Radiation (Heat Transfer) Examples: 40 Problems with Answers

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

Heat transfer through electromagnetic waves that require no medium — the only form of heat transfer that works through a vacuum.

The sun warms you even through the vacuum of space — that's radiation.

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: Radiation (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 radiation (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

hard

A grey body (

\varepsilon = 0.8

A = 0.5\,\text{m}^2

) at

500\,\text{K}

sits in surroundings at

300\,\text{K}

. Find net radiative power loss. (

\sigma = 5.67\times10^{-8}

)

Answer

P_{net} \approx 1235\,\text{W}

First step

T^4 = 500^4 = 6.25\times10^{10}

;

T_s^4 = 300^4 = 8.10\times10^{9}

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Example 2

hard

Two concentric spherical shells: inner at

T_1 = 600\,\text{K}

, outer at

T_2 = 300\,\text{K}

, both black bodies. The inner shell has area

0.5\,\text{m}^2

. Find the net power radiated by the inner shell. (

\sigma = 5.67\times10^{-8}

)

Example 3

challenge

The Sun's surface temperature is

\approx 5800\,\text{K}

. Using Wien's law (

b = 2.90\times10^{-3}\,\text{m}\cdot\text{K}

), find the peak emission wavelength.

Practice Problems

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

Example 1

easy

Which heat-transfer mode warms you from the Sun across the vacuum of space?

Example 2

easy

In the Stefan-Boltzmann law

P = \sigma A T^4

, which temperature scale must

T

be in?

Example 3

easy

If the absolute temperature of a radiating body doubles, by what factor does its radiated power change? (

P = \sigma A T^4

)

Example 4

easy

Is thermal radiation (infrared from a warm object) the same as nuclear radiation?

Example 5

easy

Why are objects meant to radiate heat (like radiators) often painted matte black?

Example 6

easy

Does radiation require a medium (like air or metal) to transfer heat?

Example 7

easy

Why are emergency blankets shiny silver?

Example 8

easy

A warm object in a cold vacuum (e.g. a satellite in space) loses heat by which method only?

Example 9

medium

A black body has area

2 \text{ m}^2

at 300 K. Find its radiated power. (

\sigma = 5.67 \times 10^{-8} \text{ W/(m}^2\text{K}^4)

)

Example 10

medium

A radiating body at 200 K is heated to 600 K. By what factor does its radiated power increase?

Example 11

medium

Convert 127°C to kelvin, then state the factor by which radiated power exceeds that at 200 K.

Example 12

medium

Two stars have the same size. Star A is at 6000 K, star B at 3000 K. How many times more power does A radiate?

Example 13

medium

A surface radiates 500 W at 400 K. Keeping temperature fixed but tripling the area, find the new radiated power.

Example 14

medium

Why does a cup of tea cool faster in a cold room than in a warm room, considering radiation?

Example 15

medium

A black body at 500 K with area

0.5 \text{ m}^2

radiates power. Find it. (

\sigma = 5.67\times10^{-8}

)

Example 16

challenge

A black body radiates 1000 W at 300 K. Find its radiated power if heated to 450 K (same area).

Example 17

challenge

A satellite (

A = 4 \text{ m}^2

, black body) in space at 290 K radiates heat. Find its radiated power. (

\sigma = 5.67\times10^{-8}

)

Example 18

challenge

A body at 400 K radiates into surroundings at 300 K. The net power is

P = \sigma A (T^4 - T_s^4)

with

A = 1 \text{ m}^2

. Find the net radiated power. (

\sigma = 5.67\times10^{-8}

)

Example 19

medium

A black body (

A = 3 \text{ m}^2

) is at 400 K. Find its radiated power. (

\sigma = 5.67\times10^{-8}

)

Example 20

medium

A radiating body at 250 K is heated to 500 K. By what factor does its radiated power increase?

Example 21

easy

Convert

27\,^\circ\text{C}

to kelvin for use in

P = \sigma A T^4

Example 22

easy

A black body at

T = 100\,\text{K}

is heated to

T = 200\,\text{K}

. By what factor does its radiated power rise?

Example 23

medium

A black body has area

1.0\,\text{m}^2

400\,\text{K}

. Find its radiated power. (

\sigma = 5.67\times10^{-8}\,\text{W/(m}^2\text{K}^4)

)

Example 24

medium

A surface at

300\,\text{K}

radiates

P_1

. The same surface at

600\,\text{K}

radiates

P_2

. Find

P_2/P_1

Example 25

medium

Two black bodies have areas

A

and

4A

at the same temperature. Compare their radiated powers.

Example 26

medium

A grey body has emissivity

\varepsilon = 0.6

, area

2.0\,\text{m}^2

, at

500\,\text{K}

. Find the radiated power. (

\sigma = 5.67\times10^{-8}

)

Example 27

medium

A body at

T = 350\,\text{K}

sits in surroundings at

300\,\text{K}

. Treat it as a black body,

A = 1.0\,\text{m}^2

. Find the net radiated power. (

\sigma = 5.67\times10^{-8}

)

Example 28

medium

Convert

327\,^\circ\text{C}

to kelvin and compute the radiated power for

A = 0.50\,\text{m}^2

, black body. (

\sigma = 5.67\times10^{-8}

)

Example 29

medium

A spherical black body of radius

0.10\,\text{m}

is at

500\,\text{K}

. Find its radiated power. (

\sigma = 5.67\times10^{-8}

)

Example 30

medium

Star A has temperature

T_A = 3000\,\text{K}

and radius

R

. Star B has

T_B = 6000\,\text{K}

and radius

R/2

. Compare their luminosities.

Example 31

medium

A black body at

250\,\text{K}

radiates

P_0

. Find its power at

1000\,\text{K}

Example 32

medium

A black body radiates

100\,\text{W}

200\,\text{K}

. What does it radiate at

400\,\text{K}

Example 33

hard

A black-body filament has area

5.0\times10^{-5}\,\text{m}^2

and operates at

3000\,\text{K}

. Find its radiated power. (

\sigma = 5.67\times10^{-8}

)

Example 34

hard

A satellite (black body,

A = 6\,\text{m}^2

) receives no sunlight in eclipse and starts at

290\,\text{K}

. Find its initial net radiative loss to deep space at

\approx 3\,\text{K}

. (

\sigma = 5.67\times10^{-8}

)

Example 35

hard

A black body radiates

P_0 = 200\,\text{W}

T_0 = 400\,\text{K}

. To double the radiated power, what temperature is required?

Example 36

hard

Compare radiated power of a person (

T = 310\,\text{K}

\varepsilon = 0.97

A = 1.7\,\text{m}^2

) to surroundings at

293\,\text{K}

. (

\sigma = 5.67\times10^{-8}

)

Example 37

challenge

A black body cools radiatively in a

0\,\text{K}

environment. Initially at

T = 500\,\text{K}

with heat capacity

C = 200\,\text{J/K}

, area

A = 0.01\,\text{m}^2

, find the initial rate of temperature decrease. (

\sigma = 5.67\times10^{-8}

)

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Related Concepts

Heat Transfer Electromagnetic Waves Conduction Convection

Background Knowledge

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

heat transferelectromagnetic waves