CAIE A-Level Physics 25.2.2 Stefan–Boltzmann Law

Practise using L = 4πσr²T⁴ to calculate stellar luminosity, radius or surface temperature, rearranging the relation and checking units.

Exam points

use L = 4πσr²T⁴ to calculate stellar luminosity, radius or surface temperature

[Maximum number: 1]

The radius of the Sun is $6.96 \times 10^{8} \mathrm{~m}$ .

Show that the temperature T of the surface of the Sun is 5770 K .

$\begin{aligned} \mathrm{L}=4 \pi \sigma r^{2} \mathrm{~T}^{4} 3.83 \times 10^{26}=4 \times \pi \times 5.67 \times 10^{-8} \times 6.96 \times 10^{82} \times \mathrm{T}^{4} \text { leading to } \mathrm{T}=5770 \mathrm{~K} \end{aligned}$

B1

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25.2.2—The Stefan–Boltzmann law L = 4 πσr 2 T 4 question 1