Summarizing Radiation

Summary

• Radiation is the rate of heat transfer through the emission or absorption of electromagnetic waves.
• The rate of heat transfer depends on the surface area and the fourth power of the absolute temperature:

  \(\cfrac{Q}{t}=\sigma eA{T}^{4}\text{,}\)

  where \(\sigma =5\text{.67}×{\text{10}}^{-8}\phantom{\rule{0.25em}{0ex}}\text{J/s}\cdot {\text{m}}^{2}\cdot {\text{K}}^{4}\) is the Stefan-Boltzmann constant and \(e\) is the emissivity of the body. For a black body, \(e=1\) whereas a shiny white or perfect reflector has \(e=0\), with real objects having values of \(e\) between 1 and 0. The net rate of heat transfer by radiation is

  \(\cfrac{{Q}_{\text{net}}}{t}=\sigma eA({T}_{2}^{4}-{T}_{1}^{4})\)

  where \({T}_{1}\) is the temperature of an object surrounded by an environment with uniform temperature \({T}_{2}\) and \(e\) is the emissivity of the object.

Glossary

emissivity

measure of how well an object radiates

greenhouse effect

warming of the Earth that is due to gases such as carbon dioxide and methane that absorb infrared radiation from the Earth’s surface and reradiate it in all directions, thus sending a fraction of it back toward the surface of the Earth

net rate of heat transfer by radiation

is \(\cfrac{{Q}_{\text{net}}}{t}=\sigma eA({T}_{2}^{4}-{T}_{1}^{4})\)

radiation

energy transferred by electromagnetic waves directly as a result of a temperature difference

Stefan-Boltzmann law of radiation

\(\cfrac{Q}{t}=\sigma eA{T}^{4},\) where \(\sigma \) is the Stefan-Boltzmann constant, \(A\) is the surface area of the object, \(T\) is the absolute temperature, and \(e\) is the emissivity