Stefan's Law (OCR A Level Physics)

Revision Note

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Katie M


Katie M



Stefan's Law

  • An objects luminosity depends on two factors:
    • Its surface 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

  • So Stefan's Law shows that the luminosity of a star is directly proportional:
    • To its radius L ∝ r2
    • To its surface area L ∝ 4πr2
    • To its surface absolute temperature L T4

  • Stefan's Law equation is given by:

L = 4πr2σT4

  • Where:
    • L = luminosity of the star (W)
    • r = radius of the star
    • σ = the Stefan-Boltzmann constant
    • T = surface temperature of the star (K)
  • The surface area of a star (or other spherical object) can be calculated using: A = 4πr2
    • Where r = radius of the star

Worked example

The surface temperature of Proxima Centuri, the nearest star to Earth, is 3000 K and its luminosity is 6.506 × 1023 W.

Calculate the radius of Proxima Centuri in kilometres and show your working clearly. 

Step 1: List the known quantities: 

    • Surface temperature, T = 3000 K
    • Luminosity, = 6.506 × 1023 W
    • Stefan's constant, σ = 5.67 × 10−8 W m−2 K−4

Step 2: Write down Stefan's Law

L = 4πr2σT4

Step 3: Rearrange the equation for r 

r space equals space square root of fraction numerator L over denominator 4 πσT to the power of 4 end fraction end root

Step 4: Substitute into the equation 

r space equals space square root of fraction numerator 6.506 cross times 10 to the power of 23 over denominator 4 straight pi cross times left parenthesis 5.67 cross times 10 to the power of negative 8 end exponent right parenthesis cross times 3000 to the power of 4 end fraction end root= 106 173 971 m

Step 5: Write the final answer to the correct amount of significant figures

    • The radius of Proximal Centuri is 106 200 km (4 s.f.)

Exam Tip

Remember to convert temperatures into Kelvin.

Check the values you obtain in your calculations. Do they make sense? Do they fit in with the magnitudes of other stars/objects that you know about?

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Katie M

Author: Katie M

Katie has always been passionate about the sciences, and completed a degree in Astrophysics at Sheffield University. She decided that she wanted to inspire other young people, so moved to Bristol to complete a PGCE in Secondary Science. She particularly loves creating fun and absorbing materials to help students achieve their exam potential.

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