# Stefan's Law(OCR A Level Physics)

Author

Katie M

Expertise

Physics

## 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

Step 4: Substitute into the equation

= 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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