
Thermal radiation is a source of electromagnetic waves, including sunlight and ultraviolet and infrared light. Thermal radiation is emitted by all objects with temperatures above absolute zero and thermal radiation is also absorbed by all objects.

The Stefan–Boltzman equation

Unlike convection and conduction, the power emitted as thermal radiation increases as the fourth power of the temperature. This means that doubling the temperature increases the amount of radiated power by a factor of 2^{4} = 16! Like other forms of heat transfer, the power is also proportional to the area; bodies with a larger surface area emit more radiative power than bodies of smaller surface area at equal temperature. Equation (24.3) gives the power of thermal radiation as a function of temperature T, area A, and emissivity ε.


(24.3)  $$P=\epsilon \sigma A{T}^{4}$$
 P  =  power (W)  ε  =  emissivity (dimensionless)  σ  =  Stefan–Boltzmann constant = 5.67×10^{8} W m^{−2} K^{−4}  A  =  emitting surface area (m^{2})  T  =  absolute temperature (K) 
 Stefan–Boltzmann equation



The temperature in equation (24.3) has units of kelvins because thermal radiation depends on the absolute temperature. The Stefan–Boltzmann constant σ has the value 5.67×10^{−8} W/(m^{2} K^{4}). At a temperature of 1 K (−272ºC), a square meter of a perfect emitter would radiate 5.67×10^{−8} W of power. This is a very small quantity, but radiative heat transfer increases quickly with temperature. At temperatures over 500°C, radiation almost always transfers more heat than convection or conduction. For example, the diagram below compares the different modes of heat transfer between two parallel plates separated by 20 cm of air.




The factor ε in equation (24.3) is the emissivity. The emissivity describes how much power is radiated by a surface compared to a perfect blackbody at the same temperature. In physics, a blackbody is a surface that appears completely black—meaning it absorbs 100% of the radiation falling on the surface and reflects nothing. A perfect blackbody absorber is also a perfect blackbody emitter and therefore has an emissivity ε = 1. Most real surfaces reflect some light and have values of emissivity that range from 0.1 to 0.95. Very shiny surfaces, such as chromed steel, have low emissivities, as low as 0.05 or less.
