Stefan-Boltzmann Law (HL IB Physics)

• The total power P radiated by a perfect black body depends on two factors:
  • Its absolute temperature
  • Its surface area

• The relationship between these is known as Stefan's Law or the Stefan-Boltzmann Law, which states:

The total energy emitted by a black body per unit area per second is proportional to the fourth power of the absolute temperature of the body

• The Stefan-Boltzmann Law can be calculated using:

• Where:
  • P = total power emitted across all wavelengths (W)
  • σ = the Stefan-Boltzmann constant
  • A = surface area of the body (m)
  • T = absolute temperature of the body (K)

• The Stefan-Boltzmann law is often used to calculate the luminosity of celestial objects, such as stars
  • Stars can be approximated as black bodies, as almost all radiation incident on a star is absorbed
  • The power emitted across all wavelengths, P, for a star is just its luminosity, L
• The surface area of a star (or other spherical object) is equal to A = 4πr²
  • Where r = radius of the star

• Substituting the above for area, A, the Stefan-Boltzmann equation then becomes:

• Where:
  • L = luminosity of the star (W)
  • r = radius of the star (m)
  • σ = the Stefan-Boltzmann constant
  • T = surface temperature of the star (K)