Thermal Radiation

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All bodies emit radiation. So why don't we all shine in the dark?

Big Ideas: 
  • Thermal radiation is emitted by all bodies warmer than absolute zero
  • Visible light is emitted by bodies hotter than 800oC
  • Bodies at room temperature emit mainly in infrared
  • Very cold objects like for example liquid helium emit mainly in microwave  (right-click and choose "Save Link As..." to download to your computer)

Some people are astonished to find out that all bodies warmer than absolute zero (-273oC) emit radiation. For example an average human emits about 300 W of thermal radiation. So why we do not notice it?  The wavelength and power emitted by a body depends on the temperature. We need temperature above about 800oC for the body to emit visible light. Bodies at the temperatures below that including room temperature emit mainly in infrared. Very cold bodies like liquid helium (-269oC) emit mainly in microwaves. The relationship between the power and wavelength emitted by a body at a given temperature is very well illustrated by the simulation 1. The relationship between the temperature and the wavelength for which maximum power is emitted is given by:

$ \lambda_{m}= \dfrac{(2.90\times10^{-3} \textnormal{ m}\cdot\textnormal{K})}{T} $

Notice that as illustrated by the examples mentioned before the higher the temperature the lower the wavelength of the emitted thermal radiation. The temperature of the sun is 5778 K 2. From the formula above we can calculate that the wavelength at maximum power is about 500 nm in the middle of visible spectrum. Clearly the animal vision evolved to be as sensitive as possible to the solar radiation. At the human body temperature (37oC) the maximum is at about 10 $ \mu $m so in far infrared. Only some snakes, bats and insects can see this radiation, we have to use a special infrared camera.

The total emitted intensity of radiation (average power emitted per unit area of radiating body) is given by:

$ I = \epsilon \sigma T^4 $

where T is temperature in degrees Kelvin, $ \sigma $ is a Stefan- Boltzmann constant = 5.67 x 10-8 W/m2K4  and $ \epsilon $ is emissivity.

Emissivity is a material constant strongly dependent on the wavelength. Higher emissivity means that the material will emit or absorb more radiation at this wavelength. As illustrated in our video some materials have high emissivity in visible and low in infrared and vice verso.  Shiny metallic surfaces have low emissivity both in visible and infrared. The human skin has emissivity of 0.98 in infrared, Sun has emissivity very close to 1.

An ideal winter paint for the house would have high emissivity in visible (most energy from the sun comes in visible) and low emissivity in infrared (the house emits infrared). For the summer we would like to have low emissivity in the visible and high in infrared to save on air conditioning. Unfortunately we do not have commercial paints like this and anyway we would be reluctant to repaint the house twice a year. 

Any object emitting thermal radiation is also absorbing radiation from the surrounding.

A person  radiates about

$ P_E = A\epsilon \sigma T^4 = (1.5 \textnormal{ m}^2)(0.98)(5.67\times10^{-8} \textnormal{ W}/ \textnormal{m}^2\textnormal{K}^4)(306 \textnormal{ K})^4 = 730 \textnormal{ W} $

Assuming surface area A=1.5 m2,$ \epsilon $=0.98 and  skin temperature = 33oC = 306 K

When this person sits in a room at 20oC he or she  absorbs:

$ P_A = A\epsilon \sigma T^4 = (1.5 \textnormal{ m}^2)(0.98)(5.67\times10^{-8} \textnormal{ W}/ \textnormal{m}^2\textnormal{K}^4)(293 \textnormal{ K})^4 = 615 \textnormal{ W} $

So the net loss of energy is about 115 W. This is ignoring the effect on clothes but the order of magnitude is consistent with our energy input from food. In reality a dressed person looses about 50% of this heat to radiation and the rest to convection, evaporation and heat exchange due to breathing.

 Figure 1.  On a typical day, different amounts of heat are radiated from different objects in the same environment.  The above pictures were taken with a normal camera (top) and an infrared camera (bottom) on a 24oC day in July.  Objects emitting more radiation appear lighter and those emitting less radiation appear dark.  


Figure 2.  The top picture was taken on a cool day where the people are much hotter than the environment and so stand out as being much lighter in colour in IR camera.  The day the bottom picture was taken, the surface temperature of the person's clothing is ~29oC but the surface temperature of the concrete is 38oC and so the person appears darker than the surroundings.   



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