Blackbody Radiation
3. Temperature and the Electromagnetic Spectrum
Learning outcomes
- I can explain how the wavelength of maximum emission changes with temperature.
- I can relate object temperature to the color of emitted light.
- I can identify the regions of the electromagnetic spectrum associated with thermal radiation.
- I can compare the thermal radiation emitted by objects at different temperatures.
- I can apply these ideas to astronomical and everyday examples.
Temperature and the Electromagnetic Spectrum
Temperature Changes the Radiation an Object Emits
All objects with temperatures above absolute zero emit electromagnetic radiation.
However, objects at different temperatures do not emit the same amounts or distribution of wavelengths.
As an object's temperature increases:
- it emits more thermal radiation overall
- the intensity of the radiation increases
- the wavelength of maximum emission becomes shorter
- sufficiently hot objects begin emitting significant visible light
- the apparent color of very hot objects changes
This creates an important connection between:
temperature ↔ wavelength ↔ electromagnetic spectrum ↔ color
The Electromagnetic Spectrum
Thermal radiation is electromagnetic radiation.
The electromagnetic spectrum, from longest wavelength to shortest wavelength, is:
radio → microwave → infrared → visible → ultraviolet → X-ray → gamma ray
As wavelength decreases:
frequency increases
and photon energy also increases.
For electromagnetic radiation in a vacuum:
c = fλ
where:
- c = speed of light
- f = frequency
- λ = wavelength
Thermal Radiation Across the Spectrum
Thermal radiation is not restricted to one particular part of the electromagnetic spectrum.
A thermal emitter produces a continuous range of wavelengths.
Which wavelengths are most important depends strongly on temperature.
For many objects encountered in everyday life:
thermal radiation is mainly infrared
For very hot objects, substantial amounts can extend into the visible region.
Extremely hot objects can emit strongly at even shorter wavelengths.
Everyday Objects and Infrared Radiation
Objects around room temperature have peak wavelengths in the infrared region.
Examples include:
- people
- buildings
- furniture
- roads
- animals
- plants
- water
These objects do not normally glow visibly because their strongest thermal emission occurs at wavelengths longer than visible light.
A thermal camera detects some of this infrared radiation and converts the measurements into a visible image.
Wavelength of Maximum Emission
A thermal spectrum contains many wavelengths, but there is one wavelength at which the emitted spectral intensity reaches a maximum.
This is called the wavelength of maximum emission or peak wavelength.
It is represented by:
λ_max
As temperature increases:
λ_max decreases
Therefore:
hotter object → shorter peak wavelength
and:
cooler object → longer peak wavelength
This relationship is one of the most important ideas when interpreting thermal radiation spectra.
Wien's Displacement Law
The relationship between temperature and peak wavelength is described by Wien's displacement law:
λ_max T = 2.90 × 10⁻³ m·K
or:
λ_max = (2.90 × 10⁻³)/T
where:
- λ_max = peak wavelength, in m
- T = absolute temperature, in K
This shows that peak wavelength is inversely proportional to absolute temperature.
If temperature increases, peak wavelength decreases.
Worked Example: Human Body
A person's body temperature is approximately:
310 K
Calculate the approximate wavelength of maximum emission.
λ_max = (2.90 × 10⁻³)/310
λ_max ≈ 9.35 × 10⁻⁶ m
Therefore:
λ_max ≈ 9.4 μm
This lies in the infrared region.
This explains why humans are easily detected by infrared thermal cameras.
Worked Example: The Sun
The Sun's visible surface has a temperature of approximately:
5800 K
Calculate its approximate peak wavelength.
λ_max = (2.90 × 10⁻³)/5800
λ_max ≈ 5.0 × 10⁻⁷ m
or:
λ_max ≈ 500 nm
500 nm lies within the visible part of the electromagnetic spectrum.
This helps explain why so much of the Sun's radiation reaches us as visible light.
Comparing the Sun and a Person
The difference is enormous.
| Object | Approximate Temperature | Peak Wavelength | Main Region |
|---|---|---|---|
| Human body | 310 K | 9.4 μm | Infrared |
| Sun | 5800 K | 0.50 μm | Visible |
The hotter Sun has a much shorter peak wavelength.
This illustrates:
higher temperature → shorter λ_max
Temperature and the Shape of the Spectrum
Increasing temperature does more than shift the peak.
A hotter object also emits more radiation overall.
When comparing two blackbody curves, the hotter object's curve generally:
- rises higher
- has a larger area underneath it
- peaks at a shorter wavelength
Therefore, two important changes occur simultaneously:
temperature increases → intensity increases
and:
temperature increases → peak wavelength decreases
Total Radiation and Temperature
The total amount of radiation emitted by a blackbody increases very rapidly with temperature.
The Stefan–Boltzmann law gives:
P = σAT⁴
For equal surface areas:
P ∝ T⁴
This means that a relatively modest increase in absolute temperature can produce a large increase in emitted radiation.
For example, if absolute temperature doubles:
P_new/P_old = 2⁴
P_new/P_old = 16
The hotter object emits 16 times as much total power if its surface area and emissivity remain unchanged and it is treated as a blackbody.
Temperature and Visible Color
At everyday temperatures, objects emit mainly infrared radiation and do not glow visibly.
As temperature increases, the thermal spectrum extends increasingly into the visible region.
A heated object may progress through appearances such as:
no visible glow → dull red → bright red → orange → yellowish → white
The change occurs because the distribution of emitted wavelengths changes as temperature rises.
Why Red Appears First
Visible light extends approximately from:
violet: shorter wavelengths
to:
red: longer wavelengths
As a relatively cool hot object begins producing enough visible radiation to be seen glowing, the longer-wavelength red region is often the first part of the visible spectrum to become prominent.
The object therefore appears dull red.
As temperature increases, greater amounts of shorter-wavelength visible radiation are produced.
The appearance progresses toward orange, yellow and eventually a broader whitish glow.
White-Hot Objects
A white-hot object is not emitting only white light.
Instead, it emits a broad range of visible wavelengths strongly enough that their combination appears approximately white.
It is also emitting large amounts of invisible radiation.
Therefore:
visible color represents only part of the complete thermal spectrum.
Red-Hot Does Not Mean Red-Only
A glowing red object still emits a continuous spectrum.
It may emit:
- large amounts of infrared
- red visible light
- smaller amounts of other visible wavelengths
The color we observe depends on the relative intensity of wavelengths reaching our eyes.
This is important when interpreting thermal emission.
Comparing Cooler and Hotter Objects
Consider three objects:
Object A — 300 K
Approximately room temperature.
Its thermal radiation peaks in the infrared.
It does not visibly glow.
Object B — 1000 K
Much hotter.
It emits substantially more radiation and may begin producing visible red light.
Object C — 6000 K
Extremely hot.
It emits enormous amounts of radiation across visible and other wavelengths.
Its peak is at a much shorter wavelength.
The general trend is:
300 K → infrared
1000 K → mainly infrared, with increasing visible emission
6000 K → strong visible emission
Thermal Cameras
A thermal camera detects infrared radiation rather than ordinary visible light.
Warmer surfaces generally emit more thermal radiation than cooler surfaces with similar emissivity.
Thermal cameras can therefore identify temperature differences.
Applications include:
- finding heat loss from buildings
- locating electrical faults
- checking machinery
- firefighting
- search and rescue
- monitoring animals
- medical screening applications
The visible colors shown on a thermal image are usually false colors assigned by software.
The object itself is not necessarily emitting those visible colors.
Night Vision and Thermal Imaging
Thermal imaging should not be confused with all forms of night vision.
Some night-vision systems amplify small amounts of visible or near-infrared light reflected from objects.
Thermal cameras detect infrared radiation emitted by the objects themselves.
Therefore, thermal imaging can often detect warm objects even when there is little visible illumination.
Stars and Temperature
Stars provide one of the most important applications of thermal radiation.
Stars approximately behave like blackbody emitters, although their spectra contain additional features such as absorption lines.
A star's overall spectrum can therefore provide information about its surface temperature.
Red Stars and Blue Stars
Star color provides a useful indication of surface temperature.
In general:
red stars → cooler
orange stars → somewhat hotter
yellow-white stars → hotter
blue-white stars → very hot
This sometimes surprises students because red is commonly associated with heat.
Among stars:
blue stars are hotter than red stars.
Why Blue Stars Are Hotter
Wien's law explains this relationship.
Higher temperature produces a shorter peak wavelength:
T ↑ → λ_max ↓
Blue light has a shorter wavelength than red light.
Therefore, a star whose thermal spectrum is shifted strongly toward shorter visible wavelengths tends to be hotter than one whose spectrum is weighted toward longer wavelengths.
However, real star color depends on the full visible spectrum, not simply one single emitted wavelength.
Estimating the Temperature of a Star
Suppose a star has a peak wavelength of:
725 nm
Convert to metres:
725 nm = 7.25 × 10⁻⁷ m
Use Wien's law:
T = (2.90 × 10⁻³)/λ_max
T = (2.90 × 10⁻³)/(7.25 × 10⁻⁷)
T ≈ 4000 K
This star would be cooler than the Sun.
Example: A Hot Blue Star
Suppose a star has a surface temperature of:
10,000 K
Calculate its peak wavelength.
λ_max = (2.90 × 10⁻³)/10,000
λ_max = 2.90 × 10⁻⁷ m
Therefore:
λ_max = 290 nm
This wavelength lies in the ultraviolet region.
Yet the star can still appear blue-white because it also emits enormous amounts of visible light.
This demonstrates an important point:
the peak wavelength does not have to lie in the visible spectrum for an object to emit visible light.
The Sun's Color
The Sun's spectrum peaks near the visible region, but it emits a broad continuous spectrum.
It produces:
- ultraviolet
- visible light
- infrared
The Sun appears approximately white when viewed from space because it emits strongly across the visible spectrum.
Its appearance from Earth's surface can change because Earth's atmosphere scatters and absorbs different wavelengths.
Earth and Infrared Radiation
Earth also emits thermal radiation.
However, Earth's temperature is much lower than the Sun's.
The average surface temperature is roughly:
288 K
Using Wien's law:
λ_max ≈ (2.90 × 10⁻³)/288
λ_max ≈ 1.01 × 10⁻⁵ m
or approximately:
10 μm
This lies in the infrared region.
Therefore:
Sun → much shorter-wavelength radiation
Earth → mainly longer-wavelength infrared radiation
This distinction is fundamental to Earth's energy balance and climate.
Fire and Hot Objects
A fire provides an everyday example of temperature affecting emitted radiation.
Different regions of a fire can have different temperatures.
Hot soot particles and other heated materials emit thermal radiation.
Some of this radiation is visible, producing the familiar glow.
Much of the thermal radiation is also infrared.
You can therefore feel energy from a fire even when you are not touching the hot gases.
Incandescent Light Bulbs
Traditional incandescent bulbs heat a thin filament to a very high temperature.
The filament emits thermal radiation.
Some of this radiation lies in the visible spectrum, producing light.
However, a substantial fraction is emitted as infrared radiation.
This is one reason incandescent bulbs are inefficient as lighting devices: much of their electrical energy ultimately leaves as thermal energy rather than useful visible light.
Thermal Radiation in Engineering
Understanding the relationship between temperature and wavelength is important in engineering.
Applications include:
- infrared thermometers
- thermal cameras
- furnaces
- spacecraft
- industrial temperature monitoring
- building inspections
- electronics
- remote sensing
For example, an infrared thermometer can estimate temperature without touching an object by measuring its emitted radiation.
This is useful when the object is:
- extremely hot
- moving
- difficult to reach
- hazardous
Astronomical Applications
Astronomers cannot normally place thermometers directly on stars and planets.
Instead, they analyze electromagnetic radiation arriving at telescopes.
The spectrum can provide information about:
- temperature
- chemical composition
- motion
- density
- atmospheric properties
Thermal radiation therefore allows scientists to investigate objects located enormous distances away.
Reading a Thermal Radiation Curve
When given several blackbody curves, use two main clues.
Peak Position
Curve farther toward shorter wavelengths:
hotter object
Curve farther toward longer wavelengths:
cooler object
Curve Height and Area
Higher curve with larger area:
more radiation emitted
A hotter blackbody therefore usually has both:
higher intensity + shorter peak wavelength
Predicting Changes
Suppose an object is heated.
You should predict:
Temperature increases
↓
Total radiation emitted increases
↓
Radiation curve becomes higher
↓
Peak wavelength becomes shorter
↓
Increasing amounts of shorter-wavelength radiation are emitted
At sufficiently high temperatures, visible glow becomes noticeable.
This chain of reasoning can be applied to stars, furnaces, fires, metals and many other thermal systems.
Common Mistakes
Mistake: "Hot objects emit only infrared radiation."
Hot objects emit a continuous range of wavelengths. The distribution depends on temperature.
Mistake: "Peak wavelength is the only wavelength emitted."
It is simply the wavelength at which the spectral intensity is greatest.
Mistake: "A red-hot object emits only red light."
It emits many wavelengths, including substantial infrared radiation.
Mistake: "Red stars are hotter than blue stars."
Blue stars are generally hotter because their radiation is shifted toward shorter wavelengths.
Mistake: "If a star's peak is ultraviolet, it cannot be visible."
It can still emit very large amounts of visible light.
Mistake: "Temperature in Wien's law can be measured in Celsius."
Wien's law requires kelvin.
Mistake: "Thermal-camera colors are the actual colors emitted by objects."
Thermal images normally use artificial colors to represent detected infrared intensity or calculated temperature.
Key Terms
Electromagnetic spectrum — complete range of electromagnetic radiation arranged according to wavelength or frequency.
Thermal radiation — electromagnetic radiation emitted by matter because of its temperature.
Infrared radiation — electromagnetic radiation with wavelengths longer than visible red light.
Visible light — small portion of the electromagnetic spectrum detectable by the human eye.
Ultraviolet radiation — electromagnetic radiation with wavelengths shorter than visible violet light.
Peak wavelength — wavelength at which a thermal spectrum has its maximum spectral intensity.
Wien's displacement law — relationship showing that peak wavelength is inversely proportional to absolute temperature.
Blackbody spectrum — continuous distribution of electromagnetic radiation emitted by an ideal blackbody.
Absolute temperature — temperature measured from absolute zero using the kelvin scale.
Thermal imaging — detection of infrared radiation to investigate temperature patterns.
Color temperature — description relating the color of thermal radiation to the temperature of an ideal blackbody.
Continuous spectrum — uninterrupted range of emitted wavelengths.
Key Takeaways
- All objects above absolute zero emit electromagnetic radiation.
- The distribution of thermal radiation depends strongly on temperature.
- Everyday objects emit much of their thermal radiation in the infrared region.
- As temperature increases, the total radiation emitted increases.
- As temperature increases, the wavelength of maximum emission becomes shorter.
- Wien's law is λ_max T = 2.90 × 10⁻³ m·K.
- Thermal calculations involving Wien's law require temperature in kelvin.
- A thermal emitter produces a continuous spectrum, not one single wavelength.
- Objects begin glowing visibly when they become sufficiently hot.
- Increasing temperature can change the apparent glow from red toward orange, yellow and white.
- Thermal cameras detect infrared radiation emitted by objects.
- Human bodies emit most strongly in the infrared at wavelengths around 9–10 μm.
- The Sun's spectrum peaks near the visible region because its surface temperature is about 5800 K.
- Earth is much cooler and emits primarily infrared radiation.
- Stellar color and spectra provide information about surface temperature.
- Blue stars are generally hotter than red stars.
- An object's peak wavelength can lie outside the visible spectrum even when the object still emits visible light.
Check Your Understanding
- How does the wavelength of maximum emission change when an object's temperature increases?
- Which region of the electromagnetic spectrum contains most thermal radiation emitted by a human body?
- Why does a room-temperature object not normally glow visibly?
- State Wien's displacement law.
- Calculate the peak wavelength of an object at 1000 K.
- A thermal spectrum peaks at 10 μm. Is the radiation mainly visible or infrared?
- Explain why a heated metal begins glowing red before appearing orange or yellow.
- Compare the thermal radiation emitted by objects at 300 K and 3000 K.
- Why are blue stars generally hotter than red stars?
- A star's spectrum peaks at 500 nm. Estimate its surface temperature.
- Why can a 10,000 K star appear blue-white even if its peak wavelength lies in the ultraviolet?
- Compare the thermal radiation emitted by the Sun and Earth.
- Explain how a thermal camera can detect a person in darkness.
- Explain how astronomers can estimate the temperature of a distant star without physically measuring it.