Specific Heat Capacity Examples: 47 Problems with Answers

Start with the recap, study the fully worked examples, then use the practice problems to check your understanding of Specific Heat Capacity.

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

Concept Recap

Specific heat capacity is the amount of energy needed to raise the temperature of 1 kilogram of a substance by 1 degree Celsius (equivalently, by 1 kelvin).

Some substances warm up quickly, while others need much more energy for the same temperature change.

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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: Specific Heat Capacity 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 specific heat capacity 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

medium

750\text{ W}

kettle heats

0.6\text{ kg}

of water (

c = 4200\text{ J/(kg}\cdot{}^\circ\text{C)}

) from

20^\circ\text{C}

100^\circ\text{C}

, ignoring losses. How long does it take?

Answer

t = 268.8 s

First step

Heat needed:

Q = (0.6)(4200)(80) = 201600\text{ J}

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Example 2

medium

Two cups: A has

0.3\text{ kg}

of water at

30^\circ\text{C}

, B has

0.3\text{ kg}

70^\circ\text{C}

. Mixed perfectly with no losses, what is the final temperature?

Example 3

hard

0.2\text{ kg}

of copper (

c_{Cu} = 400

) at

250^\circ\text{C}

is dropped into

0.5\text{ kg}

of water (

c = 4200

) at

20^\circ\text{C}

. Find the final temperature (perfect calorimeter).

Example 4

hard

A solar panel delivers

200\text{ W/m}^2

usable power. If you want to warm

50\text{ kg}

of water (

c = 4200

) by

20^\circ\text{C}

2

hours, what panel area is required?

Example 5

challenge

A swimming pool holds

30\,000\text{ kg}

of water (

c = 4200

). A

20\text{ kW}

heater runs

8\text{ h/day}

with 10% heat loss. Find

\Delta T

per day.

Practice Problems

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

Example 1

easy

How much heat raises

2 \text{ kg}

of water (

c=4200

) by

10^\circ\text{C}

Example 2

easy

Heating

1 \text{ kg}

of a metal by

20^\circ\text{C}

takes

9000 \text{ J}

. Find its specific heat.

Example 3

easy

How much does

0.5 \text{ kg}

of water (

c=4200

) rise in temperature when given

21000 \text{ J}

Example 4

easy

Two substances get the same heat and mass; one rises more in temperature. Which has the lower specific heat?

Example 5

easy

Find the heat to warm

3 \text{ kg}

of aluminium (

c=900

) by

5^\circ\text{C}

Example 6

easy

\Delta T

15^\circ\text{C}

equals what change in kelvin?

Example 7

easy

It takes

4200 \text{ J}

to raise

1 \text{ kg}

of water by

1^\circ\text{C}

. How much for

1 \text{ kg}

3^\circ\text{C}

Example 8

easy

Find the heat to warm

0.25 \text{ kg}

of copper (

c=400

) by

40^\circ\text{C}

Example 9

medium

500 \text{ g}

of water (

c=4200

) is heated from

20^\circ\text{C}

80^\circ\text{C}

. Find the heat in kilojoules.

Example 10

medium

1500 \text{ W}

kettle heats

1 \text{ kg}

of water (

c=4200

) by

70^\circ\text{C}

. How long does it take (ignoring losses)?

Example 11

medium

0.2 \text{ kg}

of oil (

c=2000

) and

0.2 \text{ kg}

of water (

c=4200

) each receive

4200 \text{ J}

. Which warms more, and by how much more?

Example 12

medium

How much heat is released when

2 \text{ kg}

of water (

c=4200

) cools from

90^\circ\text{C}

25^\circ\text{C}

Example 13

medium

A heater adds

50000 \text{ J}

2 \text{ kg}

of a substance, raising it

25^\circ\text{C}

. Find the specific heat.

Example 14

medium

Equal heat is given to

1 \text{ kg}

each of water (

c=4200

) and iron (

c=450

). The iron rises

40^\circ\text{C}

. By how much does the water rise?

Example 15

medium

0.1 \text{ kg}

of water (

c=4200

) at

15^\circ\text{C}

absorbs

12600 \text{ J}

. Find the final temperature.

Example 16

medium

How much heat warms

0.8 \text{ kg}

of aluminium (

c=900

) from

25^\circ\text{C}

75^\circ\text{C}

Example 17

medium

800 \text{ W}

immersion heater runs for

60 \text{ s}

0.5 \text{ kg}

of water (

c=4200

). Find the temperature rise (ignore losses).

Example 18

challenge

0.3 \text{ kg}

of metal at

120^\circ\text{C}

is dropped into

0.5 \text{ kg}

of water (

c=4200

) at

18^\circ\text{C}

, reaching

25^\circ\text{C}

. Find the metal's specific heat.

Example 19

challenge

2000 \text{ W}

heater warms

5 \text{ kg}

of water (

c=4200

) but loses heat at

400 \text{ W}

to surroundings. How long to raise the water by

20^\circ\text{C}

Example 20

challenge

1 \text{ kg}

of water (

c=4200

) at

30^\circ\text{C}

is mixed with

m

kg at

80^\circ\text{C}

to reach

50^\circ\text{C}

. Find

m

Example 21

easy

Find the heat needed to raise

0.5\text{ kg}

of water (

c=4200\text{ J/(kg}\cdot{}^\circ\text{C)}

) by

4^\circ\text{C}

Example 22

easy

2\text{ kg}

block of iron (

c = 450\text{ J/(kg}\cdot{}^\circ\text{C)}

) is warmed by

15^\circ\text{C}

. Find the heat absorbed.

Example 23

easy

1.5\text{ kg}

piece of copper (

c = 400\text{ J/(kg}\cdot{}^\circ\text{C)}

) cools by

30^\circ\text{C}

. How much heat does it release?

Example 24

easy

How much heat is needed to raise

0.25\text{ kg}

of aluminium (

c = 900\text{ J/(kg}\cdot{}^\circ\text{C)}

) by

20^\circ\text{C}

Example 25

easy

A material absorbs

20000\text{ J}

when

4\text{ kg}

of it warms by

25^\circ\text{C}

. Find its specific heat.

Example 26

easy

How much heat warms

200\text{ g}

of water (

c = 4200\text{ J/(kg}\cdot{}^\circ\text{C)}

) from

20^\circ\text{C}

25^\circ\text{C}

Example 27

medium

Equal masses of water (

c = 4200

) and iron (

c = 450

) each gain

9000\text{ J}

. Which warms more, and what is the ratio of temperature rises (

\Delta T_{Fe}/\Delta T_{H_2O}

Example 28

medium

1.2\text{ kg}

of olive oil (

c = 1970\text{ J/(kg}\cdot{}^\circ\text{C)}

) is heated from

25^\circ\text{C}

90^\circ\text{C}

. How much heat is required?

Example 29

medium

0.3\text{ kg}

aluminium pan (

c = 900

) and the

1.5\text{ kg}

of water (

c = 4200

) inside it are both heated from

20^\circ\text{C}

100^\circ\text{C}

. Total heat?

Example 30

medium

2.5\text{ kg}

of water (

c = 4200

) cools from

80^\circ\text{C}

30^\circ\text{C}

. How much heat is released?

Example 31

medium

1200\text{ W}

heater warms

4\text{ kg}

of water (

c = 4200

) for

5\text{ min}

with no losses. Find

\Delta T

Example 32

medium

0.4\text{ kg}

of substance

X

absorbs

11200\text{ J}

and warms

20^\circ\text{C}

. Find

c_X

Example 33

medium

How much heat warms

5\text{ kg}

of water (

c = 4200

) from

10^\circ\text{C}

40^\circ\text{C}

? Express in kJ.

Example 34

medium

0.5\text{ kg}

glass bottle (

c = 840

) cools from

90^\circ\text{C}

25^\circ\text{C}

. How much heat is released?

Example 35

medium

1800\text{ W}

kettle takes

3\text{ min}

to fully heat water with no losses. If the water is

1.0\text{ kg}

(

c = 4200

), find

\Delta T

Example 36

hard

2500\text{ W}

heater loses

300\text{ W}

to the air. How long to raise

3\text{ kg}

of water (

c = 4200

) by

40^\circ\text{C}

Example 37

hard

0.4\text{ kg}

of metal at

200^\circ\text{C}

is dropped into

0.6\text{ kg}

of water (

c = 4200

) at

20^\circ\text{C}

, settling at

30^\circ\text{C}

. Find the metal's specific heat (ignore the container).

Example 38

hard

How much water (kg) at

15^\circ\text{C}

must be added to

2\text{ kg}

of water at

90^\circ\text{C}

to reach

50^\circ\text{C}

? Use

c = 4200

Example 39

hard

0.1\text{ kg}

of iron (

c_{Fe} = 450

) at

400^\circ\text{C}

is quenched in

0.3\text{ kg}

of oil (

c_o = 2000

) at

25^\circ\text{C}

. Find

T_f

Example 40

hard

Compare the heat needed to warm

1\text{ kg}

of water by

1^\circ\text{C}

versus the heat needed to warm

1\text{ kg}

of air (

c_{air} \approx 1005

) by

1^\circ\text{C}

. Ratio?

Example 41

challenge

0.5\text{ kg}

of copper (

c_{Cu} = 400

) at

300^\circ\text{C}

is added to an aluminium calorimeter (

m = 0.2\text{ kg}

c_{Al} = 900

) holding

0.3\text{ kg}

of water (

c = 4200

) at

20^\circ\text{C}

. Find

T_f

Example 42

challenge

A car of mass

1500\text{ kg}

traveling at

20\text{ m/s}

brakes to a stop. If all kinetic energy heats

5\text{ kg}

of brake material (

c = 800

), find

\Delta T

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Related Concepts

Thermal Equilibrium Thermal Energy Temperature Ideal Gas Law

Background Knowledge

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

thermal equilibriumthermal energytemperature