IB Physics SL B.1.16 Luminosity and Brightness

Practise converting luminosity to apparent brightness with spherical spreading, using inverse-square ratios and combining measured brightness with a known luminosity to infer…

Exam points

calculate b = L/(4πd²) with distance in metres and brightness in W m⁻²
use inverse-square ratios to compare radiation intensity at two distances without recalculating L
infer astronomical distance from known luminosity and measured brightness, noting absorption biases

[Maximum number: 2]

The diagram shows a simplified energy-balance model for the Earth surface–atmosphere system.

Figure for Question B.1.16—Luminosity and brightness question 1 — IB Physics SL

The following data are given:

\begin{aligned} \text { Average albedo of Earth } & =0.30 \\ \text { Average global temperature of the surface } & =288 \mathrm{~K} \\ \text { Average Earth-Sun distance } & =1.5 \times 10^{11} \mathrm{~m} \end{aligned}

Show, with reference to the solar constant, that the total power radiated by the Sun is about $4 \times 10^{26} \mathrm{~W}$ .

Recognition that $r=1.5 \times 10^{11} \mathrm{m}$ AND $S=1.36 \times 10^{3} \mathrm{W} \mathrm{m}^{-2}$ $4 \pi\left(1.5 \times 10^{11}\right)^{2} \times 1.36 \times 10^{3}$ or $3.8 \times 10^{26} \mathrm{W}$

Unit is not required.

The values of r and S must be seen to award MP1.

Allow ECF from use of\n $\nS=1.4 \times 10^{3} \mathrm{Wm}^{-2}\n$

All question bank results loaded

B.1.16—Luminosity and brightness question 1