14.7 Radiation

Electromagnetic Radiation and Heat Transfer

Radiation is the only heat transfer method that doesn't need a medium. Unlike conduction and convection, which require matter to carry energy, radiation moves through empty space as electromagnetic waves. This is how the Sun's energy reaches Earth across 150 million km of vacuum.

Heat transfer by electromagnetic radiation

Thermal radiation happens when an object emits electromagnetic waves because of its temperature. Every object above absolute zero emits some thermal radiation. When those waves hit another object, the energy can be absorbed, raising that object's temperature.

The amount of thermal radiation an object emits depends on two things:

• Temperature: Hotter objects emit far more thermal radiation than cooler ones.
• Emissivity ($\epsilon$): A measure of how effectively a surface emits thermal radiation, on a scale from 0 to 1. A matte black surface has an emissivity near 1, while a polished metal surface might be closer to 0.05. Higher emissivity means more radiation emitted at the same temperature.

Electromagnetic radiation includes a wide range of wave types: radio waves, microwaves, infrared, visible light, ultraviolet, X-rays, and gamma rays. For thermal radiation at everyday temperatures, most of the energy is in the infrared range.

Temperature and radiated color relationship

The color of light an object emits is directly tied to its temperature. As an object gets hotter, the peak wavelength of its emitted radiation shifts toward shorter wavelengths. This relationship is described by Wien's displacement law:

$\lambda_{max} = \frac{b}{T}$

• $\lambda_{max}$ is the peak wavelength (the wavelength where emission is strongest)
• $T$ is the absolute temperature in kelvins
• $b$ is Wien's displacement constant: $2.898 \times 10^{-3}$ m·K

At room temperature (~300 K), objects emit mostly in the infrared, which is invisible to us. As temperature rises, the peak shifts into the visible spectrum. You can see this progression when heating metal: it first glows dull red, then orange, then yellow, and eventually white or bluish-white at very high temperatures.

The Sun, with a surface temperature of about 5,800 K, emits most strongly in the yellow-green part of the visible spectrum. Stars that are hotter than the Sun appear blue-white, while cooler stars appear red.

Stefan-Boltzmann law for heat transfer

The Stefan-Boltzmann law gives you the total radiant power emitted by an object. The key feature of this law is the $T^4$ dependence: radiated power scales with the fourth power of absolute temperature.

$P = \epsilon \sigma A T^4$

Where:

• $P$ = radiant heat power (watts, W)
• $\epsilon$ = emissivity of the surface (unitless, between 0 and 1)
• $\sigma$ = Stefan-Boltzmann constant: $5.67 \times 10^{-8}$ W·m$^{-2}$·K$^{-4}$
• $A$ = surface area of the object (m$^2$)
• $T$ = absolute temperature of the object (K)

That fourth-power relationship has dramatic consequences. If you double an object's absolute temperature, the radiated power increases by a factor of $2^4 = 16$.

Net heat transfer between two objects accounts for the fact that both objects radiate toward each other. The net rate is:

$P_{net} = \epsilon \sigma A (T_1^4 - T_2^4)$

• $T_1$ is the temperature of the hotter object
• $T_2$ is the temperature of the cooler surroundings (or the cooler object)

This net equation is what you'll use in most problems, since real objects are always exchanging radiation with their environment.

Blackbody radiation and absorption

A blackbody is an idealized object that absorbs all incoming electromagnetic radiation and re-emits it based solely on its temperature. No real object is a perfect blackbody, but many approximate this behavior closely (a furnace cavity, for example).

Two properties worth remembering:

• Good emitters are also good absorbers. A matte black surface that radiates efficiently also absorbs incoming radiation efficiently.
• Good reflectors are poor emitters. A shiny silver surface reflects most incoming radiation and emits very little, which is why emergency blankets are metallic.

Photons are the particles that carry electromagnetic energy. Each photon carries a discrete amount of energy related to its frequency. Higher-frequency radiation (like UV or X-rays) carries more energy per photon than lower-frequency radiation (like infrared or radio waves). For this introductory course, the main takeaway is that radiation transfers energy in these discrete packets, connecting the wave and particle descriptions of light.