2026-03-21 · Heat-Temperature-Notes

HEAT AND TEMPERATURE

Thermal Energy, Heat and Temperature - Grade XI Physics

9.1 Molecular Concept of Thermal Energy, Heat and Temperature

Molecular Concept of Thermal Energy

Thermal energy is the total kinetic energy of all the molecules in a substance due to their random motion. It depends on:

Temperature (average kinetic energy per molecule)
Number of molecules (mass of substance)

Thermal Energy ∝ N × (KE)avg
Where: N = Number of molecules, (KE)avg = Average kinetic energy per molecule

Molecular Concept of Heat

Heat is the transfer of thermal energy from one body to another due to temperature difference. It is energy in transit.

Characteristics of Heat:

Energy in transit from hot to cold body
Flows due to temperature difference
Cannot be contained, only transferred
SI unit: Joule (J)

Molecular Concept of Temperature

Temperature is a measure of average kinetic energy of molecules in a substance. It determines the direction of heat flow.

T ∝ (KE)avg
Average kinetic energy = (3/2)kT
Where: k = Boltzmann constant, T = Absolute temperature

Low Temperature

Slow molecular motion

High Temperature

Rapid molecular motion

Cause and Direction of Heat Flow

Cause of Heat Flow:

Difference in kinetic energy of molecules
Temperature difference between bodies
Tendency to reach thermal equilibrium

Direction of Heat Flow:

From higher temperature to lower temperature
From higher average kinetic energy to lower average kinetic energy
From body with more vigorous molecular motion to body with less vigorous motion

Example:

When a hot cup of tea is placed in a cold room:

Tea molecules have higher average kinetic energy
Room air molecules have lower average kinetic energy
Heat flows from tea to room air
This continues until thermal equilibrium is reached

9.2 Thermal Equilibrium and Zeroth Law of Thermodynamics

Thermal Equilibrium

Two bodies are said to be in thermal equilibrium when there is no net heat flow between them, i.e., they are at the same temperature.

Characteristics:

No heat transfer between bodies
Same temperature
Stable state
Molecular kinetic energies are equal on average

Body A

Temperature: T₁

🔥

Hot

↔️

Body B

Temperature: T₂

❄️

Cold

→

Equilibrium

Temperature: T

⚖️

Equal T

Zeroth Law of Thermodynamics

If two systems are each in thermal equilibrium with a third system, then they are in thermal equilibrium with each other.

Statement:

Let systems A and B are separately in thermal equilibrium with system C. Then systems A and B are in thermal equilibrium with each other.

This law provides the theoretical foundation for temperature measurement.

If A ⇋ C and B ⇋ C, then A ⇋ B
Where: ⇋ represents thermal equilibrium

Significance:

Defines the concept of temperature
Justifies the use of thermometers
Establishes temperature as a fundamental property
Forms the basis of temperature scale

9.3 Thermal Equilibrium as Working Principle of Mercury Thermometer

Working Principle

Mercury thermometer works on the principle of thermal equilibrium and the Zeroth law of thermodynamics.

Working Mechanism:

Thermometer bulb contains mercury (system C)
When placed in contact with body to be measured (system A), heat transfer occurs
Eventually, thermometer and body reach thermal equilibrium
At equilibrium, both have same temperature
Mercury expansion indicates the temperature

Mercury Thermometer Working

100°C

75°C

50°C

25°C

0°C

Mercury expands when heated and contracts when cooled

Steps in Temperature Measurement:

Contact: Thermometer bulb placed in contact with object
Heat Transfer: Heat flows between object and mercury
Equilibrium: Thermal equilibrium established
Indication: Mercury level stabilizes indicating temperature

Requirements for Accurate Measurement:

Thermometer must reach thermal equilibrium with object
Sufficient time for heat transfer
Minimal heat capacity of thermometer compared to object
Good thermal contact between thermometer and object

Example of Zeroth Law Application:

When measuring human body temperature:

Body (A) and thermometer mercury (C) come in contact
Heat flows until thermal equilibrium
Mercury expands to indicate body temperature
If same thermometer is used for another person (B), and shows same reading, then persons A and B have same temperature

Advantages of Mercury Thermometer

Wide temperature range (-39°C to 357°C)
Uniform expansion
Visible meniscus
Quick response due to low specific heat
Does not wet glass

Limitations

Toxic mercury
Fragile glass
Requires waiting for equilibrium
Cannot record maximum temperature

Numerical Examples

Example 1:

Calculate the average kinetic energy of gas molecules at 27°C. (Boltzmann constant k = 1.38 × 10⁻²³ J/K)

Solution:

Given: T = 27°C = 300 K, k = 1.38 × 10⁻²³ J/K

Average kinetic energy = (3/2)kT

= (3/2) × 1.38 × 10⁻²³ × 300

= 6.21 × 10⁻²¹ J

Example 2:

Two bodies A and B are at temperatures 50°C and 20°C respectively. If they are brought in contact, in which direction will heat flow?

Solution:

Heat flows from higher temperature to lower temperature.

Since 50°C > 20°C, heat will flow from body A to body B.

Example 3:

A mercury thermometer initially at 20°C is placed in contact with a hot object. After some time, the mercury level rises to indicate 80°C. Explain what happened according to Zeroth law.

Solution:

Initially: Thermometer (20°C) and hot object (T > 20°C) are not in thermal equilibrium.

Heat flows from hot object to thermometer mercury until thermal equilibrium is established.

At equilibrium: Both thermometer and object are at 80°C.

This demonstrates the Zeroth law - both systems are now in thermal equilibrium.

Multiple Choice Questions

1. Temperature is a measure of:

(a) Total kinetic energy of molecules

(b) Potential energy of molecules

(d) Total energy of molecules

2. Heat flows from one body to another due to:

(a) Difference in mass

(b) Difference in volume

(d) Difference in density

3. Two bodies are in thermal equilibrium when:

(a) They have same mass

(b) They have same volume

(d) They are made of same material

4. Zeroth law of thermodynamics states that:

(a) Heat flows from hot to cold body

(b) Energy cannot be created or destroyed

(d) Work can be converted to heat

5. Mercury thermometer works on the principle of:

(a) First law of thermodynamics

(b) Second law of thermodynamics

(d) Conservation of energy

6. The average kinetic energy of gas molecules is given by:

(a) kT

(b) (1/2)kT

(d) 2kT

7. Heat is:

(a) A property of matter

(b) Energy in transit ✓

(d) A form of matter

8. When thermal equilibrium is reached:

(a) Heat flow stops ✓

(b) Molecular motion stops

(d) Volume becomes constant

9. The SI unit of thermal energy is:

(a) Kelvin

(b) Celsius

(d) Calorie

10. In a mercury thermometer, mercury expands due to:

(a) Increase in mass

(b) Increase in molecular kinetic energy ✓

(d) Decrease in pressure

```html Thermal Energy, Heat and Temperature - Grade XI Physics

9.1 Molecular Concept of Thermal Energy, Heat and Temperature

Molecular Concept of Thermal Energy

Thermal energy is the total kinetic energy of all the molecules in a substance due to their random motion. It depends on:

Temperature (average kinetic energy per molecule)
Number of molecules (mass of substance)

Thermal Energy ∝ N × (KE)avg
Where: N = Number of molecules, (KE)avg = Average kinetic energy per molecule

Molecular Concept of Heat

Heat is the transfer of thermal energy from one body to another due to temperature difference. It is energy in transit.

Characteristics of Heat:

Energy in transit from hot to cold body
Flows due to temperature difference
Cannot be contained, only transferred
SI unit: Joule (J)

Molecular Concept of Temperature

Temperature is a measure of average kinetic energy of molecules in a substance. It determines the direction of heat flow.

T ∝ (KE)avg
Average kinetic energy = (3/2)kT
Where: k = Boltzmann constant, T = Absolute temperature

Low Temperature

Slow molecular motion

High Temperature

Rapid molecular motion

Cause and Direction of Heat Flow

Cause of Heat Flow:

Difference in kinetic energy of molecules
Temperature difference between bodies
Tendency to reach thermal equilibrium

Direction of Heat Flow:

From higher temperature to lower temperature
From higher average kinetic energy to lower average kinetic energy
From body with more vigorous molecular motion to body with less vigorous motion

Example:

When a hot cup of tea is placed in a cold room:

Tea molecules have higher average kinetic energy
Room air molecules have lower average kinetic energy
Heat flows from tea to room air
This continues until thermal equilibrium is reached

9.2 Thermal Equilibrium and Zeroth Law of Thermodynamics

Thermal Equilibrium

Two bodies are said to be in thermal equilibrium when there is no net heat flow between them, i.e., they are at the same temperature.

Characteristics:

No heat transfer between bodies
Same temperature
Stable state
Molecular kinetic energies are equal on average

Body A

Temperature: T₁

🔥

Hot

↔️

Body B

Temperature: T₂

❄️

Cold

→

Equilibrium

Temperature: T

⚖️

Equal T

Zeroth Law of Thermodynamics

If two systems are each in thermal equilibrium with a third system, then they are in thermal equilibrium with each other.

Statement:

Let systems A and B are separately in thermal equilibrium with system C. Then systems A and B are in thermal equilibrium with each other.

This law provides the theoretical foundation for temperature measurement.

If A ⇋ C and B ⇋ C, then A ⇋ B
Where: ⇋ represents thermal equilibrium

Significance:

Defines the concept of temperature
Justifies the use of thermometers
Establishes temperature as a fundamental property
Forms the basis of temperature scale

9.3 Thermal Equilibrium as Working Principle of Mercury Thermometer

Working Principle

Mercury thermometer works on the principle of thermal equilibrium and the Zeroth law of thermodynamics.

Working Mechanism:

Thermometer bulb contains mercury (system C)
When placed in contact with body to be measured (system A), heat transfer occurs
Eventually, thermometer and body reach thermal equilibrium
At equilibrium, both have same temperature
Mercury expansion indicates the temperature

Mercury Thermometer Working

100°C

75°C

50°C

25°C

0°C

Mercury expands when heated and contracts when cooled

Steps in Temperature Measurement:

Contact: Thermometer bulb placed in contact with object
Heat Transfer: Heat flows between object and mercury
Equilibrium: Thermal equilibrium established
Indication: Mercury level stabilizes indicating temperature

Requirements for Accurate Measurement:

Thermometer must reach thermal equilibrium with object
Sufficient time for heat transfer
Minimal heat capacity of thermometer compared to object
Good thermal contact between thermometer and object

Example of Zeroth Law Application:

When measuring human body temperature:

Body (A) and thermometer mercury (C) come in contact
Heat flows until thermal equilibrium
Mercury expands to indicate body temperature
If same thermometer is used for another person (B), and shows same reading, then persons A and B have same temperature

Advantages of Mercury Thermometer

Wide temperature range (-39°C to 357°C)
Uniform expansion
Visible meniscus
Quick response due to low specific heat
Does not wet glass

Limitations

Toxic mercury
Fragile glass
Requires waiting for equilibrium
Cannot record maximum temperature

Temperature Scale Conversions

Temperature Scale Relationships

(C - 0)/100 = (F - 32)/180 = (K - 273.15)/100 = (R - 0)/80
Where: C = Celsius, F = Fahrenheit, K = Kelvin, R = Réaumur

Conversion Formulas:

Celsius to Fahrenheit: F = (9/5)C + 32
Fahrenheit to Celsius: C = (5/9)(F - 32)
Celsius to Kelvin: K = C + 273.15
Kelvin to Celsius: C = K - 273.15
Fahrenheit to Kelvin: K = (5/9)(F - 32) + 273.15

Example 1: Temperature Conversion

Convert 100°C to Fahrenheit and Kelvin.

Solution:

To Fahrenheit:

F = (9/5)C + 32 = (9/5) × 100 + 32 = 180 + 32 = 212°F

To Kelvin:

K = C + 273.15 = 100 + 273.15 = 373.15 K

Example 2: Absolute Zero Conversion

Express absolute zero (-273.15°C) in Fahrenheit and Kelvin.

Solution:

To Fahrenheit:

F = (9/5)(-273.15) + 32 = -491.67 + 32 = -459.67°F

To Kelvin:

K = -273.15 + 273.15 = 0 K

Example 3: Room Temperature Conversion

Room temperature is 72°F. Convert it to Celsius and Kelvin.

Solution:

To Celsius:

C = (5/9)(F - 32) = (5/9)(72 - 32) = (5/9) × 40 = 22.22°C

To Kelvin:

K = C + 273.15 = 22.22 + 273.15 = 295.37 K

Faulty and Arbitrary Thermometers

Faulty Thermometer:

A thermometer that does not show correct readings due to manufacturing defects or calibration errors.

Correction Formula:

(Correct reading - LFP)/(UFP - LFP) = (Faulty reading - LFP')/(UFP' - LFP')
Where: LFP = Lower Fixed Point, UFP = Upper Fixed Point

Example 4: Faulty Thermometer

A faulty thermometer has its lower fixed point at 5°C and upper fixed point at 105°C. When this thermometer reads 60°C, what is the correct temperature?

Solution:

Given:

Standard LFP = 0°C, UFP = 100°C

Faulty LFP' = 5°C, UFP' = 105°C

Faulty reading = 60°C

Using the formula:

(C - 0)/(100 - 0) = (60 - 5)/(105 - 5)

C/100 = 55/100

C = 55°C

Therefore, the correct temperature is 55°C.

Example 5: Another Faulty Thermometer

A thermometer reads 5°C when ice is melting and 95°C when steam is condensing under normal atmospheric pressure. What is the correct temperature when it reads 50°C?

Solution:

Given:

Standard LFP = 0°C, UFP = 100°C

Faulty LFP' = 5°C, UFP' = 95°C

Faulty reading = 50°C

Using the formula:

(C - 0)/(100 - 0) = (50 - 5)/(95 - 5)

C/100 = 45/90 = 0.5

C = 50°C

Therefore, the correct temperature is 50°C.

Arbitrary Thermometer:

A thermometer with arbitrary fixed points (not 0°C and 100°C).

Conversion Formula:

(C - 0)/(100 - 0) = (X - LFP_X)/(UFP_X - LFP_X)
Where: X = Reading on arbitrary scale, LFP_X, UFP_X = Fixed points on arbitrary scale

Example 6: Arbitrary Thermometer

An arbitrary thermometer has its lower fixed point at 10°A and upper fixed point at 160°A. What is the temperature on this scale when it is 40°C?

Solution:

Given:

Standard LFP = 0°C, UFP = 100°C

Arbitrary LFP_A = 10°A, UFP_A = 160°A

Celsius reading = 40°C

Using the formula:

(40 - 0)/(100 - 0) = (A - 10)/(160 - 10)

40/100 = (A - 10)/150

0.4 = (A - 10)/150

A - 10 = 60

A = 70°A

Therefore, 40°C = 70°A.

Additional Numerical Examples

Example 7: Molecular Kinetic Energy

Calculate the average kinetic energy of gas molecules at 27°C. (Boltzmann constant k = 1.38 × 10⁻²³ J/K)

Solution:

Given: T = 27°C = 300 K, k = 1.38 × 10⁻²³ J/K

Average kinetic energy = (3/2)kT

= (3/2) × 1.38 × 10⁻²³ × 300

= 6.21 × 10⁻²¹ J

Example 8: Heat Flow Direction

Two bodies A and B are at temperatures 50°C and 20°C respectively. If they are brought in contact, in which direction will heat flow?

Solution:

Heat flows from higher temperature to lower temperature.

Since 50°C > 20°C, heat will flow from body A to body B.

Example 9: Thermal Equilibrium Application

A mercury thermometer initially at 20°C is placed in contact with a hot object. After some time, the mercury level rises to indicate 80°C. Explain what happened according to Zeroth law.

Solution:

Initially: Thermometer (20°C) and hot object (T > 20°C) are not in thermal equilibrium.

Heat flows from hot object to thermometer mercury until thermal equilibrium is established.

At equilibrium: Both thermometer and object are at 80°C.

This demonstrates the Zeroth law - both systems are now in thermal equilibrium.

Example 10: Complex Temperature Conversion

The temperature of a body is increased by 30°C. Find the corresponding increase in (a) Fahrenheit scale and (b) Kelvin scale.

Solution:

(a) Fahrenheit Scale:

The relationship between Celsius and Fahrenheit scales shows that for every 5°C change, there is a 9°F change.

Therefore: ΔF = (9/5) × ΔC = (9/5) × 30 = 54°F

(b) Kelvin Scale:

The Kelvin and Celsius scales have the same unit size, so:

ΔK = ΔC = 30 K

Example 11: Faulty Thermometer with Negative Reading

A faulty thermometer reads 2°C when ice melts and 102°C when steam condenses. What is the correct temperature when it reads 40°C?

Solution:

Given:

Standard LFP = 0°C, UFP = 100°C

Faulty LFP' = 2°C, UFP' = 102°C

Faulty reading = 40°C

Using the formula:

(C - 0)/(100 - 0) = (40 - 2)/(102 - 2)

C/100 = 38/100 = 0.38

C = 38°C

Therefore, the correct temperature is 38°C.

Multiple Choice Questions

1. Temperature is a measure of:

(a) Total kinetic energy of molecules

(b) Potential energy of molecules

(d) Total energy of molecules

2. Heat flows from one body to another due to:

(a) Difference in mass

(b) Difference in volume

(d) Difference in density

3. Two bodies are in thermal equilibrium when:

(a) They have same mass

(b) They have same volume

(d) They are made of same material

4. Zeroth law of thermodynamics states that:

(a) Heat flows from hot to cold body

(b) Energy cannot be created or destroyed

(d) Work can be converted to heat

5. Mercury thermometer works on the principle of:

(a) First law of thermodynamics

(b) Second law of thermodynamics

(d) Conservation of energy

6. The average kinetic energy of gas molecules is given by:

(a) kT

(b) (1/2)kT

(d) 2kT

7. Heat is:

(a) A property of matter

(b) Energy in transit ✓

(d) A form of matter

8. When thermal equilibrium is reached:

(a) Heat flow stops ✓

(b) Molecular motion stops

(d) Volume becomes constant

9. The SI unit of thermal energy is:

(a) Kelvin

(b) Celsius

(d) Calorie

10. In a mercury thermometer, mercury expands due to:

(a) Increase in mass

(b) Increase in molecular kinetic energy ✓

(d) Decrease in pressure

11. The conversion formula from Celsius to Fahrenheit is:

(a) F = C + 32

(b) F = (5/9)C + 32

(d) F = 9C + 32

12. Absolute zero in Celsius is:

(a) 0°C

(b) -100°C

(d) -459.67°C

13. A faulty thermometer with LFP at 4°C and UFP at 104°C reads 54°C. The correct temperature is:

(a) 50°C ✓

(b) 54°C

(d) 60°C

14. For an arbitrary scale with LFP = 20°X and UFP = 120°X, when C = 50°C, the reading in X scale is:

(a) 50°X

(b) 60°X

(d) 80°X