14.7 Radiation

Electromagnetic radiation plays a crucial role in heat transfer, allowing energy to move through space without a medium. This process involves visible light, radio waves, and infrared radiation. The amount and color of radiation emitted depend on an object's temperature and surface properties.

The Stefan-Boltzmann law describes how radiant heat power relates to an object's temperature. As temperature increases, the peak wavelength of emitted radiation shifts, changing the color we perceive. This phenomenon explains why heated objects glow and stars have different colors.

Electromagnetic Radiation and Heat Transfer

Heat transfer by electromagnetic radiation

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• Electromagnetic radiation transfers energy through space as waves without requiring a medium (vacuum)
• Includes visible light, radio waves, X-rays, and infrared radiation
• Thermal radiation occurs when an object emits electromagnetic waves due to its temperature
  • Energy carried by these waves can be absorbed by another object, increasing its temperature
• Amount of thermal radiation emitted depends on object's temperature and surface properties
  • Hotter objects emit more thermal radiation than cooler objects
  • Objects with higher emissivity (ability to emit thermal radiation) radiate more energy than those with lower emissivity (matte black vs shiny metal)

Temperature and radiated color relationship

• Color of radiated energy related to temperature of emitting object
• As temperature increases, peak wavelength of emitted radiation shifts to shorter wavelengths (Wien's displacement law)
  • $\lambda_{max} = \frac{b}{T}$, where $\lambda_{max}$ is peak wavelength, $T$ is absolute temperature, and $b$ is Wien's displacement constant ($2.898 \times 10^{-3}$ m·K)
• Cooler objects emit most radiation in infrared region, not visible to human eye (room temperature objects)
• As temperature increases, object begins to emit radiation in visible spectrum
  • Color changes from red to orange to yellow to white to blue as temperature increases (heated metal, stars)
• Sun, with surface temperature of ~5,800 K, emits most radiation in visible region, peaking in yellow-green part of spectrum

Stefan-Boltzmann law for heat transfer

• Describes relationship between rate of heat transfer by radiation and temperature of an object
• Total radiant heat power (energy per unit time) emitted by an object proportional to its absolute temperature raised to the fourth power
• Equation for Stefan-Boltzmann law: $P = \epsilon \sigma A T^4$
  1. $P$ is radiant heat power (watts)
  2. $\epsilon$ is emissivity of object's surface (unitless, 0 to 1)
  3. $\sigma$ is Stefan-Boltzmann constant ($5.67 \times 10^{-8}$ W·m$^{-2}$·K$^{-4}$)
  4. $A$ is surface area of object (m$^2$)
  5. $T$ is absolute temperature of object (K)
• To calculate net heat transfer rate between two objects: $P_{net} = \epsilon \sigma A (T_1^4 - T_2^4)$
  • $T_1$ is absolute temperature of hotter object
  • $T_2$ is absolute temperature of cooler object
• Small changes in temperature result in significant changes in rate of heat transfer by radiation due to fourth-power dependence on temperature (doubling temperature increases radiation by factor of 16)

Electromagnetic spectrum and radiation properties

• The electromagnetic spectrum encompasses all types of electromagnetic radiation, including radio waves, microwaves, infrared, visible light, ultraviolet, X-rays, and gamma rays
• Each type of radiation is characterized by its wavelength and frequency
  • Wavelength is the distance between consecutive wave crests
  • Frequency is the number of wave cycles passing a fixed point per second
• Photons are the fundamental particles of electromagnetic radiation, carrying discrete amounts of energy
• Blackbody radiation refers to the theoretical perfect emitter and absorber of electromagnetic radiation
  • Real objects approximate blackbody behavior to varying degrees
• Absorption and emission of radiation:
  • Absorption occurs when an object takes in electromagnetic energy
  • Emission is the process by which an object releases electromagnetic energy