Heat Transfer Examples in Physics

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

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 spontaneous flow of thermal energy from a hotter object to a cooler one until they reach thermal equilibrium (the same temperature).

Heat always flows from hot to cold on its own — reversing this requires external work.

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: Heat Transfer 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 heat transfer 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

Identify the primary mode of heat transfer in each case: (a) a metal spoon in hot soup, (b) warmth from a campfire, (c) a pot of water being heated on a stove.

Answer

\text{(a) Conduction, (b) Radiation, (c) Convection}

First step

(a) The metal spoon heats up by conduction — direct contact transfers energy through molecular collisions.

Full solution

2
(b) The campfire warmth reaches you by radiation — infrared electromagnetic waves carry energy through air.
3
(c) The water circulates by convection — hot water rises and cool water sinks, creating circulation currents.

Heat transfers through three mechanisms: conduction (direct contact), convection (fluid circulation), and radiation (electromagnetic waves). Most real situations involve a combination of all three.

Example 2

medium

A glass window (

k = 0.8 \text{ W/(m·K)}

, area

2 \text{ m}^2

, thickness

0.005 \text{ m}

) has

20°\text{C}

inside and

5°\text{C}

outside. What is the rate of heat loss through the window?

Example 3

medium

5000\text{ J}

of heat is added to

0.5\text{ kg}

of a substance and raises its temperature by

20°C

. What is the specific heat capacity?

Example 4

hard

300\text{ g}

of water (

c=4200

) at

20°C

is heated by

100

W. How long does it take to reach

50°C

(assume no losses)?

Practice Problems

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

Example 1

medium

A thermos flask uses a vacuum between its double walls. Explain why this reduces heat transfer, and which mode(s) of heat transfer it primarily blocks.

Example 2

hard

A copper rod (

k = 385 \text{ W/(m·K)}

) and an iron rod (

k = 80 \text{ W/(m·K)}

) have the same length (

0.5 \text{ m}

) and cross-sectional area (

0.001 \text{ m}^2

). Both connect a

100°\text{C}

source to a

25°\text{C}

sink. What is the rate of heat conduction through each?

Example 3

easy

Two objects touch: one at 70°C, one at 30°C. In which direction does heat flow?

Example 4

easy

When does spontaneous heat transfer between two objects stop?

Example 5

easy

Is the statement 'this object has a lot of heat' correct? Explain briefly.

Example 6

easy

A refrigerator moves heat from cold food to a warm room. Why does this not happen spontaneously?

Example 7

easy

Heat is measured in which unit?

Example 8

easy

A hot cup of coffee is left on a table. Over time, what happens to its temperature and why?

Example 9

easy

Does heat transfer depend on the temperature difference between objects?

Example 10

easy

Name the three methods of heat transfer.

Example 11

medium

How much heat must be removed from 0.5 kg of water to cool it from 50°C to 10°C? (water

c = 4200

)

Example 12

medium

A 2 kg block at 100°C transfers 50000 J of heat to its surroundings. If

c = 500

, find its new temperature.

Example 13

medium

Object A (80°C) and object B (20°C) reach equilibrium at 35°C. Did A or B have the larger heat capacity?

Example 14

medium

Why does a metal spoon in hot soup get hot quickly while a wooden spoon stays cool?

Example 15

medium

A heater supplies 4200 J every second to 1 kg of water (

c = 4200

). How long to raise it by 10°C?

Example 16

medium

Two cups of water, 0.1 kg and 0.3 kg, both cool from 60°C to 40°C. Which released more heat?

Example 17

medium

A warm 1 kg metal (

c = 400

) cools from 90°C to 30°C in a room. How much heat did it give to the room?

Example 18

challenge

0.3 kg of hot metal (

c = 400

) at 200°C is dropped into 0.4 kg water (

c = 4200

) at 25°C. Find the equilibrium temperature.

Example 19

challenge

A 2 kW heater warms 5 kg of water (

c = 4200

). Ignoring losses, how long to raise the temperature from 20°C to 50°C?

Example 20

challenge

A 1500 W heater is only 80% efficient at warming 2 kg of water (

c = 4200

) by 25°C. How long does it take?

Example 21

medium

How much heat must be added to 1.5 kg of water to raise it from 15°C to 45°C? (water

c = 4200

)

Example 22

medium

A hot 0.5 kg stone (

c = 800

) cools from 120°C to 40°C in air. How much heat does it give to the air?

Example 23

easy

How much heat is needed to raise

0.2\text{ kg}

of water by

25°C

? (

c = 4200

Example 24

easy

1.5\text{ kg}

block of aluminum (

c=900

) heats up by

10°C

. How much heat was added?

Example 25

medium

0.3\text{ kg}

iron block (

c=450

) at

20°C

absorbs

4050\text{ J}

of heat. Find the new temperature.

Example 26

medium

0.2\text{ kg}

of metal at

80°C

is mixed with

0.3\text{ kg}

of water (

c_w=4200

) at

20°C

. They reach

30°C

. Find the metal's specific heat (

c_m

Example 27

medium

1\text{ kW}

kettle heats

0.5\text{ kg}

of water from

20°C

100°C

(

c=4200

). How long does it take if all the energy goes into the water?

Example 28

medium

Calculate the rate of heat conduction through a

0.01\text{ m}

thick steel plate (

k=50

), area

0.5\text{ m}^2

, with

200°C

on one side and

20°C

on the other.

Example 29

medium

A wall is twice as thick. By what factor does the conductive heat loss rate change (other things equal)?

Example 30

medium

0.5\text{ kg}

of water at

90°C

is mixed with

0.5\text{ kg}

of water at

20°C

(

c=4200

). Find the equilibrium temperature.

Example 31

hard

0.5\text{ kg}

aluminum block (

c=900

) at

250°C

is dropped into

1.5\text{ kg}

of water (

c=4200

) at

15°C

. Find the equilibrium temperature.

Example 32

hard

How long does a

2\text{ kW}

heater take to melt

0.5\text{ kg}

of ice already at

0°C

? (

L_f = 334{,}000\text{ J/kg}

Example 33

hard

A black surface emits at temperature

T = 500\text{ K}

. Using Stefan–Boltzmann (

\sigma = 5.67\times 10^{-8}

), find the power per unit area radiated.

Example 34

hard

2\text{ kg}

100°C

water is boiled away to steam at

100°C

. How much heat is needed? (

L_v = 2.26\times 10^6\text{ J/kg}

Example 35

challenge

How much heat must be removed from

0.2\text{ kg}

of steam at

100°C

to turn it into water at

20°C

? (

L_v = 2.26\times 10^6

c_w=4200

Example 36

medium

0.4\text{ kg}

copper rod (

c=385

) cools from

90°C

25°C

. How much heat does it release?

← Back to Heat Transfer Practice Mode

Related Concepts

Thermal Energy Conduction Convection Radiation (Heat Transfer)

Background Knowledge

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

thermal energy