IB Physics HL B 2 2 Emissivity Questions

Practise IB Physics HL B.2.2 by analysing emissivity, net radiation and planetary energy balance with Stefan–Boltzmann models.

Exam points

Use ε = P/(σT⁴) and Stefan–Boltzmann scaling to compare surface radiation; derive an emissivity ratio from temperature or peak-wavelength information.
Derive a planet’s equilibrium-temperature relationship by balancing absorbed stellar power, including albedo, with emitted power εσAT⁴.
Calculate net radiation intensity from a grey surface and its surroundings using εσ(T₁⁴ − T₂⁴).
Calculate atmospheric re-radiation towards Earth by subtracting outgoing intensity from the surface emission εσT⁴.

[Maximum number: 3]

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

Figure for Question IB Physics HL B 2 2 Emissivity Questions question 1 — IB Physics HL

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}

Determine the average intensity re-radiated by the atmosphere towards the surface. Assume that the emissivity of the surface is 0.90 .

Emitted intensity $=5.67 \times 10^{-8} \times 0.90 \times 288^{4}\approx351 \mathrm{~W} \mathrm{~m}^{-2}$

Intensity leaving Earth $=238 \mathrm{~W} \mathrm{~m}^{-2}$

Re-radiated intensity $=351-238=113 \mathrm{~W} \mathrm{~m}^{-2}$

Marking guidance:

Ignore units as they are not required for the answer.

The steps in the calculation must be checked.

Accept outgoing intensity $=240 \mathrm{~W} \mathrm{~m}^{-2}$ for MP2.

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IB Physics HL B 2 2 Emissivity Questions question 1