Conduction Examples: 45 Problems with Answers

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

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

Concept Recap

Heat transfer through direct physical contact between particles, where faster-moving (hotter) particles collide with and pass kinetic energy to slower-moving (cooler) neighbours.

Touch a hot pan — heat flows from the pan to your hand through direct contact.

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: Conduction 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 conduction 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

A rod conducts

Q_0

watts at

\Delta T_0

. The rod is then replaced by one twice as thick with the same

k

A

, and

\Delta T_0

. What fraction of

Q_0

now flows?

Answer

\frac{Q}{Q_{0}} = \frac{1}{2}

First step

Q \propto 1/d

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Example 2

medium

A house loses

5000 \text{ W}

by conduction through walls. Adding insulation cuts the loss to

1500 \text{ W}

at the same indoor-outdoor temperature difference. By what factor did the effective

k/d

change?

Example 3

hard

A single-pane window loses

4800 \text{ W}

. Replacing it with a triple-pane that cuts the effective

k/d

by a factor of

10

at the same

\Delta T

saves how many watts?

Example 4

challenge

A composite wall has two layers (each

A=1\text{ m}^2

): brick (

k=0.6

d=0.1 \text{ m}

) and fiberglass (

k=0.04

d=0.05 \text{ m}

). Inside

20°C

, outside

-5°C

. Find

Q

and the temperature at the brick-fiberglass interface.

Practice Problems

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

Example 1

easy

You touch a metal railing and a wooden bench, both at room temperature. Which feels colder and why?

Example 2

easy

By what mechanism does heat travel along a metal rod heated at one end?

Example 3

easy

A wall conducts heat with

Q = \frac{kA\Delta T}{d}

. If the temperature difference

\Delta T

doubles, what happens to the heat flow?

Example 4

easy

In the conduction formula

Q = \frac{kA\Delta T}{d}

, what does

d

represent?

Example 5

easy

Are metals generally good or poor conductors of heat?

Example 6

easy

Is a wooden spoon a conductor or an insulator of heat?

Example 7

easy

Through which state of matter does conduction work best: solids, liquids, or gases?

Example 8

easy

Heat conducts through a wall at 200 W. If you double the wall area

A

, what is the new heat flow rate?

Example 9

medium

A glass window has

k = 0.8 \text{ W/(m}\cdot {}^\circ \text{C)}

, area

2 \text{ m}^2

, thickness

0.005 \text{ m}

, and

\Delta T = 15°C

. Find the conduction heat flow.

Example 10

medium

A rod conducts 600 W. If its thickness (length)

d

is tripled with all else fixed, find the new heat flow.

Example 11

medium

Two rods, copper (

k = 400

) and steel (

k = 50

), have identical size and

\Delta T

. How many times more heat does copper conduct?

Example 12

medium

A 0.01 m thick steel plate (

k = 50

) of area

0.5 \text{ m}^2

has a 40°C difference across it. Find the heat flow.

Example 13

medium

Why are house walls often built with a layer of trapped air or foam between bricks?

Example 14

medium

A window loses 4800 W by conduction. Adding a second pane creates an air gap, lowering the effective

k

by a factor of 4. Find the new heat loss.

Example 15

medium

Heat flows through a composite slab at 300 W. The cross-sectional area is halved and the thickness is also halved. Find the new heat flow.

Example 16

challenge

A composite wall has two layers in series, each conducting heat. Layer 1 alone would pass 600 W, layer 2 alone 300 W (at the same overall

\Delta T

). Series conductances combine like

\frac{1}{Q} = \frac{1}{Q_1} + \frac{1}{Q_2}

. Find the actual heat flow.

Example 17

challenge

A 0.002 m thick copper base (

k = 400

, area

0.01 \text{ m}^2

) of a pan must conduct 8000 W. What temperature difference across the base is required?

Example 18

challenge

Heat conducts through a metal bar at 500 W with

\Delta T = 50°C

. If you simultaneously double the area, double

\Delta T

, and double the length

d

, find the new heat flow.

Example 19

medium

A brick wall has

k = 0.6 \text{ W/(m}\cdot {}^\circ \text{C)}

, area

5 \text{ m}^2

, thickness

0.2 \text{ m}

, and

\Delta T = 20°C

. Find the conduction heat flow.

Example 20

medium

A conducting bar carries 400 W. If its thermal conductivity

k

is doubled with all else fixed, find the new heat flow.

Example 21

easy

A wall has

k=0.5 \text{ W/(m}\cdot {}^\circ \text{C)}

A=4 \text{ m}^2

d=0.1 \text{ m}

\Delta T=10°C

. Find

Q

Example 22

easy

Heat conducts through a slab at

1000 \text{ W}

. If

\Delta T

is halved, find the new heat flow.

Example 23

easy

A copper rod (

k=400

) of area

0.0004 \text{ m}^2

and length

0.2 \text{ m}

has

\Delta T=50°C

. Find the heat flow.

Example 24

medium

A glass pane (

k=0.8

) is

2 \text{ m}^2

0.004 \text{ m}

thick, with inside

22°C

and outside

-2°C

. Find the heat-loss rate.

Example 25

medium

An insulating foam (

k=0.04

) is

0.05 \text{ m}

thick,

10 \text{ m}^2

, with

\Delta T = 25°C

. Find

Q

Example 26

medium

An iron rod (

k=80

) of area

0.0002 \text{ m}^2

and length

0.5 \text{ m}

has

200°C

at one end and

50°C

at the other. Find

Q

Example 27

medium

A copper rod and an aluminum rod of identical size connect the same hot and cold reservoirs. Copper conducts

480 \text{ W}

. If

k_{Cu}=400

and

k_{Al}=235

, find aluminum's rate.

Example 28

medium

A pan base (

k=200

A=0.02 \text{ m}^2

d=0.005 \text{ m}

) must transfer

4000 \text{ W}

. Find the required

\Delta T

Example 29

medium

Heat conducts at

300 \text{ W}

through a slab. If

k

doubles and

d

also doubles (with

A

\Delta T

fixed), find the new

Q

Example 30

medium

0.005 \text{ m}

thick steel plate (

k=50

) of area

1 \text{ m}^2

has

200°C

on one side and

20°C

on the other. Find

Q

Example 31

medium

A wall conducts

250 \text{ W}

. Both the area

A

and the

\Delta T

are doubled, but

d

also doubles. Find the new

Q

Example 32

hard

A composite wall has two layers in series at the same

\Delta T_{\text{total}}

. Layer 1 alone passes

400 \text{ W}

, layer 2 alone

600 \text{ W}

. Find the actual heat flow. (Use

1/Q = 1/Q_1 + 1/Q_2

Example 33

hard

A double-glazed window has two glass panes (

k=0.8

, each

0.004 \text{ m}

thick) separated by a

0.012 \text{ m}

air gap (

k=0.025

). Area

2 \text{ m}^2

\Delta T = 20°C

. Find the total heat flow. Assume layers in series.

Example 34

hard

Two rods of equal length and area carry heat in parallel between the same two reservoirs. Copper (

k=400

) and steel (

k=50

). Find the ratio of heat flows

Q_{\text{Cu}}/Q_{\text{steel}}

Example 35

hard

A copper rod (

k=400

) of area

0.0002 \text{ m}^2

and length

0.5 \text{ m}

has

\Delta T = 100°C

. How long does it take to conduct

1600 \text{ J}

Example 36

hard

A house loses

3000 \text{ W}

by conduction through walls when

\Delta T = 25°C

. Find the loss when

\Delta T = 10°C

Example 37

hard

A composite slab has glass (

k=0.8

d=0.005 \text{ m}

) and wood (

k=0.15

d=0.020 \text{ m}

) in series. Area

1 \text{ m}^2

\Delta T_{\text{total}}=30°C

. Find

Q

Example 38

hard

A rod connects

300°C

and

100°C

ends. At the midpoint of a uniform rod, what is the steady-state temperature?

Example 39

hard

A copper rod and a steel rod of equal

A

and

d

are joined end-to-end (in series). One free end is at

200°C

, the other at

0°C

. With

k_{Cu}=400

and

k_{\text{steel}}=50

, find the temperature at the junction.

Example 40

hard

Why are heat sinks on CPUs made of aluminum or copper rather than plastic?

Example 41

challenge

A cylindrical metal rod conducts

80 \text{ W}

. It is then replaced by a rod of the same length but twice the radius (same material, same

\Delta T

). Find the new heat flow.

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Related Concepts

Heat Transfer Temperature Convection Radiation (Heat Transfer)

Background Knowledge

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

heat transfertemperature