Thermal Energy Examples in Physics

Start with the recap, study the fully worked examples, then use the practice problems to check your understanding of Thermal Energy.

This page combines explanation, solved examples, and follow-up practice so you can move from recognition to confident problem-solving in Physics.

Concept Recap

The total kinetic energy of all particles (atoms and molecules) in an object due to their random motion.

The energy of jiggling atoms and molecules—what we experience as temperature.

Read the full concept explanation →

How to Use These Examples

Read the first worked example with the solution open so the structure is clear.
Try the practice problems before revealing each solution.
Use the related concepts and background knowledge badges if you feel stuck.

What to Focus On

Core idea: Thermal Energy starts by identifying what is warmer, what is cooler, and what energy or state variable changes.

Common stuck point: Students often know a formula related to thermal energy but skip the recognition step: Am I tracking thermal energy transfer, particle motion, temperature change, or pressure-volume-temperature relationships? That leads to a correct-looking substitution attached to the wrong physical model.

Sense of Study hint: Ask: Am I tracking thermal energy transfer, particle motion, temperature change, or pressure-volume-temperature relationships?

Worked Examples

Example 1

easy

How much thermal energy is needed to heat

2 \text{ kg}

of water from

20°\text{C}

80°\text{C}

? The specific heat capacity of water is

c = 4186 \text{ J/(kg·°C)}

Answer

Q \approx 502 \text{ kJ}

First step

Use the thermal energy formula:

Q = mc\Delta T

Full solution

2
Temperature change: $\Delta T = 80 - 20 = 60°\text{C}$ .
3
$Q = 2 \times 4186 \times 60 = 502{,}320 \text{ J} \approx 502 \text{ kJ}$

Thermal energy (heat) required to change an object's temperature depends on its mass, specific heat capacity, and the temperature change. Water has a very high specific heat, requiring lots of energy to heat.

Example 2

medium

0.5 \text{ kg}

iron block (

c = 450 \text{ J/(kg·°C)}

) at

200°\text{C}

is dropped into

2 \text{ kg}

of water (

c = 4186 \text{ J/(kg·°C)}

) at

20°\text{C}

. What is the final equilibrium temperature?

Example 3

medium

800 \text{ W}

kettle heats

1.0 \text{ kg}

of water (

c = 4200

) from

20°\text{C}

100°\text{C}

. Ignoring losses, find the time required.

Example 4

medium

Equal heat is given to

1 \text{ kg}

water (

c = 4200

), causing a

10°\text{C}

rise, and to

1 \text{ kg}

oil (

c = 2100

). Find the oil's temperature rise.

Practice Problems

Try these problems on your own first, then open the solution to compare your method.

Example 1

medium

3 \text{ kg}

aluminum block (

c = 900 \text{ J/(kg·°C)}

) absorbs

54{,}000 \text{ J}

of thermal energy. What is the temperature increase?

Example 2

hard

1200 \text{ kg}

car traveling at

30 \text{ m/s}

brakes to a stop. If all kinetic energy is converted to thermal energy in the brakes (

4 \text{ kg}

of steel,

c = 500 \text{ J/(kg·°C)}

), by how much do the brakes heat up?

Example 3

easy

Which has more thermal energy: a large iceberg at 0°C or a cup of boiling water at 100°C? Explain in one line.

Example 4

easy

How much heat is needed to raise 2 kg of water by 10°C? (water

c = 4200 \text{ J/(kg·°C)}

)

Example 5

easy

A substance loses 5000 J of thermal energy. Did its particles speed up or slow down on average?

Example 6

easy

Heat 0.5 kg of aluminium (

c = 900 \text{ J/(kg·°C)}

) by 20°C. Find the heat required.

Example 7

easy

Two identical copper blocks are at 50°C and 80°C. Which has more thermal energy?

Example 8

easy

True or false: heat and thermal energy are the same thing.

Example 9

easy

If 3 kg of water cools by 5°C, how much thermal energy does it release? (water

c = 4200 \text{ J/(kg·°C)}

)

Example 10

easy

A gas is heated and its particles move faster. What happened to its thermal energy?

Example 11

medium

How much heat raises 0.25 kg of water from 20°C to 80°C? (water

c = 4200 \text{ J/(kg·°C)}

)

Example 12

medium

It takes 12600 J to raise 1.5 kg of a metal by 20°C. Find its specific heat.

Example 13

medium

Mixing 1 kg of water at 80°C with 1 kg at 20°C (no losses), what is the final temperature?

Example 14

medium

A 2 kg iron block (

c = 450 \text{ J/(kg·°C)}

) gains 18000 J of heat. Find its temperature rise.

Example 15

medium

Water (

c = 4200

) and oil (

c = 2000

), same mass, both gain the same heat. Which heats up more?

Example 16

medium

A 0.1 kg metal at 100°C (

c = 500

) is dropped into 0.1 kg water at 20°C (

c = 4200

). Will the final temperature be closer to 20°C or 100°C?

Example 17

medium

How much heat is released when 0.5 kg of water cools from 90°C to 30°C? (water

c = 4200

)

Example 18

challenge

0.2 kg of metal at 150°C (

c = 500

) is placed in 0.5 kg water at 20°C (

c = 4200

). Find the equilibrium temperature (no losses).

Example 19

challenge

A 0.05 kg lead bullet (

c = 130

) at 30°C hits a wall at 200 m/s and stops. If half its KE becomes thermal energy in the bullet, find its temperature rise.

Example 20

challenge

Equal heat

Q

is added to 1 kg of water (

c = 4200

) and 1 kg of copper (

c = 385

). Water rises 5°C. How much does copper rise?

Example 21

medium

How much heat raises 0.4 kg of copper (

c = 385

) by 50°C?

Example 22

medium

Equal masses of two metals gain the same heat. Metal P has

c = 200

, metal Q has

c = 800

. Which warms more?

Example 23

easy

How much heat raises

1 \text{ kg}

of water by

25°\text{C}

? (water

c = 4200 \text{ J/(kg·°C)}

)

Example 24

easy

0.2 \text{ kg}

of iron (

c = 450

) is heated by

30°\text{C}

. Find the heat required.

Example 25

easy

0.5 \text{ kg}

of copper (

c = 385

) cools by

40°\text{C}

. Find the heat released.

Example 26

easy

Heat

0.4 \text{ kg}

of aluminium (

c = 900

) from

20°\text{C}

50°\text{C}

. Find the heat absorbed.

Example 27

easy

An object loses

4000 \text{ J}

of thermal energy. State whether the average particle KE rose or fell.

Example 28

medium

Mix

0.5 \text{ kg}

water at

80°\text{C}

with

1.5 \text{ kg}

water at

20°\text{C}

(no losses). Find the final temperature.

Example 29

medium

Determine the specific heat of a metal if

25200 \text{ J}

raises

3 \text{ kg}

of it by

30°\text{C}

Example 30

medium

0.3 \text{ kg}

aluminium pot (

c = 900

) and

0.5 \text{ kg}

water (

c = 4200

) inside both rise from

20°\text{C}

80°\text{C}

. Find the total heat required.

Example 31

medium

1500 \text{ W}

heater warms

4 \text{ L}

of water (density

1000 \text{ kg/m}^3

c = 4200

) by

30°\text{C}

. Find the heating time, ignoring losses.

Example 32

medium

0.1 \text{ kg}

of ice at

0°\text{C}

is added to

0.5 \text{ kg}

of water at

40°\text{C}

. Latent heat of fusion of ice

L_f = 334000 \text{ J/kg}

; water

c = 4200

. Find the final temperature (assume all ice melts).

Example 33

medium

How much energy must be removed to cool

2 \text{ kg}

of water from

80°\text{C}

20°\text{C}

? (

c = 4200

)

Example 34

hard

0.4 \text{ kg}

of steel (

c = 500

) at

300°\text{C}

is quenched in

1 \text{ kg}

water (

c = 4200

) at

20°\text{C}

, container losses neglected. Find the final temperature.

Example 35

hard

0.02 \text{ kg}

copper bullet (

c = 385

) at

30°\text{C}

hits a target at

200 \text{ m/s}

and stops. If all KE becomes thermal energy in the bullet, find its temperature rise.

Example 36

hard

A solar collector with effective area

2 \text{ m}^2

receives

700 \text{ W/m}^2

. With

60\%

efficiency, how long to heat

50 \text{ kg}

water (

c = 4200

) from

20°\text{C}

50°\text{C}

Example 37

hard

200 \text{ g}

of water at

90°\text{C}

is poured into a

300 \text{ g}

glass cup (

c = 840

) at

20°\text{C}

(water

c = 4200

). Find the equilibrium temperature, ignoring losses.

Example 38

hard

An immersion heater rated

50 \text{ W}

is left in

0.1 \text{ kg}

of water (

c = 4200

) for

5 \text{ min}

. Find the temperature rise, ignoring losses.

Example 39

hard

Heat at rate

200 \text{ W}

is fed into

0.5 \text{ kg}

of ice at

0°\text{C}

. Find the time to melt all the ice. Use

L_f = 334000 \text{ J/kg}

Example 40

hard

Two metal blocks A and B with

m_A = m_B

and

c_A = 2 c_B

are given equal heat

Q

. State the ratio

\Delta T_A : \Delta T_B

Example 41

challenge

1500 \text{ kg}

car at

20 \text{ m/s}

brakes to rest. If all KE becomes thermal energy in

5 \text{ kg}

of steel brake material (

c = 500

), find the temperature rise.

Example 42

challenge

50 \text{ g}

ice cube at

0°\text{C}

is dropped into

250 \text{ g}

water at

30°\text{C}

. Find the final temperature, assuming all ice melts and no losses. Use water

c = 4200

L_f = 334000 \text{ J/kg}

Example 43

challenge

Water at the base of a

50 \text{ m}

waterfall converts all gravitational PE into thermal energy of the same water. Find the temperature rise. (

g = 9.8 \text{ m/s}^2

c = 4200

)

← Back to Thermal Energy Practice Mode

Related Concepts

Kinetic Energy Energy Heat Transfer Temperature

Background Knowledge

These ideas may be useful before you work through the harder examples.

kinetic energyenergy