Stefan's Law (AQA A Level Physics): Revision Note

Stefan's law

• 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:

$P=\sigma A{T}^4$

• Where:

  • $P$ = total power emitted across all wavelengths (W)

  • $\sigma$ = the Stefan-Boltzmann constant

  • $A$ = surface area of the body (m²)

  • $T$ = absolute temperature of the body (K)

• The Stefan-Boltzmann law is often used to calculate the luminosity of celestial objects, such as stars

• The surface area of a star (or other spherical object) is equal to $A=4\pi r^2$

  • Where $r$ = radius of the star

• The Stefan-Boltzmann equation then becomes:

$L=4\pi r^2\sigma T^4$

• Where:

  • $L$ = luminosity of the star (W)

  • $r$ = radius of the star (m)

  • $\sigma$ = the Stefan-Boltzmann constant

  • $T$ = surface temperature of the star (K)