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

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

Calculate the radius of Proxima Centauri, in km.

Answer:

Step 1: List the known quantities

• Surface temperature, T = 3000 K

• Luminosity, L = 6.506 × 10²³ W

• Stefan's constant, σ = 5.67 × 10⁻⁸ W m⁻² K⁻⁴

Step 2: Write down Stefan's law

$L=4\mathrm{\pi }{r}^2\sigma T^4$

Step 3: Rearrange the equation for radius r 

$r=\sqrt{\frac{L}{4\mathrm{\pi }\sigma T^4}}$

Step 4: Substitute the values into the equation 

$r=\sqrt{\frac{6.506\times {10}^{23}}{4\mathrm{\pi }\times (5.67\times {10}^{-8})\times {3000}^4}}=1.062\times {10}^8\mathrm{m}$

Step 5: Write the final answer in the correct unit

• The radius of Proximal Centauri is $1.062\times {10}^5\mathrm{km}$ or $106200\mathrm{km}$ (4 s.f.)

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?