

The heat required is calculated using

Q = mc\Delta T

. Here,

m = 2 \text{ kg}

c = 4.18 \times 10^3 \text{ J kg}^{-1} \text{ K}^{-1}

, and

\Delta T = 5 \text{ K}

. Thus,

Q = 2 \times 4.18 \times 10^3 \times 5 = 41.8 \text{ kJ}

62.99 cm

63.01 cm

63.02 cm

63.03 cm

Correct Answer: A

Solution:

The actual length can be calculated using the formula for linear expansion. The length decreases slightly when cooled.

83.3 °C

100 °C

120 °C

50 °C

Correct Answer: A

Solution:

Use the formula for linear expansion:

\Delta L = \alpha L \Delta T

, where

\Delta L/L = 0.0001

16.33 x 10⁻⁵ K⁻¹

49 x 10⁻⁵ K⁻¹

24.5 x 10⁻⁵ K⁻¹

3 x 10⁻⁵ K⁻¹

Correct Answer: A

Solution:

The relation between volume expansion coefficient (αᵥ) and linear expansion coefficient (αₗ) is αᵥ = 3αₗ. Therefore, αₗ = αᵥ/3.

298.15 K

273.15 K

250.15 K

300.15 K

Correct Answer: A

Solution:

The conversion from Celsius to Kelvin is done by adding 273.15 to the Celsius temperature. Thus, 25°C + 273.15 = 298.15 K.

Melting occurs when a solid turns into a gas directly.

Melting is the process where a liquid turns into a solid.

Melting is the process where a solid turns into a liquid.

Melting occurs when a gas turns into a liquid.

Correct Answer: C

Solution:

Melting is the change of state from solid to liquid.

Heat transfer through a metal rod.

Warm air rising above a heated surface.

Heat transfer through a vacuum.

Heat transfer through direct contact with a hot object.

Correct Answer: B

Solution:

Convection involves the flow of matter within a fluid due to unequal temperatures, such as warm air rising.

20,000 J

10,000 J

15,000 J

25,000 J

Correct Answer: A

Solution:

The heat required for the phase change is given by

Q = m \cdot L_f

, where

m = 100

g and

L_f = 200

J/g. Thus,

Q = 100 \times 200 = 20,000

The land heats up faster than the water during the day.

The water heats up faster than the land during the day.

The land cools down faster than the water during the day.

The water cools down faster than the land during the day.

Correct Answer: A

Solution:

A sea breeze occurs because the land heats up faster than the water during the day, causing the air above the land to rise and cooler air from the sea to move in.

True or False

Correct Answer: False

Solution:

A hot utensil is said to have a high temperature, as temperature is a measure of the 'hotness' of a body.

Correct Answer: True

Solution:

In the Kelvin absolute temperature scale, zero Kelvin is the point where substances have the least possible molecular activity, known as absolute zero.

Correct Answer: True

Solution:

The Kelvin scale assigns 273.16 K to the triple point of water, which is an exact relation by choice.

Correct Answer: True

Solution:

Conduction involves heat transfer between neighboring parts of a body through molecular collisions, without the flow of matter.

Correct Answer: False

Solution:

The Celsius temperature of the melting point of water is very close to, but not exactly 0 °C, due to the choice of the triple point of water as a fixed point.

Correct Answer: True

Solution:

The zero of the Kelvin scale corresponds to the temperature where every substance in nature has the least possible molecular activity.

Correct Answer: True

Solution:

The specific heat capacity of a substance is defined as the heat required to change its temperature by 1 degree per unit mass.

Correct Answer: True

Solution:

Latent heat of vaporization refers to the energy needed to convert a liquid into a gas at constant temperature.

Correct Answer: False

Solution:

During melting, the temperature of a substance remains constant while it transitions from solid to liquid, as the heat supplied is used to change the state.

Correct Answer: True

Solution:

Conduction involves heat transfer through direct contact and molecular collisions, with no movement of the matter itself.

Correct Answer: True

Solution:

During the phase transition from solid to liquid, the temperature remains constant as the heat energy is used to change the state rather than increase the temperature.

Correct Answer: False

Solution:

The latent heat of fusion is the heat required to change a substance from solid to liquid without a change in temperature. The latent heat of vaporization is for liquid to gas.

Correct Answer: True

Solution:

The Celsius temperature scale uses the triple point of water as a fixed point, which is assigned the value of 0.01°C.

Correct Answer: True

Solution:

Temperature is indeed a measure of the 'hotness' of a body and is quantitatively represented by temperature scales using a thermometer.

Correct Answer: True

Solution:

The triple point of water is a unique temperature and pressure at which water can coexist in solid, liquid, and vapor phases, making it a reliable standard fixed point.

Correct Answer: True

Solution:

Temperature is indeed a measure of how hot or cold a body is, as described in the text.

Correct Answer: True

Solution:

Convection is the process where heat is transferred by the movement of a fluid, caused by temperature differences within the fluid.

Correct Answer: False

Solution:

Convection involves the transfer of heat through the flow of matter within a fluid due to temperature differences, not just molecular collisions.

Correct Answer: True

Solution:

The Kelvin scale starts at absolute zero, the point where all molecular motion theoretically stops.

Correct Answer: True

Solution:

A sea breeze occurs during the day when the land heats up faster than the water, causing the warm air over the land to rise and cooler air from the sea to move in to replace it.

Correct Answer: True

Solution:

The triple point on a phase diagram is the condition under which all three phases (solid, liquid, and vapor) of a substance coexist in equilibrium.

Correct Answer: False

Solution:

Convection involves the transfer of heat through the movement of fluid (liquid or gas) due to temperature differences, not just molecular collisions.

Correct Answer: True

Solution:

The Kelvin and Celsius temperature scales have the same unit size, differing only in their starting points.

Correct Answer: True

Solution:

During melting, the temperature remains constant as the solid changes to liquid, even though heat is being absorbed.

Correct Answer: True

Solution:

Specific heat capacity is defined as the amount of heat required to change the temperature of a unit mass of a substance by one degree Celsius or Kelvin.

Correct Answer: False

Solution:

A hot utensil is said to have a high temperature, whereas an ice cube has a low temperature.

Correct Answer: True

Solution:

Regelation is the process where increased pressure lowers the melting point of ice, causing it to melt. When the pressure is relieved, the water refreezes.

Correct Answer: False

Solution:

The Kelvin and Celsius temperature scales have the same unit size; they differ only in their zero points.

Correct Answer: True

Solution:

The Kelvin scale and Celsius scale have the same unit size, but the Kelvin scale starts at absolute zero, not the freezing point of water.

Correct Answer: False

Solution:

Heat transfer requires a temperature difference between two systems.

Correct Answer: False

Solution:

Heat transfer always involves a temperature difference between two systems or parts of a system.

Correct Answer: True

Solution:

The Kelvin absolute temperature scale (T) has the same unit size as the Celsius scale (Tc), but differs in the origin.

Correct Answer: True

Solution:

The Kelvin temperature scale is related to the Celsius scale by the equation

T = t + 273.15

, where

T

is the temperature in Kelvin and

t

is the temperature in Celsius.

Correct Answer: False

Solution:

During the melting process, the temperature remains constant until the entire amount of the solid substance melts.

Correct Answer: True

Solution:

Newton's Law of Cooling describes that the rate at which a body loses heat is proportional to the difference in temperature between the body and its surrounding environment.

Correct Answer: True

Solution:

During a phase change, such as melting or boiling, the temperature of a substance remains constant because the heat energy is used to change the state of the substance rather than change its temperature.

Correct Answer: True

Solution:

The Kelvin scale is defined such that the triple point of water is exactly 273.16 K.

Correct Answer: True

Solution:

The original Celsius scale was defined with the melting point of ice and boiling point of water at exactly 0°C and 100°C. However, the current scale uses the triple point of water as a reference.

Correct Answer: True

Solution:

The coefficient of linear expansion quantifies the change in length per degree change in temperature for a material.

Correct Answer: False

Solution:

The Celsius temperature scale originally assigned 0°C and 100°C to the melting and boiling points of water, respectively, but now the triple point of water is used as a fixed point.

Correct Answer: False

Solution:

The latent heat of fusion is the heat required to change a substance from solid to liquid without changing its temperature. The latent heat of vaporization is for liquid to vapor.

Correct Answer: False

Solution:

In conduction, heat is transferred through molecular collisions without any flow of matter.

Correct Answer: True

Solution:

Newton's Law of Cooling describes that the rate of heat loss of a body is directly proportional to the difference in temperature between the body and its surroundings.

Correct Answer: False

Solution:

Heat transfer always involves a temperature difference between two systems or parts of a system. Without a temperature difference, no heat transfer occurs.

Correct Answer: True

Solution:

The Kelvin scale's zero point, or absolute zero, is where substances have the least possible molecular activity.

Correct Answer: True

Solution:

Heat transfer is driven by temperature differences, as energy flows from a hotter region to a cooler one.

Correct Answer: False

Solution:

During melting, the temperature remains constant while the substance transitions from solid to liquid, as the heat is used to change the state.

Correct Answer: False

Solution:

The melting point of a substance depends on pressure; it is defined at standard atmospheric pressure.

Correct Answer: True

Solution:

During a change of state, such as melting or boiling, the temperature remains constant while the substance absorbs or releases heat.

Correct Answer: True

Solution:

The original Celsius temperature scale had its fixed points at 0 °C for the melting point of ice and 100 °C for the boiling point of water.

Correct Answer: False

Solution:

During melting, the temperature remains constant as the solid turns into a liquid, despite heat being added.

Correct Answer: True

Solution:

Regelation is the phenomenon where ice melts under pressure and refreezes when the pressure is reduced.

Correct Answer: True

Solution:

In the original Celsius scale, the fixed points were exactly at 0 °C for the melting point of ice and 100 °C for the boiling point of water.

Correct Answer: True

Solution:

The relation between the coefficient of volume expansion

\alpha_v

and the coefficient of linear expansion

\alpha_l

\alpha_v = 3 \alpha_l

Correct Answer: True

Solution:

The latent heat of vaporization is indeed the heat required to change a substance from liquid to vapor without a change in temperature.

Correct Answer: True

Solution:

The ideal gas equation accurately describes the relationship between pressure, volume, and temperature for an ideal gas.

Correct Answer: False

Solution:

The coefficient of linear expansion can vary with temperature, and it is often assumed constant over small temperature ranges for simplicity in calculations.

Correct Answer: True

Solution:

Heat transfer occurs because of a temperature difference between a system and its surroundings.

Correct Answer: True

Solution:

The melting point is defined as the temperature at which the solid and liquid phases of a substance coexist in thermal equilibrium.

Correct Answer: True

Solution:

The Celsius and Kelvin scales both have the same unit size, but the Kelvin scale starts at absolute zero, whereas the Celsius scale starts at the freezing point of water.

Correct Answer: False

Solution:

The Celsius temperature of the boiling point of water is not exactly 100 °C at 1 atm pressure due to the definition based on the triple point of water. It is close to, but not exactly 100 °C.

Correct Answer: True

Solution:

When a liquid is in equilibrium with its vapor, both phases have the same pressure and temperature, although they differ in molar volume.

Correct Answer: False

Solution:

Heat transfer always involves a temperature difference between two systems or parts of the same system.

Thermal Properties of Matter

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Summary

Chapter 10: Thermal Properties of Matter

Summary

Learning Objectives

Detailed Notes

Chapter Ten: Thermal Properties of Matter

10.1 Introduction

10.2 Temperature and Heat

10.3 Measurement of Temperature

10.4 Ideal-Gas Equation and Absolute Temperature

10.5 Thermal Expansion

10.6 Specific Heat Capacity

10.7 Calorimetry

10.8 Change of State

10.9 Heat Transfer

10.10 Newton's Law of Cooling

Summary

Points to Ponder

Exam Tips & Common Mistakes

Common Mistakes and Exam Tips

Common Pitfalls

Tips for Success

Practice & Assessment

Multiple Choice Questions

Correct Answer: A

Q2.A calorimeter contains 200 g of water at 25°C. A 0.5 kg block of copper at 100°C is placed in it, and the final equilibrium temperature is 30°C. What is the specific heat capacity of copper? Assume no heat loss to the surroundings. (Specific heat capacity of water = 4.18 J/g°C)

Correct Answer: A

Q3.Which of the following is true about the melting point of a substance?

Correct Answer: B

Q4.A pan filled with hot food cools from 94 °C to 86 °C in 2 minutes in a room at 20 °C. Using Newton's Law of Cooling, how long will it take for the pan to cool from 71 °C to 69 °C under the same conditions?

Correct Answer: B

Q5.A 10 kW drilling machine is used to drill a bore in a small aluminum 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 aluminum = 0.91 J/g·K.

Correct Answer: B

Q6.Which of the following statements correctly describes the process of convection?

Correct Answer: B

Q7.A copper block of mass 2.5 kg is heated to 500 °C and placed on ice. How much ice can it melt? (Specific heat of copper = 0.39 J g⁻¹ K⁻¹; heat of fusion of water = 335 J g⁻¹)

Correct Answer: A

Correct Answer: A

Correct Answer: B

Q10.Which of the following is an example of a phase change?

Correct Answer: A

Q11.A calorimeter contains 150 cm³ of water at 27 °C. A 0.20 kg block of metal at 150 °C is dropped into it, raising the final temperature to 40 °C. If the water equivalent of the calorimeter is 0.025 kg, what is the specific heat capacity of the metal? Assume no heat loss to the surroundings.

Correct Answer: A

Q12.A gas is contained in a cylinder with a movable piston. Initially, the gas is at a pressure of 1 atm, a volume of 2 L, and a temperature of 300 K. If the gas expands to a volume of 4 L at constant temperature, what is the final pressure of the gas?

Correct Answer: A

Q13.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°C)

Correct Answer: A

Q14.Which of the following describes the process of melting?

Correct Answer: A

Q15.Which of the following statements is true about the ideal gas equation?

Correct Answer: A

Correct Answer: B

Correct Answer: A

Q18.What happens to the temperature of a substance during a change of state?

Correct Answer: C

Q19.A copper block of mass 1.5 kg is heated to 400°C and then placed in a calorimeter containing 500 g of water at 25°C. If the final equilibrium temperature is 45°C, what is the specific heat capacity of copper? (Specific heat capacity of water = 4.18 J/g°C)

Correct Answer: A

Q20.During an experiment, a copper block of mass 2.5 kg is heated to 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 \text{ J g}^{-1} \text{ K}^{-1}; heat of fusion of water = 335 \text{ J g}^{-1})

Correct Answer: B

Q21.A brass wire 1.8 m long at 27°C is cooled to -39°C. What is the tension developed in the wire if its diameter is 2.0 mm? (Coefficient of linear expansion of brass = 2.0 \times 10^{-5} \text{ K}^{-1}; Young's modulus of brass = 0.91 \times 10^{11} \text{ Pa})

Correct Answer: A

Q22.The ideal gas equation is given by PV=μRTPV = \mu RTPV=μRT. If the pressure PPP is doubled while keeping the number of moles μ\muμ and the gas constant RRR constant, what happens to the volume VVV if the temperature TTT is also doubled?

Correct Answer: A

Q23.Which of the following best describes the process of convection?

Correct Answer: C

Q24.A liquid in equilibrium with its vapor has the same pressure and temperature throughout the system. What is the primary reason for this uniformity?

Correct Answer: B

Q25.A brass rod of length 1.5 m is heated from 20°C to 220°C. What is the change in length of the rod? (Coefficient of linear expansion for brass = 2.0×10−5 K−12.0 \times 10^{-5} \text{ K}^{-1}2.0×10−5 K−1)

Correct Answer: C

Q26.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?

Correct Answer: A

Q27.The specific heat capacity of a substance is defined by the relation C=QmΔTC = \frac{Q}{m \Delta T}C=mΔTQ​. If 500 J of heat is added to a 250 g sample, raising its temperature by 2 °C, what is the specific heat capacity of the substance?

Correct Answer: A

Q28.What happens to a glass of ice-cold water left on a table on a hot day?

Correct Answer: C

Q29.Which of the following processes involves a change of state from liquid to solid?

Correct Answer: B

Q30.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)